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Predicting Short-Term Hospital Inpatient Bed Needs for Up to Four Days in Advance
by
Salem Jabr
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering University of Toronto
© Copyright by Salem Jabr 2017
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Predicting Short-Term Hospital Inpatient Bed Needs for Up to
Four Days in Advance
Salem Jabr
Master of Applied Science
Graduate Department of Mechanical and Industrial Engineering
University of Toronto
2017
Abstract
The Scarborough Hospital embarked a corporate initiative called Bed Mapping, which maps a
better path for inpatient care and has patients in the right bed. A tool is needed to perform short-
term predictions of inpatient bed needs.
This thesis provides an inpatient demand predictive tool that uses historical, scheduled surgery,
and current occupancy data to predict inpatient bed needs for up to four days in advance. It uses
staff generated Estimated Discharge Date (EDD), Length of Stay (LOS) distributions, and a Monte
Carlo simulation model by Liu [36] to make predictions. First, the tool was tested using
retrospective CIHI expected patient LOS data to calculate EDD, and showed that the tool’s error
is within 12 beds (5.52%) on day-1 and increases as we go further from day-1. The tool was further
tested and showed that if EDD’s were accurate then the tool’s error is within two beds (0.88%) on
day-1.
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Acknowledgments
I would like to thank my supervisor, Professor Michael Carter for giving me the opportunity to be
part of his team and for his endless support since I started my Masters research journey. A special
recognition for his patient guidance, encouragement, expertise, and immense knowledge that he
has provided me throughout the years. His patience and reassurance every time I am stressed about
my research or personal life helped me to continue until the end.
I would also like to thank my manager at The Scarborough Hospital, Alfred Ng for his trust,
continuous support, and valuable input into this research problem. His guidance and experience
was critical in every aspect of the project. Also, I am very grateful to be part of his Innovation and
Performance Improvement team at the hospital; I had the chance to learn a lot and contribute to
various problems. I would like to thank the whole team for their guidance and discussion about
my research problem, and for their comments and advice every time I approach any team member.
In particular, I would like to thank Tharshini Kamalachandra for her time, guidance, and expertise.
Tharshini was always available for help and always found time to meet with me, I would like to
thank her for her patience and support.
From Health Records at The Scarborough Hospital, I would like to thank Noor Ahmed and Jasmine
for their help in providing the data I need for my research and support in understanding the various
data fields that exist in the data extracts. I would like to thank Daniel Smith and Sameer Jadavji
from Surgery department for providing data and help in understanding flow of elective patients.
Also, I would like to thank Tian Mu Liu for giving me the opportunity to use his simulation model.
He provided a lot of support and helped me in understanding the very little details of his model.
I would like to thank my beloved parents Mohammed and Zainab for everything they have done
for me, and for all the love and belief. Their ultimate support, encouragement, and trust brought
me to where I am now. I cannot thank them enough for all they have done for me. Also, I would
like to thank my brother Abdulla for his love and constant support throughout the years in good
and bad times, I would like to thank him for being a supportive brother and my best friend.
Lastly, I would like to thank my wife Reem for her patience and support throughout the times. I
am glad to have an understanding wife who sacrificed a lot so that I could succeed.
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Table of Contents
Acknowledgments ........................................................................................................................ iii
Table of Contents ......................................................................................................................... iv
List of Tables ............................................................................................................................... vii
List of Figures ............................................................................................................................. viii
List of Abbreviations .....................................................................................................................x
Introduction ............................................................................................................1
1.1 Introduction ..........................................................................................................................1
1.2 Background ..........................................................................................................................2
1.2.1 Hospital Overview ...................................................................................................2
1.2.2 Bed Capacity Management at TSH..........................................................................3
1.3 Research Question ...............................................................................................................4
1.3.1 Research Objective ..................................................................................................4
1.3.2 Research Scope ........................................................................................................4
Problem Analysis ...................................................................................................6
2.1 Patient Flow Process ............................................................................................................6
2.1.1 Urgent Admissions...................................................................................................7
2.1.2 Elective Admissions.................................................................................................8
2.1.3 Stay in Hospital ......................................................................................................10
2.1.4 Discharge ...............................................................................................................11
Literature Review ................................................................................................14
3.1 Motivation for predicting short-term inpatient demand.....................................................14
3.2 Types of data considered ...................................................................................................15
3.3 Estimated Date of Discharge (EDD) ..................................................................................16
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3.4 Hospital wide versus specific service demand prediction .................................................17
3.5 Practical application of prediction models .........................................................................18
3.6 Forecasting methods used ..................................................................................................20
3.7 Use of Monte Carlo simulation in predictions ...................................................................21
3.8 Summary of findings..........................................................................................................21
Methodology .........................................................................................................23
4.1 Model Design .....................................................................................................................23
4.1.1 Current patients list and expected discharge ..........................................................25
4.1.2 Elective patient admissions and expected discharge .............................................35
4.1.3 Urgent patient admissions and expected discharge ...............................................43
4.2 Prediction Process ..............................................................................................................47
Model Testing, Results, and Discussion .............................................................52
5.1 Method 1: Model testing using CIHI expected patient LOS to calculate the EDD ...........53
5.1.1 Data preparation for testing and validation ............................................................53
5.1.2 Test Results ............................................................................................................54
5.1.3 Analysis and Discussion ........................................................................................57
5.2 Method 2: Model testing using EDD as actual discharge date ..........................................59
5.2.1 Data preparation for testing and validation ............................................................59
5.2.2 Test Results ............................................................................................................61
5.2.3 Analysis and Discussion ........................................................................................64
5.3 Investigation of current TSH approach in making predictions ..........................................65
Conclusion ............................................................................................................67
Future Research ...................................................................................................69
References .....................................................................................................................................71
Appendix A EDD Decision Support Tool .................................................................75
Appendix B Modifying input data for the Generic Simulation Model ..................78
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Appendix C Complete Keyword Database ...............................................................83
Appendix D Analysis of Urgent patients bed needs prediction ..............................91
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List of Tables
Table 1-1: Breakdown of patient admissions into three categories for past fiscal years ................ 3
Table 4-1: Discharge probability calculation for EDD = 2 days hence at a surgery unit ............. 27
Table 4-2: One record in the EDD accuracy database .................................................................. 27
Table 4-3: Frequency table of actual LOS of all patients that belong to HIG 402 and have ELOS
of 7.6 days ..................................................................................................................................... 32
Table 4-4: Table to calculate the expected value of total LOS of patients greater than or equal to
9 days for HIG 402 with ELOS 7.6 days ...................................................................................... 33
Table 4-5: Sample current census ................................................................................................. 34
Table 4-6: Sample LOS frequency table for John Smith - Total Knee Replacement ................... 37
Table 4-7: Sample record in the Elective Surgery database ......................................................... 38
Table 5-1: Summary of MAD and MAPE by day in the 4-day prediction horizon ...................... 57
Table 5-2: Sources of error for method 1...................................................................................... 58
Table 5-3: Summary of MAD and MAPE by day in the 4-day prediction horizon ...................... 63
Table 5-4: Sources of error for method 2...................................................................................... 64
Table 5-5: Actual versus corporate meeting prediction of patients by end of day 1 .................... 66
Table B-1: Number of days to shift back depending on the first day of prediction ..................... 81
Table B-2: Sample admission day shifting for Saturday (Shift Back 6 days) .............................. 82
Table C-1: Complete Keyword database ...................................................................................... 83
Table D-1: Prediction error due to Urgent patients only .............................................................. 91
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List of Figures
Figure 2-1: Overview of patient flow process ................................................................................ 6
Figure 2-2: Boxplot of urgent admissions by day of week for General Campus ........................... 7
Figure 2-3: Histogram of net transfers from critical care to inpatient units at the General .......... 11
Figure 4-1: Process to predict current census bed needs .............................................................. 25
Figure 4-2: Sample EDD accuracy database ................................................................................ 28
Figure 4-3: EDD accuracy distribution given that EDD = 1 day hence ....................................... 29
Figure 4-4: EDD accuracy distribution given that EDD = 3 days hence ...................................... 30
Figure 4-5: Sample output of discharge prediction of current census .......................................... 35
Figure 4-6: Process to predict elective patients bed needs ........................................................... 36
Figure 4-7: Sample Elective Surgery database ............................................................................. 38
Figure 4-8: Sample Keyword database ......................................................................................... 40
Figure 4-9: Sample OR schedule obtained from SIS .................................................................... 41
Figure 4-10: Sample output of discharge prediction of elective patients ..................................... 43
Figure 4-11: Sample output of Generic Bed Planning Model ...................................................... 44
Figure 4-12: Process to prepare prediction of urgent patients bed needs ..................................... 45
Figure 4-13: Predicted Urgent patients bed needs ........................................................................ 47
Figure 4-14: Outline of the prediction process ............................................................................. 48
Figure 4-15: Predictive model welcome window ......................................................................... 48
Figure 4-16: Predictive model window that shows successful data import .................................. 49
Figure 4-17: Predictive model window that asks user to start running the model ........................ 49
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Figure 4-18: Sample Result Summary sheet ................................................................................. 51
Figure 5-1: Prediction versus actual values matrix ....................................................................... 55
Figure 5-2: Matrix to show number of beds mismatch between the actual and prediction results55
Figure 5-3: Matrix to show prediction mismatch in percentage terms ......................................... 56
Figure 5-4: Absolute error for the 4-day prediction horizon ........................................................ 56
Figure 5-5: Absolute percentage error for the 4-day prediction horizon ...................................... 57
Figure 5-6: Current census created using DAD ............................................................................ 60
Figure 5-7: EDD accuracy database for testing in model ............................................................. 60
Figure 5-8: Prediction versus actual values matrix ....................................................................... 61
Figure 5-9: Matrix to show number of beds mismatch between actual and prediction results .... 62
Figure 5-10: Matrix to show prediction mismatch in percentage terms ....................................... 62
Figure 5-11: Absolute error for the 4-day prediction horizon ...................................................... 63
Figure 5-12: Absolute percentage error for the 4-day prediction horizon .................................... 63
Figure A-1: EDD Decision Support Tool user interface .............................................................. 75
Figure A-2: Selecting admission date from pop-up calendar ....................................................... 76
Figure A-3: All questions answered in the tool to calculate an EDD ........................................... 77
Figure B-1: Sample DAD extract before processing .................................................................... 79
Figure B-2: Sample DAD extract that contains breakdown of critical care stay .......................... 80
Figure B-3: Resulting DAD data after combining the two DAD extracts .................................... 80
x
List of Abbreviations
Abbreviation Description
ADD Actual Discharge Date
ANB Admitted No Beds
ARIMA Autoregressive Integrated Moving Average
ASU Acute Surgical Units
CCU Coronary Care Unit
CHE Centre for Healthcare Engineering
CIHI Canadian Institute for Health Information
DA Direct Admissions
DAD Discharge Abstract Database
DES Discrete Event Simulation
DS Day Surgery
ED Emergency Department
EDD Estimated Discharge Date
ELOS Expected Length of Stay
HBAM Health Based Allocation Model
HIG HBAM Inpatient Grouping
ICU Intensive Care Unit
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LOS Length of Stay
MAD Mean Absolute Deviation
MAE Mean Absolute Error
MAP Morning Admission Program
MAPE Mean Absolute Percentage Error
MOHLTC Ministry of Health and Long-Term Care
OR Operation Room
PFP Patient Flow Process
PMAP Peadiatric Morning Admission Program
QBP Quality Based Procedures
RTDC Real-Time Demand Capacity
SCU Special Care Unit
SIS Surgical Information Systems
TSH The Scarborough Hospital
VBA Visual Basic for Applications
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Introduction
1.1 Introduction
Emergency Department (ED) overcrowding [1] and surgery cancellations are problems frequently
encountered by hospital managers [3]. In response, the Ontario Ministry of Health and Long-Term
Care (MOHLTC) published a report introducing plans to reduce ED wait times [2]. According to
the report, the unavailability of inpatient beds causes patients to wait long hours in the ED before
being admitted. Furthermore, Dimitriadis et al. [3] reported that lack of beds is the second major
reason for surgery cancellations. Typically, hospital managers react to the high demand and lack
of beds by surging, which means opening extra beds; this is costly because the beds have to be
staffed and maintained. Frequent surging indicates a failure to understand hospital capacity
management and the inability to implement processes to reduce the Length of Stay (LOS) of
inpatients. The Canadian Institute of Health Information (CIHI) defines LOS as the number of
days a patient spends in the hospital from time of admission to time of discharge [18]. Unlike
outpatients, inpatients occupy a bed in the hospital and therefore consume scarce resources such
as beds and equipment, and they need the timely attention of the clinical staff, including nurses
and doctors.
Inpatients are considered one of the major cost drivers in hospitals [4, 7], and proper bed capacity
management strategies are needed to utilize available bed capacity efficiently. Hence, the lack of
decision support tools causes hospital management teams to operate under a high level of
uncertainty, which forces them to make last-minute decisions. For instance, opening extra beds
might not always be the best strategy for controlling increasing demand because excess bed
capacity translates into a low bed occupancy rate and therefore increases waste. At the opposite
extreme, low bed capacity translates into a high occupancy rate, resulting in poor quality care, bed
blockage, ambulance diversions, the need for overtime staff, nurse dissatisfaction, and long wait
times [5]. Bed demand capacity planning involves tasks such as predicting demand for beds and
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matching expected short-term demand to existing capacity; it allows management teams to plan
proactively, and thus improve patient flow and access to care, increase patient satisfaction, and
decrease operating costs.
A major corporate initiative called Bed Mapping was launched during the summer of 2015 as part
of The Scarborough Hospital (TSH) strategic plan for 2015-2019. Its aim is to map out a better
strategy for inpatient care by providing patients with care that is better coordinated and timely and
puts patients in the right bed the first time. A short-term demand capacity predictive tool is required
to achieve the expected benefits of the Bed Mapping initiative. This collaborative research is
undertaken by The Centre for Healthcare Engineering (CHE) at the University of Toronto and
TSH.
The prediction of short-term inpatient demand for beds facilitates capacity planning, nurse staffing,
and the availability of services such as tests and labs, and cost control [5, 6]. The focus of this
thesis is the prediction of inpatient bed needs for up to four days in advance.
The short-term predictive tool will be used to support resource planning by providing short-term
estimates of bed needs; it will change the hospital from a reactive to a proactive institution. The
current hospital system lacks this feature, and adding this capability will improve the overall bed
demand capacity planning.
1.2 Background
1.2.1 Hospital Overview
Located in Scarborough, Ontario, TSH is considered one of Canada’s largest urban community
hospitals. Currently, it delivers patient care at two hospital campuses (General and Birchmount)
and five community satellites. It is situated in one of the most diverse communities in Canada,
and delivers a range of programs and services that are just as diverse. For example, it delivers
specialized services such as cardio-respiratory, critical care, orthopeadic surgery, maternal
newborn and child care, peadiatrics, nephrology, palliative care, and stroke.
The hospital has a total of about 533 staffed beds across both campuses. It has 16 inpatient nursing
units at the General Campus, and 12 inpatient nursing units at the Birchmount Campus. Each year
TSH serves about 28,000 admissions classified into three categories: Urgent (~16,000), Elective
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(~7,500), and Newborn (~4,500). See table 1-1 for a breakdown of patient admissions for the past
three fiscal years across both campuses.
Table 1-1: Breakdown of patient admissions into three categories for past fiscal years
Fiscal Year
Admission Category
Urgent Elective Newborn Total
April 2013 – March 2014 16,735 7,603 4,507 28,845
April 2014 – March 2015 16,077 7,675 4,521 28,273
April 2015 – March 2016 15,310 7,466 4,345 27,121
Table 1-1 shows the breakdown of historical patient admissions into three categories as specified
in the admission category field in the Discharge Abstract Database (DAD), which is published
annually by the CIHI. The DAD captures administrative, clinical, and demographic information
on hospital discharges. According to the DAD, Urgent means patients that have a life threatening
condition or require immediate assessment and treatment. Elective means patients who are
preregistered and/or would be found on an elective booking list [12]. Newborns are recently born
children.
1.2.2 Bed Capacity Management at TSH
Bed capacity management is the allocation and provision of beds in hospitals, where beds in
specialist units are considered a scarce resource [9]. Due to public funding, capacity refers to
funded bed capacity, which is the number of beds that have staff and resources allocated to them.
Therefore, demand exceeds capacity once the demand for beds exceeds the funded number of beds.
However, physical capacity is a less common term that refers to the number of beds a hospital
could physically hold given no restriction on budgets.
The Scarborough Hospital runs a daily bed capacity meeting known as the Corporate Bed Meeting.
This meeting takes place at 9 a.m. with patient care managers, clinical resource leaders, charge
nurses, patient flow coordinators, and bed allocation staff. The intent of the meeting is to gain a
global picture of daily patient flow demand and inpatient capacity, and to develop appropriate
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action plans to ensure that capacity meets demand. Currently, the approach is based on simple
deterministic spreadsheet calculations where managers report on the current census, the number
of confirmed and expected discharges for the day, the number of elective patients, the ED patients
with beds assigned, the remaining unplaced ED admitted patients, and the number of transfers to
estimate if capacity will meet demand for the day.
It is obvious that bed capacity management at TSH is missing a key element, which is the
prediction of short-term inpatient demand for beds. The current process of using simple
calculations of admissions and discharges without accounting for LOS is not sufficient to make
short-term predictions, and this leads to the need of a predictive tool.
1.3 Research Question
1.3.1 Research Objective
The objective of this research is to contribute to demand capacity planning by making timely
predictions of inpatient bed needs for a short-term 4-day period. The prediction results will support
decision making that happens during the Corporate Bed Meeting. Prediction must be carried out
using software that is accessible to TSH and can be easily implemented within the existing hospital
system.
The final product of this research project is a Microsoft Excel VBA based tool with user friendly
interface by which users can run simulations and view predictions in the 4-day timeframe. The
prediction will utilize historical and real-time inpatient data, obtained from the hospital database.
The results of the prediction should indicate the number of predicted inpatient beds for day 1, day
2, day 3 and day 4. Also, the tool should predict bed occupancy and verify if demand for beds will
meet capacity given that the number of funded beds is known.
1.3.2 Research Scope
The tool predicts acute inpatient beds needs but excludes prediction for mental health patients,
maternal and newborns because units with such patients are considered separate departments and
their bed capacity cannot be shared among other hospital units. In addition, the tool excludes Day
Surgery patients because they do not require a bed and leave the hospital on the same day of
surgery.
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This thesis is organized as follows: Chapter 2 introduces and analyzes the problem. Chapter 3
reviews relevant literature in (1) motivation for short-term prediction of demand for beds; (2)
Types of data used to make prediction; (3) Hospital wide versus specific service demand
prediction; (4) Practical applications of predictive models; (5) Forecasting methods used in
prediction; and (6) Use of Monte Carlo Simulation in predictions. Chapter 4 outlines the
methodology used to perform the prediction, and Chapter 5 discusses test results and findings.
Finally, conclusion and future research are reported in Chapters 6 and 7 respectively.
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Problem Analysis
2.1 Patient Flow Process
The patient flow process (PFP) is the study of how patients move through the hospital system
starting from the time they arrive at the hospital to the time they are discharged. The inflow of
patients into the inpatient units creates demand for beds; outflow of patients out of the inpatient
units creates capacity. See figure 2-1 for an overview of a patient flow process.
Figure 2-1: Overview of patient flow process
Based on our investigation, we identified two main sources of external inflow into the hospital
inpatient units: Urgent and Elective patient admissions. Urgent admissions include patients
admitted through the ED or as emergency cases, those directly admitted by a physician, and those
directly admitted by a clinic. Elective admissions are patients undergoing scheduled surgeries.
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The figure also shows the interaction between critical care and acute inpatient units. Critical Care
patients create internal demand for acute inpatient beds by being transferred into the acute inpatient
units; similarly, acute inpatients create demand for critical care beds. The acute inpatient units in
Figure 2-1 include patients who need an acute care, Alternative Level of Care (ALC), or step-down
care. The ALC patients are patients who no longer require acute care services but wait in acute
care beds until they are placed in a more appropriate setting such as a long term care [1], and the
step-down care units provide an intermediate level of care for patients with care needs between a
regular acute unit and a critical care unit. An example of a step-down unit is the Acute Surgical
Unit (ASU), which is explained in detail in section 2.1.2.
The following sections explain each stage in the patient flow process.
2.1.1 Urgent Admissions
Urgent admissions, or unplanned admissions, include surgery and medicine patients. Two years of
historical DAD data (April 1, 2013 to March 31, 2015) was used to analyze the volume of urgent
admissions at the General Campus. Figure 2-2 shows boxplots of the number of urgent admissions
by day of week. It can be seen that admissions are higher during weekdays than at weekends;
however, the difference is not significant.
Figure 2-2: Boxplot of urgent admissions by day of week for General Campus
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The prediction of demand for beds generated by urgent admissions requires information such as
arrival rate by day of week and length of stay of patients [10]. This will help understand the number
of patients expected to be admitted and their expected discharge date. It is also imperative to
understand the breakdown of patient stays and include only the acute bed stay, ALC stay, and step-
down stay in the prediction, excluding critical care stays. The required information is found in
DAD and could be extracted from the hospital database systems. The DAD is prepared by the
Health Records department in the hospital. Health records staff review the charts of each
discharged patient in order to prepare the DAD data. As a result, the data is not up to date and is
only available about two months after the fact.
2.1.2 Elective Admissions
Elective admissions, or planned admissions, refer to surgery patients. At TSH, there are six main
types of elective admissions. They are listed as follows:
1. Morning Admission Program (MAP) patients.
2. Pediatric Morning Admission Program (PMAP) patients.
3. Acute Surgical Unit (ASU) patients.
4. Intensive Care Unit (ICU) patients.
5. Coronary Care Unit (CCU) patients.
6. Day Surgery (DS) or Outpatients
Elective surgery patients scheduled to occupy a bed in an inpatient unit are called Morning
Admission Program (MAP), and pediatrics scheduled for surgery are called Pediatric Morning
Admission Program (PMAP). The MAP and PMAP patients are included in the predictive model.
Elective surgery patients scheduled to enter an Acute Surgical Unit (ASU) immediately after the
procedure as part of the episode of care are referred to as ASU patients. The ASU is a step-down
unit which is located in the same floor as the standard surgical inpatient units. A step-down care
is different from the standard care, and usually has a nurse to patient ratio of 1 to 2. At TSH, the
ASU is managed by the Surgery department, and is treated as a standard inpatient unit. For
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example, elective patients could be discharged home from the ASU if their condition stabilizes
and are ready to be discharged. Therefore, we include the ASU patients in the predictive model.
Surgery patients scheduled to enter an Intensive Care Unit (ICU) immediately after the procedure
are referred to as ICU patients, and surgery patients scheduled to enter a Coronary Care Unit
(CCU) immediately after the procedure are referred to as CCU patients. The ICU and CCU are
critical care units that provide critical care to patients. Patients who do not occupy a bed in an
inpatient unit are called Day Surgery (DS) patients or outpatients; therefore, they do not have an
impact on the inpatient bed needs and are not included in this study.
The ICU and CCU elective patients are not included in the predictive model. In addition, the
volume of such patients is very small. In the fiscal year 2014-2015, there were 38 ICU/CCU cases
out of the total of 7,675 elective cases across both campuses, and in the fiscal year 2015-2016,
there were 65 ICU/CCU cases out of the total of 7,466 elective cases across both campuses.
The flow of the elective patients depends on how they are identified. The MAP and PMAP patients
occupy a bed in the inpatient units after surgery. The ASU patients initially flow into the ASU
unit, and once their condition stabilizes, they are either moved to the regular inpatient units or
discharged home directly. The ICU and CCU patients flow to the critical care unit, and once their
condition stabilizes, they are moved to either an ASU or to the regular inpatient units depending
on their condition. Patients are rarely discharged home directly from the ICU/CCU.
The Surgery department at TSH uses surgery management software called Surgical Information
Systems (SIS). It provides valuable data about each scheduled surgery, including patient
demographics, the type of surgical procedure, the surgeon’s name, and whether a patient is a DS,
MAP, PMAP, ASU, ICU, or CCU. This data can be extracted any time to provide information
about upcoming surgeries for up to two weeks in advance. In addition, SIS provides historical
surgical data that could be used for analysis.
The prediction of demand for beds generated by elective admissions requires information such as
the number of elective patients scheduled to arrive each day within the prediction timeframe, and
the expected length of stay to know when they are expected to be discharged. The number of
scheduled admissions for upcoming days can be extracted anytime from SIS.
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2.1.3 Stay in Hospital
Admitted patients are provided a bed upon admission, or have to wait for a bed in the ED. At TSH,
patients who have to wait until a bed becomes available are called Admit No Beds (ANB).
During hospital stay, patients are placed in different wards depending on the specialty care needed.
In an ideal world, every patient would be placed in the right bed the first time; however, in reality
patients are transferred between wards, or bed spaced, due to capacity restrictions. Bed spacing is
when patients are cared for outside their intended service ward. In addition, it is not uncommon
for care needs to change during a patient stay. For example, patients are admitted for a kidney
disease, but later during their stay, they experience a cardiac arrest and therefore need cardiology
care.
Critical care patients are transferred to acute inpatient wards once their condition stabilizes and
they no longer need a critical care bed. Similarly, patients are transferred from an inpatient ward
to a critical care ward if their condition changes and a critical care bed is required. Internal
Transfers data (April 1, 2013-March 31, 2016), obtained from the hospital’s Meditech system, was
used to investigate the volume of transfers between critical care and inpatient units. Figure 2-3
shows a histogram of net number of transfers from critical care to inpatient units at the General
campus.
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Figure 2-3: Histogram of net transfers from critical care to inpatient units at the General
It can be seen that during the three-year period, there were 381 days with zero net transfers and
311 days with one net transfer from critical care to inpatient units. Again, length of stay data is
required to quantify the demand for inpatient beds caused by the critical care internal transfers.
Therefore, the rate of transfers between critical care and inpatient units and length of stay of
patients at the units is needed to understand the inpatient bed needs.
The hospital uses a health information system called Medworxx for bed management. Medworxx
provides nightly data that captures the bed occupancy twice on a daily basis, one at 12:30 a.m. and
the other at 7 a.m. The nightly data extract is used to determine the list of patients occupying a bed
at 12:30 a.m. or 7 a.m., and to know other necessary information like Admission date and time,
current length of stay and current location. The current length of stay means how long a patient
stayed from the date of admission to the date the nightly data was extracted.
2.1.4 Discharge
Interprofessional teams provide a full spectrum of care for patients. An interprofessional team
consists of healthcare professionals such as physicians, nurses, occupational therapists, patient care
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managers, and social workers. Every day, the interprofessional team conducts daily meetings
called bullet rounds. During bullet rounds, a patient’s condition is discussed and the question is
raised whether the patient is “medically fit” and ready for discharge. Once a patient is ready for
discharge, the patient is given a discharge date. Currently, many units at TSH provide the discharge
date of patients on the day of discharge. The number of discharges are then communicated during
the corporate daily bed meeting to understand the capacity and help in making decisions. As
mentioned earlier, the process of reporting the number of discharges on the day of discharge is not
enough to make short-term predictions. There is a need to make discharge predictions over a longer
time period.
At TSH, there is an ongoing interest by hospital managers to quantify the discharge process, or
patient outflow, in terms of the estimated discharge date (EDD). By definition, the EDD is a team
generated prediction of a patient’s discharge date based on the expected length of stay, patient
condition, and staff judgment to understand if a patient is “medically fit” and ready for discharge.
It is a well-established best practice in patient flow, which is being used by many organizations
across the globe [11]. Ideally, the EDD has to be assigned within 24-48 hours of a patient’s
admission to ensure that the prediction is effectively used during the daily corporate bed meeting,
and used to make capacity predictions in advance. Also, the EDD has to be updated as the condition
of the patient changes.
The task of assigning an EDD to patients is not easy; nurses and clinical staff are sometimes
reluctant to provide estimates, worrying that they might be held responsible if a patient were not
discharged. The EDD is prevalent in units where the care path of patients is predictable, or known,
and the EDD could be estimated within 24-48 hours of admission. However, some patients do not
have a defined care pathway, which makes it hard to estimate a discharge date within 24-48 hours
of admission. Appendix A describes an excel based EDD Decision Support Tool that was designed
to assist nurses and staff to assign an EDD, however, it was not widely adopted. This tool uses an
Expected Length of Stay (ELOS) value that depends on six factors:
1. Age of patient
2. In case the patient had a critical care stay
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3. Type of flagged intervention (Cardioversion, Cell Saver, Chemotherapy, Dialysis, Feeding
Tube, Heart Resuscitation, Invasive Ventilation (Long), Invasive Ventilation (Short),
Paracentesis, Parenteral Nutrition, Pleurocentesis, Radiotherapy, Tracheostomy, and
Vascular Access Devices)
4. Number of flagged interventions
5. Whether the patient had an Out of Hospital (OOH) intervention
6. Whether the patient is expected to be discharged home or to a home care setting
Currently, there are two units at the General Campus that capture the EDD for its patients. One
unit is a surgery unit, and the other is a medicine unit. The EDD is recorded on whiteboards, and
there is an ongoing interest to capture the EDDs electronically to utilize the benefit of EDDs across
the organization and in discharge planning. The nightly extract by Medworxx is capable of
capturing EDDs of patients if inputted electronically into the system.
Medworxx is currently building tools that keep track of the EDD input and the EDD log with a
timestamp of when it was inputted. It is expected by the end of year 2016, the tools will be ready
for use. Therefore, the predictive model is built and validated with the assumption that EDD exists
for all patients in the hospital electronically. In addition, it is assumed that the EDD is discussed
and updated daily during bullet rounds. This ensures that the EDDs used are up to date.
14
Literature Review
This review analyzes work related to the prediction of short-term inpatient bed demand. It explores
the motivation for research in the area of predicting inpatient demand for beds, the benefits of
using predictions to reduce costs and utilize resources, and the types of data used to perform the
prediction such as historical data that contains patient specific LOS, patient identifiers like age,
gender, and diagnosis. It also explores the practical implementation of tools developed for the
short-term prediction, and forecasting methods used to run the prediction such as Time series
analysis, Markov chains, and complex statistical models. Finally, it gives an example how Monte
Carlo Simulation was used to forecast hotel arrivals and occupancy, which will lead to the use of
Monte Carlo simulation in the prediction of short-term hospital inpatient bed needs.
3.1 Motivation for predicting short-term inpatient demand
The prediction of short-term hospital inpatient demand is a challenging area for healthcare decision
makers [13, 34]. Decision makers, who have little knowledge of forecasting techniques, tend to
use simple mathematical calculations along with personal experience to perform daily predictions
[29]. While it is important to estimate inpatient demand in real time to make effective resource and
staffing plans [30], poor management and resource allocation increase operational costs and result
in decreased patient safety. Broyles et al. [5] believe that hospital inpatient units are similar to
inventory levels in manufacturing systems, organ banks, and blood banks, but the hospital system
is more complex. According to the authors, inpatients consume the most treatment time and more
resources than any other hospital patient type.
Recent studies have shown that a predictive tool can be used to drive behaviour in the inpatient
units and improve flow [31-33]. Appropriately used and shared among service providers, such a
tool will improve the overall quality of care and patient flow. Peck et al. [37] characterized the
value of predictive analytics in facilitating hospital patient flow. They used admission predictions
and current state information, generated in the ED, to influence the prioritization of physicians
15
between treating and discharging inpatients. That is, they explored how physicians in an inpatient
unit would operate once they receive the prediction results. Discrete Event Simulation (DES)
model, a tool used to explore various “what-if” scenarios to make decisions, was used to
investigate the ED and inpatient unit flow. It was found that the benefits of sharing prediction
output could result in reduced boarding time of around 11% to 18%, depending on the hospital
investigated. The boarding time is the length of time waiting for hospital admission from the time
a bed is requested to the time the patient left the ED.
Real-time demand capacity management (RTDC) was developed by the Institute of Healthcare
Improvement in order to encourage the interprofessional team to make daily predictions of demand
and capacity during their daily morning meetings. Consequently, Barnes et al. [34] had an
objective to automate and improve such daily discharge prediction by applying novel supervised
machine learning methods. First, the study was conducted within a single, 36 bed medical unit in
a mid-Atlantic medical center, and used available patient flow data such as admission and
discharge times, demographics, and basic admission diagnoses data. Second, the authors predicted
the patients’ probability of discharge by 2 p.m. and by midnight. Then, the total number of
discharges was derived by summing the discharge probabilities of all patients in the unit. The
model was better than the interprofessional teams in predicting the total number of daily
discharges.
It is evident that the problem of predicting inpatient demand is challenging, and therefore
motivated researchers around the globe to try to solve the problem using varying methods.
3.2 Types of data considered
Historical data is usually used by researchers to make predictions about the future [13, 6, 15, 16,
and 17]. It is assumed that past data patterns can be used to forecast future data points. For instance,
Kadri et al. [15] used one year worth of data to forecast the overcrowding of emergency department
using univariate time series model. Initially, the authors performed preliminary analysis of the data
and identified seasonal patterns, cyclical variations, trends, and outliers that cause fluctuations in
the time series. Then, the forecasts were based on daily patient attendances at the pediatric
emergency department.
16
Abraham et al. [16] used three years of daily data, compared several models for forecasting daily
emergency inpatient admissions and emergency occupancy using mean square error and concluded
that emergency admissions are largely random and unpredictable whereas emergency occupancy
can be forecasted using autoregressive integrated moving average (ARIMA) for up to one week
ahead. On the contrary, Groothuis et al. [35] used DES to predict capacities in cardiology units for
heart failure (HF) patients and concluded that arrivals could be predicted using simulation while
occupancy is predicted less accurately.
In the past, historical data was the only type of data available to perform predictions. However,
the existence of new information systems makes it possible to include additional types of real-time
data that will improve prediction accuracy. For example, real-time data, historical data, and data
pertaining to individual patient level were used to make predictions of patient’s LOS and discharge
date [6, 30]. In addition, patient arrivals data, internal transfers’ data, current census, and discharge
data were used in previous studies to predict short-term hospital occupancy.
Occupancy prediction, or prediction of bed needs, depends on accurate estimate of LOS of patients
already occupying a bed [35]. Various types of data are collected in order to find a good predictor
of LOS of patients. Initially, basic predictors are used along with simple statistical analysis of the
data to provide a hospital wide LOS estimate [27]; later researchers used more variables to predict
LOS for certain types of patients [19]. For instance, Harrison [19] used models to characterize
LOS distributions based on patients’ diagnosis, severity of illness, pre-existing comorbidity and
type of hospital. Harper et al. [10] used meteorological information, predictions of LOS, and
information on current occupancy to provide forecasts of short-term bed needs. It can be noted that
the project was unique because it included weather information in the prediction. According to the
authors, there is a relationship between the weather and health.
It can be seen that research projects use different types of data in order to perform predictions of
the same outcome, i.e. short-term bed needs. In addition to using different types of data, the
forecast methodology used is different.
3.3 Estimated Date of Discharge (EDD)
The concept of the EDD is widely used among hospitals around the globe. Establishing an EDD
for patients admitted within 24 hours is considered a measure of efficient and high quality
17
discharge planning. Failure to assign an EDD is one of the major barriers to implementing effective
discharge planning [11]. However, few studies have explored the implementation of timely EDD.
Ou et al. [11] explored the timely assignment of an EDD at the ED of an Australian hospital. The
main objective of the study was to (1) identify the determinants of assigning an EDD for planned
and unplanned admissions, and (2) identify the factors associated with variance between EDD and
Actual Discharge Date (ADD). The study had 64.1% of admitted patients with one EDD only,
another 20.7% of admitted patients had two EDDs, and only 5.4% (106) of admitted patients had
three or more EDDs documented. The remaining 9.8% did not have an EDD recorded at all. The
prevalence of timely EDDs was highest for ED admissions. In the sample, 44.8% (771) of
admissions had an ADD later than the first assigned EDD, and the study mentioned the benefit of
having a dedicated discharge facilitator in reducing variation between EDD and ADD.
No study was found in the literature that explores using the EDD to make short-term (4-day)
predictions of capacity. Resar et al. [30] used the discharge predictions of units to make daily
RTDC predictions, however, the term EDD was not used in the study. In addition, Groothuis et al.
[35] aimed at predicting capacities in cardiology units for heart failure patients only. Even with
only cardiology patients the author was unable to predict the LOS of current patients and concluded
that if doctors were able to accurately predict the LOS of current patients, the prediction accuracy
will be improved.
The lack of literature that explores the utilization of EDD in bed demand prediction motivated the
work in this research project in order to contribute to the literature.
3.4 Hospital wide versus specific service demand prediction
Attempting to create hospital wide predictions is complex and involves significant theoretical,
practical and computational challenges [6].
Groothuis et al. [35] aimed at predicting capacities in cardiology units for heart failure patients
only. Also, Kadri et al. [15] forecasted short term emergency demand based on daily patient
attendance at the pediatric ED at a regional hospital centre in Lille, France. This study only focused
on pediatric patients at one hospital and only considered emergency arrivals for the prediction.
Harrison [19] wanted to create a LOS distribution that could accurately represent the type of patient
18
in the study. He collected data from 17 different hospitals of varying sizes, and measured LOS
based on patient groups or hospital.
There is more literature on specific service prediction than on hospital wide predictions.
3.5 Practical application of prediction models
It is challenging to have hospital managers and decision makers trust the tool and use it to make
resource and staffing plans [6]. A lot of research was performed in the area, but only a few were
implemented [20]. Therefore, it is valuable to review work that created prediction tools and applied
them in hospitals, and review their benefits over predictions that depend only on managers past
experience and intuition.
Shan et al. [13] created a short-term forecasting tool that was implemented and developed with the
support of a major Hospital in New Jersey, U.S. The Decision Support System (DSS) is a
spreadsheet based Monte Carlo simulation of inpatient flow through the system. It has a simple
user interface and gives a real-time status of number of patients currently waiting for beds per
inpatient unit and number of patients discharged through those units. It does not forecast beyond
the 24 hour timeframe, but uses multiple sources of data to perform the prediction. For instance, it
used data from ED, Operation Room (OR), and Direct Admissions (DA) for patient arrivals into
12 nursing units. It also used LOS and discharge patterns to predict discharge rates at different
nursing units. In a different project, Al Nuaimi [14] published a paper that explains building four
models to assist decision makers in predicting the demand for healthcare services in Abu Dhabi
Emirate, UAE [14].
Littig and Isken [6] created an advanced computerized tool as one of the first works aimed at
hospital wide occupancy predictions. The prediction is based on simple patient flow equations, a
predictive occupancy database and a set of predictive occupancy models. For the patient flow
equations, the authors identified four inflow sources: emergency, scheduled arrivals, transfers and
direct. The authors used time series forecasts to estimate the emergency and direct patient arrivals
to the unit, and used surgical data schedules to predict scheduled arrivals. Multinomial logistic
regression was used to predict where (which unit) the patient will arrive to. Then, for the discharge
prediction, the authors used logistic regression to predict the discharge using a set of predictive
variables like admitting reason, physician, age, gender, current hospital length of stay (HLOS),
19
and unit length of stay (ULOS). This will help answer the question of the probability a patient to
be discharged in the next 24 hours given what is known about the patient today.
The model used independent variables like day of week, seasonal factors, short-term trends like
flu season, and long term trends like hospital growth. The forecast provides total number of
expected admissions to the hospital through ED for next 4 days (96 hours). The models for entire
hospital and could be further categorized by nursing unit and shift. Furthermore, it makes statistical
predictions at the individual patient level.
A sample output of the model is given below.
According to the authors, the model could be used as a simple predictive occupancy model that
uses less data types or could be a complex model that uses various data variables. In either case,
historical and real-time data from various sources must be extracted, transferred and loaded to the
POD (Predictive Occupancy Database), which was created to work for their model.
They noted that discharge prediction was harder and needed extra effort. In response, they created
a hazard probability field and matched theoretical distributions to LOS; then calculated the
probability a patient will be discharged in next 24, 48, 72 or 96 hours. Moreover, in case LOS was
not fitted to a theoretical distribution, empirical distribution was used.
Finally, the authors made a final step in fixing the overall prediction by using regression and
claimed that forecasting up to 4 days is feasible.
20
3.6 Forecasting methods used
The choice of the method to perform the prediction is the second step after data collection and
investigation. It depends on several factors such as accuracy, ease of use, availability of data,
research timeframe, and applicability.
As mentioned earlier, Time series is a widely used technique to make predictions of the expected
number of patient arrivals. It uses historical data of patient arrivals to predict the demand for the
next period. The limitation of using time series in our case is that it becomes harder to use the same
model in different hospitals without adjusting the parameters, so each hospital will have a different
model with different time series parameters.
Markov Chains [5] is another method used to make predictions about inpatient demand. It puts
higher weight on the previous state to make probability predictions about next stage. Those
methods prove to be effective but hard to implement in a hospital setting.
Data mining [17, 21, 14] is another method of predicting patient demand and LOS. Simulation is
another widely used method in healthcare. Usually, it is used to investigate system behaviour under
various scenarios but also could be used to make predictions [22, 10].
Some papers show the use of Monte Carlo simulation in making predictions [13, 23]. Monte Carlo
is being widely used in various industries other than healthcare to make predictions [24, 25, and
26]. Davies, R., et al. [26] compared Time Series and Monte Carlo simulation to predict volatile
demand for engines and concluded that Monte Carlo Simulation coded in Microsoft Excel VBA
is a better choice. In addition, Liu, T.M [36] used the Monte Carlo simulation to create a Generic
Bed Planning Model that could be applied in any hospital given that the data required is available.
To predict discharges, curve fitting for historical patients LOS is performed and then the fitted
distribution is used for discharge prediction [28]. Usually, average LOS is applied hospital wide,
but sometimes LOS analysis is detailed and patient LOS curve fitting is performed to a specific
patient service [27]. Based on initial trials at TSH, hospital managers believed that the discharge
prediction of patients already in the hospital i.e. current patients using historical LOS data did not
reflect reality. In fact, they were more amenable to using discharge predictions generated by the
21
interprofessional team because they know everything about a patient condition and could make
predictions of their discharge.
3.7 Use of Monte Carlo simulation in predictions
Monte Carlo Simulation is a methodology that uses repeated random samples of input variables
over a simulation period to determine the properties of a phenomenon. This method was first
developed by Physicists who wanted to perform simulations of their atomic physics models to
better understand the behaviour of these models. Now, Monte Carlo simulation is being applied to
a variety of disciplines and is being used in making predictions of system behaviour as well.
Zakhari et al. [24] employed Monte Carlo simulation to forecast hotel arrivals and occupancy.
Hotel arrivals and occupancy system are related to the hospital system; however, the hospital
system is complex. For instance, hotels have two types of arrivals either random or by appointment,
and each guest has a length of stay and occupies a room in the hotel thus requiring staff and
resources.
This research intends to use the approach of Monte Carlo simulation in the short-term inpatient
demand prediction in hospitals. The Excel VBA based model created by Liu, T.M. [36] will be
used and adjusted in order to make forecasts, and then the output of results will be provided in
Excel. The application Monte Carlo simulation in forecasting is new in Canada, especially in
applying such approach in healthcare.
3.8 Summary of findings
In summary, the literature review covered a range of areas that are related to the prediction of bed
demand. First, it showed the interest in solving such problem. Second, it explored the types of data
that different studies used. In particular, it explored the use of historical data, real-time data, and
scheduled data of patients. Third, it explored the use of EDD in the literature. Then, it showed how
the demand prediction could be made for the whole hospital or for a specific program in the
hospital, and the practical implementation of such prediction at a hospital. Finally, it explored the
various methods used to make the prediction especially the use of Monte Carlo simulation in
making predictions.
22
Currently, various commercial products exist in the market to support hospital bed management
systems. Some offer separate modules for predictive analytics, but these are expensive.
Accordingly, the aim of this research is to provide a tool that meets the basic needs of predictive
planning at low cost and will contribute to the existing literature.
23
Methodology
This chapter explains the development of a predictive model of inpatient bed needs for the next 4
days. It considers the number of patients already occupying a bed at 7 a.m. (current patients) of
the first day, the expected new admissions each day within the forecast horizon, and the expected
discharge of patients within the forecast horizon. New admissions are divided into scheduled
elective (surgery) patients and urgent emergent patients. The expected discharge is divided into
the expected discharge of current patients, the expected discharge of new elective admissions, and
the expected discharge of the new urgent admissions. The prediction will be the number of beds
needed each day in the 4-day forecast horizon.
The model was designed to use the EDD of current patients to make discharge predictions.
However, TSH currently captures EDD manually only in two units (One surgery unit and one
medicine unit), and therefore the current method that will be used to build and validate the model
will be different from the future implementation state. Hopefully, the future state will include
electronic input of the EDD for all patients into the system.
The method used to calculate the bed needs for elective and urgent patients will not change in the
future implementation state.
First, we present the model formulation. Then, the prediction process is described for current,
elective, and urgent patients, along with assumptions and limitations.
4.1 Model Design
The patient flow process and the data obtained from the hospital were used to develop the
predictive model for inpatient bed needs. The model performs forecasts of current, urgent, and
elective patient bed needs.
24
For model building and validation purposes, the historical DAD extract will be used to show the
current census at 7 a.m. of day 1. In the future implementation state, the model will depend on the
Medworxx nightly extract for real-time capture of current census at 7 a.m. The data fields in both
extracts will be the same. In particular, the DAD data fields will be organized to be in the same
format as the nightly extract. This ensures the model testing is using only data that will eventually
be available in the future state.
It should be noted that the reason the current census is captured at 7 a.m. is because the nightly
extract updates the patient census at 12:30 a.m. and 7 a.m. only. With this limitation, we decided
to use the current census captured at 7 a.m. The predictions for urgent admissions start at 7 a.m.
on day 1, but for subsequent days the prediction for urgent admissions will be for the whole day.
The methods used to estimate the bed needs generated by each of those streams will differ as will
the information sources used. The model uses information on each individual patient to make
distribution projections on their discharge timing over the next 1-4 days.
If we define n to be the number of days in the prediction timeframe ( n = 1, 2, 3, 4), and
nj ,..2,1 then,
1c is defined as the current number of patients occupying a bed at the beginning of day1 ,
je is defined as the number of elective patients scheduled to arrive at day j ,
ju is defined as the number of urgent/emergent patients expected to arrive at day j ,
jd is defined as the number of predicted discharges from current patient list in day j ,
jl is defined as the number of predicted discharges from elective patients in day j , and
jm is defined as the number of predicted discharges from urgent/emergent patients in day j .
Therefore, np is defined as the predicted number of beds needed at the end of day n
25
4.1.1 Current patients list and expected discharge
The number of patients already occupying a bed ( 1c ) and the number of when they are expected
to be discharged ( jd ) are needed to estimate the bed needs during the 4-day forecast horizon. The
discharge of current patients ( jd ) is estimated using the EDD. The EDD is not 100% accurate,
and patients might be actually discharged before, after, or the same date as the EDD. Therefore,
the prediction of when patients will be discharged is based on using past accuracy performance of
the unit assigning the EDD, or the EDD accuracy. The EDD accuracy is calculated by comparing
the Actual Discharge Date (ADD) of patients with their EDD. The process to predict the current
patients’ bed needs for the 4-day horizon is described in figure 4-1 as follows:
Figure 4-1: Process to predict current census bed needs
1. Build the EDD accuracy database
The predictive model has to predict when the current patients ( 1c ) are expected to be discharged
given that they are assigned an EDD. To investigate the EDD accuracy, we manually collected
EDD data, and compared them to the ADD of patients for a period of about two months and two
weeks (from mid-February 2016 to end April 2016) at two hospital units. One unit is a surgery
unit (28 beds), and the other is a medicine unit (25 beds). Both units are currently the only units
that capture EDD for their patients. The surgery unit captures EDD for the majority of its patients,
while the medicine unit captures the EDD for about (20%) of its patients. We identified that the
EDD accuracy depends on two categories: the unit performing the prediction, and the EDD in
terms of number of days from today to the EDD. It should be noted that the terms “EDD in terms
n
j
j
n
j
n
j
j
n
j
jj
n
j
jn mlduecp11 111
1
26
of number of days from today” and “EDD in terms of number of days hence” are used
interchangeably in this thesis.
This preliminary step involves building an EDD accuracy database. The database was built using
the data from the two units, and contains cumulative discharge probabilities of when patients are
expected to be discharged during the 4-day horizon. The probabilities are categorized by the
hospital unit making the prediction and the EDD in terms of number of days hence.
We assume that the EDD estimate for patients is reviewed daily by the interprofessional team. If
they decide not to change it, then this means they agree with the original estimate. If a change is
needed, then the EDD estimate is updated. This means that the EDD estimate is set every day for
patients. For example, assume a patient who is in the hospital for 10 days. If the EDD estimate is
initially set to 8 days i.e. to be discharged 7 days hence, then on day 5 it is changed to 4 days hence,
finally on day 7 it is changed to 3 days hence. We can assume that the EDD was estimated 10
times, and the 10 estimates are [7,6,5,4,4,3,3,2,1,0] days hence. The accuracy of the x days hence
estimates is calculated by comparing them to the Actual Discharge Date (ADD) of the patient.
For example, the ADD is compared to the EDD estimate in order to create cumulative discharge
probabilities of patients in the surgery unit with an EDD in two days. For the two-month study
period, we collected a total of 74 estimates for EDD = 2 days hence. Then, the frequency of these
estimates for a particular ADD is used to create the cumulative discharge probability. Table 4-1
shows how the data was used to create the discharge probabilities for patients in the surgery unit
with an EDD = 2 days hence. The ADD in the first row shows the day when a patient was actually
discharged . The ADD of zero means the patient was discharged today. The discharge probability
for a particular day is calculated by dividing the number of estimates (i.e. frequency) by the total
number of estimates. In the table, the probability a patient is actually discharged on day 2 given
that their EDD is in 2 days is 52
74= 0.703.
27
Table 4-1: Discharge probability calculation for EDD = 2 days hence at a surgery unit
Cumulative Discharge Probability for EDD = 2 days hence
ADD 0 1 2 3 4 5 6 7 8 9
# of estimates
(Freq.)
0 8 52 8 3 0 1 1 0 1
Discharge
Probability
0 0.108 0.703 0.108 0.041 0 0.014 0.014 0 0.014
Cum. DC
Probability
0 0.108 0.811 0.919 0.959 0.959 0.973 0.986 0.986 1
The cumulative discharge probability for the surgery unit and EDD = 2 days hence is displayed in
the EDD accuracy database as follows (See table 4-2):
Table 4-2: One record in the EDD accuracy database
EDD
# of
days
hence
Unit
Cumulative Probability of discharge in less than
1
day
2
days
3
days
4
days
5
days
6
days
7
days
8
days
9
days
10
days
2 3CP 0 0.108 0.811 0.919 0.959 0.959 0.973 0.986 0.986 1
Depending on the unit making the prediction, the same approach is used to calculate the cumulative
discharge probabilities for other EDDs in number of days hence.
For model building and validation purposes, the same cumulative discharge probabilities collected
for the two units were used for the remaining units that do not estimate an EDD. That is, remaining
surgery units will have the same cumulative discharge probabilities as the surgery unit, and the
remaining medicine units will have the same cumulative discharge probabilities as the medicine
unit. See Figure 4-2 for a sample EDD accuracy database. Column A labeled as “EDD in # of days
28
hence” refers to the number of days from today to the EDD; Column C refers to the location of the
patient in the hospital; and Columns D, E, and F refer to the cumulative discharge probabilities.
Figure 4-2: Sample EDD accuracy database
It can be seen from figure 4-2 that the surgery unit (3CP) does not have an EDD for patients if they
were leaving in more than 6 days, and the medicine unit (3C) does not have an EDD for patients
if they were leaving in more than 7 days. Therefore, we assume that those patients will be staying
in the hospital.
In the future implementation state, the EDD accuracy database will be created using EDD’s
inputted electronically into the system. In addition, TSH is planning on a corporate project that
improves bullet rounds, which will require that an EDD is inputted for all patients in a unit. For
the future state, the database has to be updated periodically to ensure the database reflects the
recent improvement in the EDD accuracy prediction. It is assumed that for every learning process,
the learning curve increases with experience, so the accuracy is expected to increase with
experience.
Based on the manual data collection, results show that the accuracy decreases as the gap between
the EDD and today increases.
Figure 4-3 shows the accuracy distribution for EDD = 1 day hence for the surgery unit at TSH.
The horizontal axis shows the day the patient is actually discharged, and the vertical axis shows
29
the probability of discharge. It can be seen that if a patient’s EDD is estimated 1 day in advance
of the predicted discharge date, then the probability of the patient actually leaving the hospital on
the first day is around 0.8.
Figure 4-3: EDD accuracy distribution given that EDD = 1 day hence
In another example, Figure 4-4 shows the accuracy distribution for EDD = 3 days hence for the
surgery unit. It can be seen that if a patient’s EDD is estimated 3 days in advance of the predicted
discharge date, then the probability of the patient actually leaving the hospital on the third day is
around 0.54. Some patients are discharged before or after the third day, with varying probabilities.
30
Figure 4-4: EDD accuracy distribution given that EDD = 3 days hence
2. Current census preparation
The model needs the current census in order to perform the prediction. For model building and
validation purposes, this step involves extracting current census from the historical DAD extract,
but for the future implementation stage, the model will use the Medworxx nightly extract. Both
extracts contain the same data fields needed for the prediction.
The census contains the patients already occupying a bed at 7 a.m. of day 1 in the forecast horizon.
It contains valuable information about patients such as demographics, admission date and time,
site, admitting unit, admit category, admitting physician, admission diagnosis, service, age, today’s
date, current length of stay and EDD.
It should be noted that some fields in the DAD extract were manually created for the current
census. For example, the today’s date field was added to show patients occupying a bed in day 1;
the current length of stay field is added to show how long patients stayed from the day of admission
31
to today’s date. In addition, the DAD does not contain the EDD data, and therefore the EDD has
to be calculated for model building and validation.
It was decided that the EDD for current patients should be estimated using the CIHI Expected LOS
(ELOS) found in the DAD extract. The CIHI calculates the ELOS for each patient using the
average acute LOS of all patients in Ontario categorized under six main factors: age of patient,
critical care stay flag, type of flagged intervention, number of flagged intervention, Out of Hospital
(OOH) flag, and discharge home flag (See Section 2.1.4 for further details). The case mix grouping
in Ontario is called the HBAM Inpatient Grouping (HIG), where HBAM is the acronym for Health
Based Allocation Model. HBAM is the funding methodology by the Ministry of Health and Long-
Term Care (MOHLTC). In summary, each patient in the DAD extract belongs to a particular HIG
and has a particular ELOS. It should be noted that it is possible for patients, that belong to a
particular HIG and have different combinations of the six factors, to have the same ELOS.
However, for this data we did not have all the six factors available in the DAD extract, and
therefore grouped the patients by HIG and ELOS.
If a patient’s current LOS is less than the ELOS, then the EDD is the difference between the ELOS
and the current LOS. For example, if a patient’s current LOS is 7 days (on October 12, 2015) and
the ELOS is 12 days, then the EDD has to be in 12 - 7 = 5 days (on October 17, 2015).
It should be noted that the actual LOS is different from the ELOS, the ELOS is how long a patient
is expected to stay in the hospital but the actual LOS is how long they actually stayed. So, if a
patient’s current LOS is greater than the ELOS, then the EDD cannot be calculated using the above
method. The patient could be actually discharged on the same day as the current LOS or later. In
this case, the EDD is calculated using the expected value for the actual LOS of historical patient
records, categorized under the same case mix grouping (HIG) and ELOS, that is greater than or
equal to the current LOS. For example, if a Medicine patient that belongs to the HIG 402 with an
ELOS of 7.6 days has a current LOS of 9 days, then the EDD is calculated using the expected
value for the actual LOS of all historical patient records with HIG 402 and ELOS of 7.6 days that
is greater than or equal to the current LOS of 9 days. Table 4-3 shows the frequency table of actual
LOS of all patients that belong to the HIG 402 with an ELOS of 7.6 days.
32
Table 4-3: Frequency table of actual LOS of all patients that belong to HIG 402 and have
ELOS of 7.6 days
Actual LOS for HIG 402 with ELOS 7.6 days
Actual LOS (days) Frequency (number of patients)
1 1
2 1
8 1
9 1
10 1
12 1
14 2
15 1
17 1
18 1
20 1
21 1
It should be noted that the data presented in table 4-3 is real, and the average actual LOS is 12.38
days. The table shows that some patients can actually stay longer than the ELOS of 7.6 days, and
since the patient in the example already stayed 9 days, then the expected value of the total LOS is
calculated as the sum of products of actual LOS greater than or equal to current LOS and the
related probability. See table 4-4 for a sample calculation.
33
Table 4-4: Table to calculate the expected value of total LOS of patients greater than or
equal to 9 days for HIG 402 with ELOS 7.6 days
Actual LOS greater than or equal to 9 days for HIG 402 with ELOS 7.6 days
LOS (days) Frequency Probability Expected Value (Actual LOS x Probability)
9 1 1/10 = 0.1 9 * 0.1 = 0.9
10 1 0.1 1
12 1 0.1 1.2
14 2 0.2 2.8
15 1 0.1 1.5
17 1 0.1 1.7
18 1 0.1 1.8
20 1 0.1 2
21 1 0.1 2.1
Sum 10 1 15 days
The EDD is then calculated by finding the difference between the expected value of the total LOS
and the current LOS, i.e., 15 – 9 = 6 days.
Please note that a patient will not be assigned the calculated EDD if the calculated value is greater
than 6 days for surgery units or 7 days for medicine units. That is, the patient is assumed to have
zero discharge probability during the 4-day prediction horizon. For example, if a Medicine patient
has a current LOS of 3 days, and the ELOS is 14 days, then the EDD is in 14-3 = 11 days, therefore,
this patient will not be assigned the calculated EDD because it is greater than 7 days and the EDD
accuracy database (See Figure 4-2) does not contain discharge probability data for EDD that goes
this far.
34
Table 4-5 shows the data fields in the current census. The AdDate shows the date and time a patient
was admitted, while the TodayDate shows the date and time the data was extracted, and the PtType
field shows if a patient is an inpatient or not. The dates in TodayDate field coincides with the date
the model will be run.
Table 4-5: Sample current census
Unit Site Prog Serv. AdDate TodayDate EDD PtType AdmReason
4CP Gen MED MED 19/9/2015
4:36
12/10/2015
7:00
16/10/2015 IN Bacterial
pneumonia
T9 Gen CAR CAR 19/9/2015
14:07
12/10/2015
7:00
IN Acute
transmural MI
3CP Gen SUR SUR 21/9/2015
10:40
12/10/2015
7:00
16/10/2015 IN Benign
neoplsm colon
3C Gen MED MED 21/9/2015
13:58
12/10/2015
7:00
17/10/2015 IN TYPE 2 DM
3. Model performs discharge predictions of current census patients
The model will perform discharge predictions of current patients within the 4-day forecast horizon.
This means that every patient currently occupying a bed with an EDD will be assigned a
cumulative probability of being discharged within 1, 2, 3, or 4 days. The cumulative discharge
probability is obtained from the EDD accuracy database. The model uses the patient’s location
(unit) and the EDD in terms of number of days hence to find a matching record in the EDD
accuracy database. The EDD in terms of number of days hence is calculated as the difference
between EDD and TodayDate fields.
As mentioned earlier, current census patients who are not assigned the calculated EDD (if EDD is
more than 6 days for Surgery patients, or more than 7 days for Medicine patients) are assumed to
be staying in the hospital during the 4-day forecast horizon, i.e. cumulative discharge probability
of zero.
35
4. Model calculates the bed needs during the 4-day forecast horizon
Once the cumulative discharge probabilities are obtained for current patients, the model sums all
of the cumulative discharge probabilities for day 1, day 2, day 3, and day 4 to show the total
number of discharges for each day ( jd ). The net number of inpatients, i.e. number of beds needed,
for each day is then calculated by subtracting the total number of discharges ( jd ) for that day from
the current census ( 1c ).
See figure 4-5 for a sample output of the prediction. The total number of discharges for Monday
is the sum of all cumulative discharge probabilities across the 9 patients, i.e. 0, and the total number
of discharges for Tuesday is 0.619. Therefore, the net number of inpatients on Monday is 9-0 = 9
inpatients, and Tuesday is 9-0.619=8.38. Since the model performs various calculations, only the
final model output is rounded to the nearest integer.
Figure 4-5: Sample output of discharge prediction of current census
4.1.2 Elective patient admissions and expected discharge
The second piece of the model is the prediction of inpatient bed needs caused by elective patients
during the 4-day forecast horizon. This is calculated by finding the number of all new expected
elective admissions ( je ) and the estimate of when they will be discharged ( jl ). The number of
new expected elective admissions ( je ) is obtained from the OR schedule that is extracted from
SIS. The number of elective discharges ( jl ) is estimated using historical LOS data of patients
categorized by the surgeon and the surgical procedure.
36
Patients do not stay in the hospital for the same amount of time even if they undergo the same
surgical procedure under the same surgeon. We found that there is a unique patient LOS
distribution for each physician performing a particular procedure. Therefore, the prediction of
when elective patients will be actually discharged is based on using past LOS distribution of the
surgeon performing the same procedure in hand.
The LOS distribution is calculated if the surgeon performs a particular procedure at least 30 times
during a fiscal year, and it’s calculated for procedures with long LOS regardless of the number of
cases performed during the fiscal year. Long LOS is defined as cases with LOS greater than four
days. Remaining procedures that are performed less frequently by a surgeon are all grouped as
“Other” under the physician name only. All of the LOS distributions are saved in a database named
the “Elective Surgery database”. The process to predict elective patients’ bed needs for the 4-day
horizon is described in figure 4-6 as follows:
Figure 4-6: Process to predict elective patients bed needs
1. Build the Elective surgery database
The model has to predict when the new elective patients ( je ) are expected to be discharged given
that we know how long similar patients stayed in the past based on the historical LOS of elective
patients. Three years of historical DAD and SIS data (April 2013 – September 2015) were used in
the investigation.
As a result, we built an Elective Surgery database, using the three years of data, that contains
cumulative discharge probabilities of when patients are expected to be discharged during the 4-
day forecast horizon. The cumulative discharge probabilities were created by combining historical
DAD and SIS data. This is because the DAD contains some of the data such as acute LOS and
Admit Category, and SIS contains the remaining data such as the surgeon’s name and the coded
surgical procedure name. The combined data has the necessary information needed to create
cumulative discharge probabilities of patients classified by surgeon’s name only, or surgeon’s
37
name and procedure. In particular, it contains the acute LOS of all elective patients who went
through a particular procedure performed by a particular surgeon.
The data is then used to create an empirical LOS distribution for each surgeon-procedure
combination given that the number of cases is at least 30 cases during a fiscal year. Procedures
with long LOS are also grouped together regardless of the number of cases performed during a
fiscal year. The remaining procedures are grouped together under the surgeon’s name only. For
example, if surgeon John Smith performed 100 total knee replacement surgeries during a fiscal
year, and each patient had a different LOS, then the table 4-6 below shows the frequency table of
how long each patient stayed. The first row shows the actual LOS of patients in days, the second
row shows the cumulative frequency of patients with the actual LOS, the third row shows the
cumulative discharge probability. It can be seen from the table that the cumulative probability a
patient is discharged in less than 3 days is 92
100= 0.92.
Table 4-6: Sample LOS frequency table for John Smith - Total Knee Replacement
Total Knee Replacement surgeries performed by John Smith
Actual LOS (Days) < 1
Day
< 2
Days
< 3
Days
< 4
Days
< 5
Days
< 6
Days
< 7
Days
< 8
Days
Cum. Number of patients
(Frequency)
0 13 92 98 99 99 99 100
Cumulative Discharge probability 0 0.13 0.92 0.98 0.99 0.99 0.99 1
The cumulative discharge probability of a patient during the 4-day forecast horizon is displayed in
the Elective Surgery database as follows (See table 4-7):
38
Table 4-7: Sample record in the Elective Surgery database
Name - Procedure Cumulative discharge probability in less than
John, Smith – Total Knee
Replacement
1
Day
2
Days
3
Days
4
Days
5
Days
6
Days
7
Days
8
Days
0 0.13 0.92 0.98 0.99 0.99 0.99 1
In a similar manner, if surgeon John Smith also performed various procedures less frequently, then
all of those procedures will be used to create another record in the database that shows surgeon’s
name only. This process is done for all surgeons in the hospital. See figure 4-7 for a sample Elective
Surgery database. First column labeled as “Surgeon – Procedure Name” refers to the name of the
surgeon and the procedure name; Columns 2, 3, 4, and 5 refer to the cumulative discharge
probabilities. The actual name of the Surgeons was hidden for confidentiality.
Figure 4-7: Sample Elective Surgery database
Since the DAD is updated every 3-4 months, then it is recommended to update the Elective Surgery
database every time the DAD is updated. The process to create the database will still be used in
the future state.
39
2. Build the Keyword database
The model uses the OR schedule, obtained from SIS, to calculate the number of new elective
patients ( je ), and uses the surgeon’s name and the procedure description in the OR schedule to
predict how many are expected to be discharged during the 4-day horizon ( jl ).
The procedure names in the Elective Surgery database are coded procedures, but the procedure
names in the OR schedules are free text fields. Nurses input the procedure description in the OR
schedule as free text, therefore the model has to understand the free text field and match it to the
appropriate coded procedure name in the Elective Surgery database.
This step involves building a Keyword database. We developed the model so that it performs a
keyword search by looking into the free text and finding trigger keywords/phrases that relate to
the coded procedure in the Elective Surgery database.
Historical OR Schedules and SIS data were used to build the Keyword database. This database
contains a list of the coded procedures and the matching keywords. The model could then easily
look for keywords and find a matching record from the Keyword database. Once the proper coded
procedure name is found, the model changes the name of Surgeon in OR Schedule to be “Last
name, First name – Procedure name”. This is then used to find a matching record in the Elective
Surgery database to find the cumulative discharge probabilities of patients.
If no match is found, then the name of the surgeon is not changed and only the surgeon’s name is
used to find a matching record in the Elective Surgery database. Since the free text field could
contain misspelled words or unorganized descriptions, the Keywords database also contains
commonly misspelled words or phrases. See Figure 4-8 for a sample keywords database. The first
column in the figure lists the name of the Surgeon, the second column lists the coded procedure
name, and the third column contains the keywords and phrases that are commonly used to describe
the coded procedure. The actual name of the surgeons was hidden for confidentiality. For the full
list, refer to Appendix C.
40
Figure 4-8: Sample Keyword database
It should be noted that the Keyword database was created for the most frequently occurring
procedures, i.e. at least 30 cases in a fiscal year, and was created for procedures with very long
LOS regardless of the number of cases in a fiscal year. The Keyword database has to be updated
periodically to ensure recent keywords are included. It should also be noted that the process to
create the database will still be used in the future state.
3. Obtain the Elective OR schedules
To make discharge predictions of elective patients, the model uses the OR schedule for each day
in the forecast horizon. The OR schedule is obtained from SIS, and lists all the patients expected
to arrive at a particular date categorized by the admission type, i.e. MAP, ASU, DS, and ICU/CCU.
It also contains the surgeon’s name, procedure description, start time of surgery, operating room
number, and other identifiers. To perform the discharge prediction, the model uses three main data
fields: Surgeon’s name, procedure description, and admission type. See Figure 4-9 for a sample
OR schedule.
41
Figure 4-9: Sample OR schedule obtained from SIS
The figure shows the fields that exist in each OR Schedule. The Admission (Column G) shows
whether a patient is classified as a MAP, ASU, DS, or ICU/CCU. This is used to decide whether
a patient is an inpatient or not. The Surgeon Name (Column B) and the Procedure Description
(Column C) fields are used to predict when a patient will be discharged.
The OR schedule is prepared in a way that is easy to analyze, and preprocessed by the model. Step
4 below describes the how the model performs the discharge predictions of elective patients in the
OR schedules.
4. Model to perform discharge predictions of elective patients in OR schedules
In this step, the model performs discharge predictions of elective patients using the prepared OR
schedules for each day within the forecast horizon. This means that every eligible patient will be
assigned a cumulative probability of being discharged within 1, 2, 3, and 4 days. First, the model
uses the Keyword database to find the matching coded procedure to the free text procedure
description in the OR schedule. Then, the cumulative discharge probabilities for each patient are
obtained from the Elective Surgery database using the Surgeon’s name and the matched coded
procedure.
42
If the free text procedure could not be matched to a record in the Keyword database, then the model
obtains the patient’s cumulative discharge probability from the Elective Surgery database using
surgeon’s name only
5. Model calculates bed needs caused by elective patients during 4-day horizon
Once the cumulative discharge probabilities are obtained for all eligible patients, the model sums
all of the cumulative discharge probabilities for day 1, 2, 3, and 4 to show the expected number of
patient discharges for each day ( jl ). The net number of elective inpatients, i.e. number of beds
needed, for each day is calculated by subtracting the cumulative number of estimated patient
discharges ( jl ) for the same day from the total number of new elective patients ( je ).
See Figure 4-10 for a sample output of discharge prediction of elective patients. The sample shows
the list of all patients scheduled for surgery on Friday, along with procedure description, and type
of admission. Also, it contains the cumulative discharge probabilities for patients during the 4-day
horizon. The surgeon’s name was hidden for confidentiality.
The total number of discharges for Friday is the sum of the cumulative discharge probabilities
across the 18 new elective patients, i.e. 0.983, and the total number of discharges for Saturday is
9.272. Therefore, the net number of elective inpatients on Friday is 18-0.983=17.017 elective
inpatients. Similarly, the net number of elective inpatients on Saturday is 18-9.272=8.728 elective
inpatients. Since the model performs various calculations, only the final model output is rounded
to the nearest integer.
43
Figure 4-10: Sample output of discharge prediction of elective patients
The model performs such calculation for each OR schedule during the 4-day timeframe. Also, the
process to do such calculation will not change in the future implementation stage.
4.1.3 Urgent patient admissions and expected discharge
The third piece of the predictive model is the prediction of inpatient bed needs caused by urgent
patients. This is calculated by estimating the number of new urgent patients for each day in the 4-
day forecast horizon ( ju ) and when they are expected to be discharged ( jm ).
The prediction of inpatient bed needs caused by urgent patients is estimated using a Monte Carlo
simulation model by Liu, T.M. [36] known as the “Generic Bed Planning Model”. It uses historical
data of patients such as the admission date and time, and length of stay in hours to create the
prediction. In addition, it can group patients into different user defined categories such as service
type (e.g. Surgery, Medicine, and Nephrology), admit category (e.g. Urgent, and Elective), and
discharge unit location.
The model works by constructing patient arrival distributions from historical patient records. It
randomly generates patient arrivals from the patient arrival distribution for each day of the week
and for different patient categories. Then, the model uses the historical patient records to assign
LOS to the randomly generated arrivals and runs for multiple weeks (warm-up period) until it
44
reaches steady state thus allowing it to use the bed occupancy at steady state in order calculate
demand for beds during a typical week [36].
The model runs for multiple iterations to calculate the average bed needs for a typical week along
with standard deviation. The output of the model is displayed as the number of beds needed for
each day of the week starting Sunday (See Figure 4-11).
Figure 4-11: Sample output of Generic Bed Planning Model
The figure shows the patient demand for beds of urgent patients. It should be noted that the results
were obtained by running the model for multiple weeks (warm-up period) before collecting the
bed needs in the last week. Each day is divided into three 8-hour shifts: Night, Day, and Evening.
The Night shift starts at 12 a.m. by default.
45
The Generic Bed Planning Model was initially built to estimate the patient demand for beds in a
hospital during a typical week. That is, the model starts with no patients in the hospital, then it
runs for multiple number of weeks therefore allowing it to reach steady state. Therefore, the
cumulative number of beds calculated at the steady state is the demand for beds in a hospital during
a typical week. However, the 4-day predictive model starts the prediction with patients already
occupying a bed (i.e. current patients), and therefore only requires estimates of number of beds
needed by Urgent patients who come and leave the hospital during the 4-days only.
In order to perform the prediction of Urgent patients bed needs for the 4-days horizon, the data
input into the Generic Bed Planning model was modified to force the model to perform predictions
of Urgent patients’ bed needs for the required 4-days only. See Appendix B for the detailed process
of modifying the data before inputting into the simulation model to make predictions for the 4-day
horizon.
It should be noted that the Generic simulation model runs separately from the 4-day predictive
model, and the simulation process takes a long time especially if it was run for multiple iterations.
In addition, the results of the simulation model do not change if it was run different times using
the same data list; therefore, we decided to save the results of the Generic simulation model in the
4-day predictive model beforehand to ensure that the predictive model retrieves the required
predictions of urgent bed needs faster. The process to predict urgent patients’ bed needs for the 4-
day horizon is described in figure 4-12 as follows:
Figure 4-12: Process to prepare prediction of urgent patients bed needs
1. Input data preprocessing
The historical DAD data is used as the input into the Generic simulation model. The data is
modifed to ensure the model is forced to make predictions for the required 4-days in forecast
horizon only. In particular, the historical input data will only contain patient records for the
required 4-days in the forecast horizon, and the other days will contain no data. Refer to Appendix
B for the details of the process.
46
2. Run the Generic simulation model
The Generic simulation model is run using the modified historical DAD data. In the model settings,
the model should run only for one week and since the input data contains only 4 days the model is
technically running for the 4 days only.
It should be noted that the results of the Generic Model take into account the internal transfers
between critical care and acute inpatient units. The patient stay in the modified DAD data is broken
down into multiple stays such as acute only, critical care, acute surgical unit, and alternative level
of care; therefore, the model is able to calculate the bed needs for all patient stays except the critical
care stay. This is done by deselecting the critical care stay before running the model. Therefore,
the critical care stay should be deselected so that the bed needs for critical care are not included in
the model output.
The results of the simulation show the prediction for the 4-day horizon, with day-1 as the day the
prediciton was run (i.e. today). It should be noted that the model is run for each day of the week.
3. Load simulation results into predictive model
The output of the Generic Simulation model is saved into the 4-day predictive model. See figure
4-13 for a sample of the cumulative urgent patient bed needs that is stored in the 4-day predictive
model.
47
Figure 4-13: Predicted Urgent patients bed needs
It can be seen from the figure that the bed needs at the General campus starting with Monday as
day 1 is 19 beds. The 19 beds were calculated based on the expected number of urgent patients
and the number of their expected discharge on Monday.
Since DAD is updated every 3 to 4 months, then it is recommended to run the Generic simulation
model periodically to have latest data included in the 4-day predictive model. Also, the process
described to calculate the bed needs by urgent patients will still be used in the future
implementation stage.
4.2 Prediction Process
This section describes the process that the model follows in order to calculate the inpatient bed
needs for the 4-day forecast horizon. The process depends on the three pieces described in section
4.1 above. An outline of the process can be seen in Figure 4-14, with an explanation of the outline
following.
48
Figure 4-14: Outline of the prediction process
1. Import current census and OR schedules
Once the model file is opened, a pop-up window appears that asks the user to automatically import
the updated current census and OR schedules into the model by clicking the update button. Figure
4-15 shows the welcome window that appears once the model is open.
Figure 4-15: Predictive model welcome window
The model starts by clearing old data, and then imports the new current census and stores it in a
worksheet named CensusImport. Similarly, the four OR schedules are stored in worksheets named
Imported, Imported1, Imported2, and Imported3 respectively.
49
Once the data is imported, a message appears that shows data import was successful, and followed
by another window that asks the user to start the prediction. Figure 4-16 shows the import
successful window, and figure 4-17 shows the start prediction window. The model then performs
calculations to predict inpatient bed needs based on current census, and elective patients. The
following sections explain each step.
Figure 4-16: Predictive model window that shows successful data import
Figure 4-17: Predictive model window that asks user to start running the model
2. Calculate bed needs based on current census
In this step, the model performs few steps in order to prepare the current census to be used for the
prediction as explained in section 4.1.1. The processed census data is saved in a different sheet
50
named Census. This sheet also contains the net inpatient needs of current census in the 4-day
forecast horizon (See Figure 4-5).
3. Calculate bed needs caused elective patients scheduled for day 1, day 2, day 3, and
day 4
In this step, the model goes in sequence to preprocess each OR schedule to be used for the
prediction as explained in section 4.1.2. The processed OR schedules are saved in different sheets
named Filtered, Filtered1, Filtered2, and Filtered3 respectively. Those sheets also contain the net
inpatient needs of OR patients scheduled for a procedure on day 1, day 2, day 3, and day 4 of the
forecast horizon. (See figure 4-10).
4. Retrieve bed needs caused by expected urgent patients
In this step, the model uses the saved Generic simulation results to find the bed needs for the
required 4-day horizon.
5. Compile all results in summary sheet
The model copies all of the results into a Result Summary sheet. The Result Summary sheet
displays prediction of inpatient demand for beds for the whole hospital during the 4-day forecast
horizon. In addition, it contains the funded bed capacity of the hospital therefore allowing the
model to calculate the Capacity-Demand gap. The Capacity-Demand gap is the difference between
the funded bed capacity and the inpatient bed needs at a given day. If demand exceeds capacity,
then the value is highlighted in red to indicate a possible issue. However, if capacity is equal to or
exceeds demand, then the value is highlighted in green. See figure 4-18 for a sample Result
Summary.
51
Figure 4-18: Sample Result Summary sheet
It can be seen that figure 4-18 also displays the breakdown of total inpatient demand for beds along
with a description. The first row of the breakdown shows the current patient census ( 1c ) captured
on day 1 (Monday) at 7 a.m. The second row shows the number of current census discharges ( jd )
at each day. The third and fourth rows show the bed needs created by the urgent and elective
patients respectively.
The results of the model could then be used by patient flow coordinators and managers to plan
proactively for the expected demand for beds. It should be noted that the predictive model is
designed with the following limitations in the future state:
1. Since bullet rounds at the hospital occur during the day after 7 a.m., then the current census
that will be captured by the nightly extract at 7 a.m. will not contain the updated EDD for
that day. Therefore, the model will use the last updated EDD.
2. It is assumed that EDD is updated daily and inputted electronically into the system.
3. This model is not a patient flow model; therefore, it does not predict where patients will
stay in the hospital and what type of service they will receive. It is possible for patients to
change services and units during their stay. In addition, the most responsible physician is
only known after a patient is discharged.
Monday Tuesday Wednesday Thursday
Funded Bed Capacity 230 230 230 230
Total inpatient demand for beds 204 221 223 217
Capacity-Demand Gap 26 9 7 13
Legend: Demand > Capacity
Capacity >= Demand
Source Description Monday Tuesday Wednesday Thursday
Current Patients Patients occupying a bed 201 204 221 223
Discharge of current patients Number of discharges based on EDD -16 -23 -25 -22
Urgent patients (non-elective) 4-day demand for beds of urgent patients 19 20 15 14
Elective patients (scheduled or operating room patients) 4-day demand for beds of elective patients 0 19 12 2
204 221 223 217
The elective or urgent code was based on the admission category in the Discharge Abstract Database(DAD)
Elective: Patients who are pre-registered and/or would be found on an elective booking list (we can also call them scheduled)
Urgent: Patients who have a life-threatening condition or require immediate assesment and treatment
Inpatient demand for beds prediction (4-day)
General Campus
Breakdown of total inpatient demand for beds
Total Inpatient demand for beds
52
Model Testing, Results, and Discussion
This chapter describes the testing of the model at The Scarborough Hospital, the results that were
obtained, and the discussion of the findings. Since the hospital does not capture the EDD
electronically, the model was tested using retrospective data (Historical DAD data) for the General
Campus, and the prediction results were compared to the actual values. The results were analyzed
using Mean Absolute Deviation (MAD) and Mean Absolute Percentage Error (MAPE). The testing
horizon is from October 12, 2015 to October 20, 2015. This period was not included in the data
used to build the model.
Since historical DAD data was used for testing, the patient records do not have EDD. Therefore,
we calculated the EDD for patients in the current census using two methods and investigated the
prediction results.
In the first method, the EDD for current census, and the EDD accuracy database were calculated
using the approach explained in section 4.1.1. In the second method, we wanted to investigate the
improvement in the prediction accuracy if accurate estimates of the EDD were used, and therefore
encourage interprofessional staff in making accurate EDD predictions. Therefore, in the second
method we used the patient’s actual discharge date as the EDD and modified the EDD accuracy
database to give 100% accuracy for those EDD predictions.
Finally, this chapter investigates the accuracy of the approach used by TSH during the daily
corporate bed meetings. As mentioned in Chapter 1 and 2, the corporate bed meeting investigates
the hospital’s condition at one point in time, i.e. 9 a.m. Current census is reported along with
discharge predictions for the day, and expected elective patients. The data reported is not
specifically used to make predictions; however, we used their data to make predictions of bed
needs until midnight of day 1 and compared them to actual results. The timeframe used is October
13, 2015 to October 20, 2015.
53
5.1 Method 1: Model testing using CIHI expected patient LOS to calculate the EDD
The model depends on three processes: the bed needs caused by urgent patients, the number of
elective patients and their predicted discharges, and the EDD of patients already occupying a bed
in the hospital. The expected inpatient bed needs caused by urgent patients is already stored in the
predictive model and the OR schedule for each day in the testing timeframe is obtained from the
SIS. In this method, the EDD for current patients was calculated using CIHI ELOS data (See
section 4.1.1).
The predictive accuracy of the model has to be tested and validated using data that was not used
to build it. The data used to prepare the predicted bed needs caused by urgent patients was based
on timeframe from April 2013 to September 2015; the Elective Surgery database was created using
data from April 2013 to September 2015; and the EDD accuracy database was created using data
collected from February 2016 to April 2016. The model was tested for the horizon of October 12,
2015 to October 20, 2015. The results of the model were compared to the actual values in terms
of MAD and MAPE.
The MAD, also called Mean Absolute Error (MAE), is measured in the same units as the data and
is used to find the magnitude of the error. It is calculated as the mean of the absolute difference
between the actual value and the prediction value, as shown below:
1
𝑛∑|𝐴𝑐𝑡𝑢𝑎𝑙 − 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛|
The Mean Absolute Percentage Error (MAPE) is expressed in generic percentage values. It is
calculated as shown below:
(1
𝑛∑
|𝐴𝑐𝑡𝑢𝑎𝑙 − 𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑖𝑜𝑛|
|𝐴𝑐𝑡𝑢𝑎𝑙|) × 100
5.1.1 Data preparation for testing and validation
The testing of the model using retrospective data is time consuming and requires a lot of manual
data preparation, and that is the reason the model was tested only for the period of October 12,
2015 to October 20, 2015.
54
Actual values calculation
In order to validate the accuracy of the predictive model, the predicted values must be compared
to the actual values. The actual values are the number of patients occupying a bed at the end of
each day in the 4-day horizon. The actual values are also obtained from DAD.
The number of patients occupying a bed at the end of each day in the 4-day horizon is calculated
by finding patient records whose admission and discharge dates and times include the date in
question. For example, if we need to calculate the number of patients occupying a bed by the end
of October 12, 2015, then a patient who was admitted on September 16, 2015 at 10:00 am and was
discharged on October 29, 2015 at 2:00 pm will be included in the count.
In case a patient has a critical care stay, then it must be investigated if the patient was occupying
an acute inpatient bed by the end of the day. This is calculated by investigating all of the admission
and discharge dates and times to and from a critical care unit, and find if they were occupying an
inpatient bed by the end of day in question. For example, if we need to calculate the number of
patients occupying a bed by end of October 12, 2015 then a patient who was admitted on
September 16, 2015 at 10:00 am and was discharged on October 29, 2015 at 2:00 pm, but was
admitted to a critical care unit on October 1, 2015 and was discharged on October 20, 2015 will
not be included in the count because the patient was not occupying an inpatient bed by end of day
at October 12, 2015.
5.1.2 Test Results
This section describes the results that were obtained after the data was prepared and run in the
model. The General Campus at TSH was selected for this testing because all of the manually
collected data used to build the model belong to the General Campus. The prediction results were
compared to actual values in terms of MAD and MAPE. The accuracy of the model improves as
the MAD and MAPE decrease.
Figure 5-1 shows the results in terms of prediction versus actual values matrix. The top row
highlighted in blue contains the actual number of beds occupied by patients by the end of each
day, and the remaining rows contain the predicted number of beds by the end of each day for the
4-day prediction horizon.
55
Figure 5-1: Prediction versus actual values matrix
It can be seen from the figure that there is a large mismatch in number of beds between the
predicted values and the actual values. Figure 5-2 shows the difference matrix between the actual
and the prediction in terms of number of beds mismatch, and figure 5-3 shows the difference in
percentage terms. The negative error values represent the over prediction, the positive error values
represent the under prediction, and the zero error means that prediction was equal to actual values.
Figure 5-2: Matrix to show number of beds mismatch between the actual and prediction
results
56
Figure 5-3: Matrix to show prediction mismatch in percentage terms
It can be seen from figure 5-2 that the error ranges from -37 patients (beds occupied) to 21 patients
(beds occupied). The average is –4.69 patients (bed occupied), which is an over prediction. In
terms of percentage, figure 5-3 shows the error range from -18.974 % to 10.145 % and the average
is -2.38% error.
The prediction error for each day of the 4-day prediction horizon was also analyzed using MAD
and MAPE. It was found that the prediction error is within 12 beds for day 1 and increases we go
further from day 1. Figure 5-4 shows the absolute error for the 4-day prediction horizon, and figure
5-5 shows the absolute percentage error for the 4-day prediction horizon.
Figure 5-4: Absolute error for the 4-day prediction horizon
57
Figure 5-5: Absolute percentage error for the 4-day prediction horizon
Table 5-1 summarizes the results shown in figures 5-4 and 5-5.
Table 5-1: Summary of MAD and MAPE by day in the 4-day prediction horizon
Day 1 Day 2 Day 3 Day 4
MAD (# beds) 12 14 13 16
MAPE (%) 5.52% 6.92% 6.51% 7.63%
5.1.3 Analysis and Discussion
It can be seen from the results presented in section 5.1.2 that there is a large mismatch between the
predicted values and the actual results. These results were expected because of three main error
sources:
1. Error due to discharge prediction of current patients (PCP).
The error due to discharge prediction of current patients accounted for 83.96% of error on day 1,
62.31% on day 2, 35.54% on day 3, and 39.72% on day 4. This is due to several reasons:
The use of ELOS to generate an EDD for patients instead of using staff generated EDD
58
In case the current LOS is greater than ELOS, then the actual LOS is used to generate
an EDD for patients
The EDD accuracy database is based on two units but applied to all units
The EDD accuracy database contains data for patients with EDD up to 6 or 7 days
hence
The majority of patients are identified as Current
2. Error due to prediction of urgent patients’ bed needs (PUP)
The error due to prediction of urgent patients’ bed needs accounted for 14.31% on day 1, 29.71%
on day 2, 49.68% on day 3, and 47.34% on day 4. This indicates that as we go further from day 1,
the prediction error of urgent patients’ bed needs increases.
3. Error due to prediction of elective patients’ bed needs (PEP)
The prediction of elective patients’ bed needs is the third source of error, and has the least error
compared to the first two errors. The error due to prediction of elective patients’ bed needs
accounted for 1.73% on day 1, 7.98% on day 2, 14.78% on day 3, and 12.94% on day 4.
Table 5-2 summarizes the three sources of error for method 1.
Table 5-2: Sources of error for method 1
Sources of error Day 1 Day 2 Day 3 Day 4
PCP 83.96% 62.31% 35.54% 39.72%
PUP 14.31% 29.71% 49.68% 47.34%
PEP 1.73% 7.98% 14.78% 12.94%
Total 100% 100% 100% 100%
Also, it can be noticed that 22 out of the 36 prediction values are considered as an over prediction.
This is because we did not assign patients an EDD (zero discharge probability for the 4-day
59
prediction horizon) in case their calculated EDD is greater than 6 days for surgery or greater than
7 days for medicine.
It can be seen that the prediction of EDD for current patients has a major impact on the accuracy
of the model. The Nursing team at TSH is expected to improve the accuracy of the EDD prediction
to improve the accuracy of the model. Section 5.2 explores the assumption that prediction
accuracy improves in case the EDD prediction improves.
5.2 Method 2: Model testing using EDD as actual discharge date
In this method, the model was tested using EDD for current patients as their actual discharge date
and assumed that the EDD is 100% accurate. This means that the EDD accuracy database was
modified to include 100% accurate estimates. This step will result in testing the model using ideal
estimates for the current patient list; however, the estimates for the elective and urgent patients
will not be modified and are similar to method 1.
The testing period is also from October 12, 2015 to October 20, 2015. The results of the model are
compared to actual values using MAD and MAPE.
5.2.1 Data preparation for testing and validation
In order to test the model, the EDD accuracy database and the current census have to be adjusted
for this method.
Current census preparation
In method 1, the EDD of patients was calculated using the ELOS. However, the EDD, in this
method, was calculated using the actual discharge date of patients. Since the DAD already contains
the discharge date of patients, then the EDD for each patient is their discharge date.
EDD accuracy database preparation
The EDD accuracy database in the model has to be adjusted so that the EDD estimates in the
current census are considered 100% accurate. Therefore, the EDD accuracy database is built using
the current patient list and their actual discharge date (as the EDD). In particular, the field named
60
“EDD in number of days hence” is calculated by finding the difference between the EDD and
TodayDate fields in the current census.
For example, if the DAD contains 10 patients currently occupying a bed at 7 a.m. on October 12,
2015, then this current list will be used to create the EDD accuracy database (see Figure 5-6 for a
sample current census).
Figure 5-6: Current census created using DAD
The EDDs in the 6th column of figure 5-6 are the actual discharge dates, but were changed to be
the EDD. The adjusted EDD accuracy database is then created using the EDD, TodayDate, and
the Unit fields of the current census. The discharge probabilities, in this case, are equal to 1 on the
actual date of discharge as shown in figure 5-7 below.
Figure 5-7: EDD accuracy database for testing in model
Actual values calculation
The actual values are calculated using the same methodology described in section 5.1.1.
61
5.2.2 Test Results
This section was prepared in a similar fashion to the section 5.1.2, and the only difference is the
use of current patient census that contains the EDD, which was calculated using the actual
discharge date of patients.
Figure 5-8 shows the results of the prediction versus actual values matrix. The top row highlighted
in blue contains the actual number of beds occupied by patients by the end of each day, and the
remaining rows contain the predicted number of beds by the end of each day for the 4-day
prediction horizon.
Figure 5-8: Prediction versus actual values matrix
It can be seen from the figure that the gap in the number of beds between the predicted values and
the actual values is reduced. This indicates that if the staff were able to improve their prediction of
EDD, then the model accuracy improves as well. Figure 5-9 shows the difference matrix between
the actual and prediction values in terms of the number of beds mismatch, and figure 5-10 shows
the difference in percentage terms. The negative error values represent the over prediction, and the
positive error values represent the under prediction
62
Figure 5-9: Matrix to show number of beds mismatch between actual and prediction
results
Figure 5-10: Matrix to show prediction mismatch in percentage terms
The error ranges from -4 patients (beds occupied) to 19 patients (beds occupied). The average is
5.22 patients (bed occupied), which is an under prediction. In terms of percentage, the error ranges
from -2.1 % to 8.4 % and the average is 2.3 % error.
The prediction error for each day of the 4-day prediction horizon was also analyzed using MAD
and MAPE. It was found that the prediction error is within 2 beds for day 1 and increases we go
further from day 1. Figure 5-11 shows the absolute error for the 4-day prediction horizon, and
figure 5-12 shows the absolute percentage error for the 4-day prediction horizon.
63
Figure 5-11: Absolute error for the 4-day prediction horizon
Figure 5-12: Absolute percentage error for the 4-day prediction horizon
Table 5-3 summarizes the results shown in figures 5-11 and 5-12.
Table 5-3: Summary of MAD and MAPE by day in the 4-day prediction horizon
Day 1 Day 2 Day 3 Day 4
MAD (# beds) 2 5 9 10
MAPE (%) 0.88% 2.49% 3.91% 4.38%
64
5.2.3 Analysis and Discussion
It can be seen from the results presented in section 5.2.2 that the gap between the predicted values
and the actual results was reduced once the EDD accuracy improved to 100%. This gives the
incentive for staff to work towards improving their predictions of EDD in order to get better model
predictions. The error of the model is within 2 beds (0.88%) and gets worse as we go further from
day 1 (the day the prediction was made). In this method, the two sources of error are:
1. The variation between actual and predicted bed needs for urgent patients (PUP)
The main source of error is the error due to prediction of urgent patients’ bed needs. The error
accounted for 89.21% on day 1, 78.83% on day 2, 77.07% on day 3, and 78.54% on day 4. This is
because the prediction of bed needs caused by urgent patients depends on the arrival rate of patients
by day of week and their estimated LOS. See Appendix D for extra analysis of prediction accuracy
of Urgent patients bed needs only.
2. The variation between actual and predicted bed needs for elective patients (PEP)
The prediction error due to prediction of elective patients’ bed needs is less than PUP. This is
because the number of scheduled elective patients is already known once the model is run. The
error accounted for 10.79% on day 1, 21.17% on day 2, 22.93% on day 3, and 21.46% on day 4.
Table 5-4 shows the two sources of error for method 2.
Table 5-4: Sources of error for method 2
Sources of error Day 1 Day 2 Day 3 Day 4
PUP 89.21% 78.83% 77.07% 78.54%
PEP 10.79% 21.17% 22.93% 21.46%
Total 100% 100% 100% 100%
Finally, it should be noted that both of method 1 and method 2 involved testing of the model using
retrospective data. It is assumed that the real-time testing would provide similar results.
65
5.3 Investigation of current TSH approach in making predictions
The Scarborough Hospital runs the Corporate Bed Meeting at 9 a.m. to gain a global picture of
daily patient demand and bed capacity, and to develop appropriate action plans to ensure that
capacity meets demand. It should be noted that this approach takes a snapshot of the hospital
condition at 9 a.m.
Managers report on seven main pieces to estimate if capacity will meet demand for the day:
1. The current census at 9 a.m.
2. The number of known discharges for the day (7 a.m. to 4 p.m.)
3. The number of expected discharges for the day (7 a.m. to 4 p.m.)
4. The number of expected discharges for the day (4 p.m. to midnight)
5. The number of new elective patients for the day
6. The unplaced ED admitted patients up until 9 a.m.
7. The number of transfers from ED for the day
We used this information to verify whether their estimates for the day meet the actual values. Our
intent was to investigate their prediction accuracy. In particular, we investigated their projections
for end of day 1. We assumed the expected discharges for the day to be known discharges for
simplification. Since nothing is discussed beyond day 1, this investigation is for day 1 only.
The testing was performed for period of October 13th, 2015 to October 20th, 2015. Since corporate
bed meetings do not occur during weekends or long weekends, there was no data for October 12,
17, and 18. See table 5-5 for the calculation summary. The actual number of patients represents
the number of patients occupying a bed by end of day 1, where the corporate meeting prediction
represents prediction of number of patients by end of day 1, and the last row represents the
mismatch between actual and predicted values.
66
Table 5-5: Actual versus corporate meeting prediction of patients by end of day 1
13 Oct 14 Oct 15 Oct 16 Oct 17 Oct 18 Oct 19 Oct 20 Oct
Actual no. of
patients 221 229 213 195 195 207 218 227
Corporate
Meeting
prediction
231 236 218 200 - - 219 228
Difference -10 -7 -5 -5 - - -1 -1
It can be seen from the table that they over predict the bed needs by 4.83 on average for end of day
1. The patient flow coordinators notes indicated frequent surging to meet increasing demand
during the day. This is because the expected number of urgent admissions after 9 a.m. is not
predicted. Also, the actual number of discharges is higher than the expected number of discharges
reported during the corporate bed meeting. This indicates that more patients are being discharged
to improve the flow of patients into the hospital.
67
Conclusion
The purpose of the research presented in this thesis was to develop, test, and validate a 4-day
predictive model. This model predicts the inpatient bed needs for up to 4 days in advance in a
hospital. The number of beds needed is calculated by finding the bed needs caused by expected
urgent patients, scheduled elective patients, and patients already occupying a bed in the hospital.
The benefit of having such a prediction in advance helps the hospitals proactively prepare for
expected high demands for its services, and therefore improve the quality of service. This model
was built in collaboration with The Scarborough Hospital in Scarborough, Ontario, however, the
same concept could be applied in any other hospital given that the important information is
available.
The unique piece in this predictive model is that it makes use of the staff estimates of patients
discharge date (EDD). This feature is expected to give a better buy-in into the model by the hospital
staff, especially the patient flow coordinators. In addition, the model contains the EDD accuracy
database which provides information on how accurate is a discharge estimate made by a hospital
unit. Also, it contains Elective Surgery database that provides discharge prediction information
about patients who undergo a surgical procedure with a particular physician.
There were a few challenges that prevented testing the model in real-time such as the unavailability
of EDDs electronically across the hospital. Therefore, the model was tested using retrospective
DAD data for the current patients, but the data sources for the two other pieces were not changed.
The first method of the testing used ELOS in order to calculate the EDD for current patients, and
the second method used actual discharge date as the EDD for current patients.
In the first method, the model did not perform well for several reasons. The first main reason is
error due to discharge prediction of current patients. In this case, the model used ELOS to calculate
EDD instead of the staff generated EDD, and the EDD accuracy database was built using data
from two units at the hospital and the database was applied to all units of the hospital. The error
from this source accounted for 83.96% on day 1, 62.31% on day 2, 35.54% on day 3, and 39.73%
68
on day 4. The second main reason is error due to prediction of urgent patients’ bed needs. The
error from this source accounted for 14.31% on day 1, 29.71% on day 2, 49.68% on day 3, and
47.34% on day 4. The third reason is error due to prediction of elective patients’ bed needs. The
error from this source accounted for 1.73% on day 1, 7.98% on day 2, 14.78% on day 3, and
12.94% on day 4.
In the second method, the model was tested using the assumption that in case the staff was able to
improve their EDD predictions, and then the model accuracy would improve. The results obtained
were as expected. The error of the model is within 2 beds on day 1 of the prediction horizon and
increases as we go further from day 1.
It should be noted that in both methods, the EDD is assumed to be available at 7 a.m. to be used
in the prediction. However, in reality, the EDD for patients is updated during bullet rounds that
occur between 9 a.m. and 11:30 a.m. In case this testing was performed in real-time, then the last
updated EDD will be used instead.
To summarize, the two testing methods provided proof that this model is capable of providing
reliable predictions of inpatient bed needs for up to 4-days in advance. The is a lot of room for
improvement in the model, however, a lot of work in the background has to be done to ensure all
the required data is available electronically.
To conclude, this research work was very helpful in having a deep knowledge of the hospital
systems and databases, the various patient populations and their demand for the limited resources,
and the use of such available data to perform predictions that are helpful to hospital management
and staff.
69
Future Research
Future research should involve developing the model so that it could be generic and could be used
in any hospital given that they have the required data. The model should be tested for a period
longer than one week. In addition, the current model could be further refined to ensure it is fully
automated and consolidated into one file, and therefore, enabling the model to operate with
minimal user interaction.
The current model could also be developed to incorporate more sophisticated predictive
approaches that improve the accuracy of the prediction, and increase the prediction horizon from
4-day to 7-day. In addition, enable the model to provide the predictions by a specific program such
as Surgery, Medicine, Cardiology, and Nephrology.
One issue that could be addressed in the future work is the flexibility of the model. Currently, the
model could be run with the assumption that the current census is extracted at 7 a.m., and in case
the current census was extracted at another time, then the urgent patient needs must be recalculated
using the simulation model by Liu, T.M. [36] in order to know the number of beds needed by
urgent patients starting at the specified another time. In the future, the model must be able to
automatically allow the user to run the prediction at various times without extra manual work.
The second issue that could be addressed in the future work is the automation of manual data
preprocessing that has to be done periodically to update the databases in the model. Since the
model is not directly connected to the hospital systems, then data extracts from the hospital systems
have to be manually preprocessed and inserted into the model. It would be better if this crucial
step was automated.
The third issue that could be addressed in the future work is the automation of manual extract of
OR schedules from SIS. Currently, SIS software has to be opened and the OR Schedule for a
particular day is extracted as an Excel file. The process should be automated in the future by having
the Excel files connect directly to the SIS database and automatically update the data every day as
required.
70
The final issue that could be addressed in the future is building the tool to include validation for
the prediction of the past four days. Once the tool is used in real time, it would provide a
validation of how accurate the prediction was. This feedback loop ensures that there is an
ongoing validation of the prediction results and prompts the user to take action, if error value
exceeds a certain threshold.
71
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75
Appendix A
EDD Decision Support Tool
Figure A-1: EDD Decision Support Tool user interface
Admit Date 20/2/2016
EDD 20/2/2016 0
Please select patient type from the drop down list Please select patient type
Age
5
Did the patient have an SCU stay ? (Special Care Unit, i.e, ICU, CCU, NICU) 2
Please select any of the Interventions provided to the patient: FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
FALSE
Please indicate if the patient had more than one intervention event:
An intervention event is defined as a trip made to the OR or surgical room,
regardless of the number of interventions performed, as long as at least one
intervention was significant
1
Did the patient have any of the listed groups of interventions out of hospital
(OOH)?
-Pacemaker implant
-Coronary angiography
-Percutaneous coronary intervention (PCI)2
Is the patient expected to be discharged to home or a home setting with
support services ? ( i.e senior's lodge, attendant care, home care, meals on
wheels, homemaking, supportive housing)
2
EDD Decision Support Tool
Cardioversion
Cell Saver
Chemotherapy
Dialysis
Feeding Tube
Heart Resuscitation
Invasive Ventilation (Long)
Invasive Ventilation (Short)
Paracentesis
Parenteral Nutrition
Pleurocentesis
Radiotherapy
Tracheostomy
Vascular Access Devices
Select Age Group
0 - 364 Days
1 - 17 Years
18 - 59 Years
60 - 79 Years
80+ Years
Home Care
Yes
No
SCU Stay
Yes
No
Interventions
# of Intervention Events
Less than 2
2
3
OOH Intervention
Yes
No
76
Figure A-1 presents an EDD Decision Support Tool to help nurses and clinical staff in assigning
EDDs. This tool was developed in Excel VBA, and the back end of the tool uses Expected Length
of Stay data (ELOS) obtained from CIHI.
The health care system in Ontario is publicly funded, and the Health Based Allocation Model
(HBAM) is the funding methodology of the MOHLTC. As a result, patients who belong to a
particular HBAM Inpatient Grouping (HIG) are expected to stay at the hospital, i.e. ELOS, a
certain amount of time depending on a list of factors. The tool contains a list of questions related
to such factors and uses the input from the user including the admit date, the type of patient, the
age, whether the patient has had a critical care stay, whether the patient has had any of the listed
interventions, and whether the patient is expected to be discharged home to find the ELOS of a
patient. Once the ELOS and the admit date are known, the tool calculates the EDD. This tool was
inspired by the Quality Based Procedure (QBP) and the best practice length of stay.
The base ELOS of a patient is calculated once the patient type is selected. The admit date of a
patient is selected from a calendar that pops up once the cell is selected (See figure A-2). Then,
the EDD is calculated once all of the questions in the tool are answered.
Figure A-2: Selecting admission date from pop-up calendar
77
The answer to some questions could add to the stay of a patient depending if it has an impact on
the particular patient type. Figure A-3 shows the full list of the questions answered, and the
calculated EDD of the patient.
Figure A-3: All questions answered in the tool to calculate an EDD
Admit Date 20/7/2016
EDD 30/7/2016 10.2
Please select patient type from the drop down list CHF(196 - Heart Failure without Coronary Angiogram)5.2811
Age
4
0.5223
Did the patient have an SCU stay ? (Special Care Unit, i.e, ICU, CCU, NICU) 2 0
Please select any of the Interventions provided to the patient: TRUE 2.547
FALSE 0
FALSE 0
FALSE 0
FALSE 0
TRUE 0
FALSE 0
FALSE 0
FALSE 0
FALSE 0
FALSE 0
FALSE 0
FALSE 0
FALSE 0
Please indicate if the patient had more than one intervention event:
An intervention event is defined as a trip made to the OR or surgical room,
regardless of the number of interventions performed, as long as at least one
intervention was significant
1
0
Did the patient have any of the listed groups of interventions out of hospital
(OOH)?
-Pacemaker implant
-Coronary angiography
-Percutaneous coronary intervention (PCI)2
0
Is the patient expected to be discharged to home or a home setting with
support services ? ( i.e senior's lodge, attendant care, home care, meals on
wheels, homemaking, supportive housing)
1 1.802
EDD Decision Support Tool
Cardioversion
Cell Saver
Chemotherapy
Dialysis
Feeding Tube
Heart Resuscitation
Invasive Ventilation (Long)
Invasive Ventilation (Short)
Paracentesis
Parenteral Nutrition
Pleurocentesis
Radiotherapy
Tracheostomy
Vascular Access Devices
Select Age Group
0 - 364 Days
1 - 17 Years
18 - 59 Years
60 - 79 Years
80+ Years
Home Care
Yes
No
SCU Stay
Yes
No
Interventions
# of Intervention Events
Less than 2
2
3
OOH Intervention
Yes
No
78
Appendix B
Modifying input data for the Generic Simulation Model
As mentioned in Section 4.1.3, The Generic Bed Planning Model was initially built to estimate the
patient demand for beds in a hospital during a typical week. This means that the model starts with
no patients in the hospital, then it runs for a user defined number of weeks until it reaches steady
state. The number of bed needs at steady state is the number of beds needed during a typical week.
It uses historical data that contains discharged patients with their admission date and time, LOS,
and various other identifiers such as service received, and discharge location. The model outputs
the results as number of beds needed for each day in the week starting with Sunday as the first day
and ends with Saturday as the seventh day. The output depends mainly on the input data and how
it was prepared. For example, if we want to find the number of beds needed by urgent patients
only, then only patients classified as urgent are used. Also, the input data could be prepared to find
bed needs by type of stay i.e. critical care stay, acute inpatient stay, or any stay defined by the user.
Since the 4-day predictive model starts the prediction with patients already occupying a bed (i.e.
current patients), we are only interested in Urgent patients who enter and leave the hospital during
the 4-day horizon to calculate the number of bed needs.
Therefore, we need to predict inpatient bed needs by urgent patients in the 4-day prediction
horizon, and display the results of the prediction in sequence starting with day 1 in place where
the Sunday results are displayed and day 4 in place where the Wednesday results are displayed,
then the input data has to be modified in order to get the desired results. The complete list of steps
required to prepare the input data is organized as follows:
1. Obtain and preprocess historical DAD data (See figures B-1, B-2, and B-3)
79
Obtain DAD extract that contains all patient records. This DAD extract contains data fields such
as Admission date and time, Discharge date and time, total LOS in days, Acute LOS in days, ALC
LOS in days, Admission Category, and Specialty Care Unit (SCU) Flag. The SCU Flag is a binary
field that shows if a patient had a critical care stay or acute stay. See figure B-1 for a sample DAD
extract.
Figure B-1: Sample DAD extract before processing
The DAD extract in figure B-1 does not show how long a patient stayed in those SCU units.
However, there is another DAD extract that shows a breakdown of their SCU stay for each patient
given that they have a SCU Flag = 1. This extract shows the admission date and time of patients
to the SCU units, and their discharge date and time. In addition, it shows the type of the SCU stay,
i.e. whether a patient had an ICU, CCU, or combination of such stays during their time at the
hospital. See figure B-2 for the DAD extract that shows the breakdown of SCU stays.
80
Figure B-2: Sample DAD extract that contains breakdown of critical care stay
The other DAD data has to be extracted for the same time period to show the breakdown of the
SCU stays for each patient and combined to the original DAD extract. Each row in the combined
DAD data shows one patient record with a breakdown of their stay into ASU, CCU, ICU, Acute
only, and ALC in hours. See figure B-3 for the preprocessed DAD extract.
Figure B-3: Resulting DAD data after combining the two DAD extracts
It should be noted that the patients classified as Urgent under Admit Category are used, while other
types are removed. In addition, patients with patient service description related to Newborns or
Maternal are also removed.
2. Remove patient records admitted outside the 4-day horizon
The simulation model was not designed to make a 4-day prediction. Also, it was not built to allow
the user to select what type of patient records to use. Therefore, to allow the model perform
predictions for patients arriving only during the 4-day horizon, the input data should only contain
patient records admitted on the required 4-day horizon. This means, if the prediction is for Friday,
Saturday, Sunday, and Monday then the input data should contain patients admitted on those days
only. In addition, the input data should contain patients admitted after 7 a.m. on Friday (i.e. day
1).
3. Shift admission day of patients to start in the Sunday to Wednesday sequence
The model calculates the bed needs by assuming that Sunday is the first day of the week, and
therefore runs the prediction starting with Sunday as day 1. To ensure that the model performs the
prediction of 4-day in the proper sequence, then the first day in the sequence has to be shifted to
81
be on Sunday. Similarly, day 2 should be shifted to be on Monday, day 3 should be shifted to be
on Tuesday, and day 4 should be shifted to be on Wednesday.
For example, if we want to predict bed needs starting Friday and ending Monday, then the admit
date of every patient inputted into the model will be shifted back 5 days. The Generic Model will
be tricked in assuming that the Friday admission was on Sunday, Saturday was on Monday, Sunday
was on Tuesday, and Monday was on Wednesday.
If this step was not performed, then the model will assume that Sunday and Monday were before
Friday and Saturday, and therefore will result in a calculation error. Table B-1 below shows how
many days the admission date and time of each patient should be shifted back depending on the
starting day of prediction.
Table B-1: Number of days to shift back depending on the first day of prediction
Starting day of prediction Number of days to shift back
Sunday No Shift needed
Monday 1 day
Tuesday 2 days
Wednesday 3 days
Thursday 4 days
Friday 5 days
Saturday 6 days
Table B-2 below shows the sample table of shifting of admission date of patients for prediction
starting Saturday (Shift Back 6 days).
82
Table B-2: Sample admission day shifting for Saturday (Shift Back 6 days)
Once all of the above steps are performed, then the input data is ready to be run in the Generic
simulation model.
83
Appendix C
Complete Keyword Database
This Appendix includes the complete Keyword database that was built for the predictive model.
The actual name of surgeons was hidden for confidentiality.
Table C-1: Complete Keyword database
Name Description Keyword
Surgeon 1 TUR Prostatectomy transurethral resection of prostate,tur
prostate,transurethral resection of the prostate
Surgeon 2 Total Knee Arthroplasty PFC total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 2 Total Shoulder Arthroplasty total shoulder arthroplasty,total shoulder
replacement,shoulder arthroplasty
Surgeon 2 Total Hip Arthroplasty Biomet
Uncemented
total hip replacement,hip arthroplasty,total hip
arthroplasty,total hip arthroplasty-left,total hip
arthroplasty-right,total left hip
replacement,total right hip replacement,total
left hip arthroplasty,total right hip arthroplasty
Surgeon 3 Total Hip Arthroplasty Summit
Depuy
total hip replacement,hip arthroplasty,total hip
arthroplasty,total hip arthroplasty-left,total hip
arthroplasty-right,total left hip
replacement,total right hip replacement,total
left hip arthroplasty,total right hip arthroplasty
84
Surgeon 3 Total Knee Arthroplasty PFC total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 3 Total Knee Arthroplasty Oxford oxford,oxford knee replacment
Surgeon 3 Total Hip Arthroplasty Corail
Pinnacle
total hip replacement,hip arthroplasty,total hip
arthroplasty,total hip arthroplasty-left,total hip
arthroplasty-right,total left hip
replacement,total right hip replacement,total
left hip arthroplasty,total right hip arthroplasty
Surgeon 4 Endovascular Abdominal Aortic
Aneurysm Repair
endovascular abdominal aortic aneurysm
repair,eaaa,endovascular abdominal aortic
aneurysm,repair of endovascular abdominal
aortic aneurysm
Surgeon 5 Tonsillectomy tonsillectomy
Surgeon 5 Septoplasty septoplasty
Surgeon 6 Total Hip Arthroplasty Biomet
Uncemented
total hip replacement,hip arthroplasty,total hip
arthroplasty,total hip arthroplasty-left,total hip
arthroplasty-right,total left hip
replacement,total right hip replacement,total
left hip arthroplasty,total right hip arthroplasty
Surgeon 6 Total Knee Arthroplasty PFC total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 6 Total Knee Arthroplasty Oxford oxford,oxford knee replacment
85
Surgeon 7 TUR Prostatectomy transurethral resection of prostate,tur
prostate,transurethral resection of the prostate
Surgeon 8 TUR Prostatectomy transurethral resection of prostate,tur
prostate,transurethral resection of the prostate
Surgeon 8 Laparoscopic Nephrectomy Laparoscopic (possible open) partial (possible
radical) right nephrectomy,laparoscopic
nephrectomy,laparoscopic partial
nephrectomy,laparoscopic radical nephrectomy
Surgeon 8 Prostatectomy Radical radical prostatectomy bilateral pelvic lymph
node dissection,radical
cystectomy/prostatectomy,radical
prostatectomy
Surgeon 9 Lumbar Disc Replacement
Arthroplasty
l5-1 pro disc arthroplasty,lumbar disc
replacement arthroplasty,disc
arthroplasty
Surgeon 9 Posterior Spinal
Decompression/Fusion
w/Instruments
posterior decompression instrumented fusion
Surgeon 9 Lumbar Decompression
Laminectomy
right minimally invasive l5-s1 decompression
and discotomy,lumbar decompression
laminectomy,central decompression L3-4 and
L4-5,central decompression
Surgeon 10 Hysterectomy total abdominal hysterectomy,abdominal
hysterectomy
Surgeon 11 Mammoplasty Reduction
Bilateral
bilateral mammoplasty reduction,bilateral
breast reduction,mammoplasty reduction
86
bilateral,mammoplasty breast
reduction,mammoplasty breast reduction
bilateral
Surgeon 12 TUR Prostatectomy transurethral resection of prostate,tur
prostate,transurethral resection of the prostate
Surgeon 12 Nephrolithotomy right percutaneous
nephrolithotomy,percutaneous
nephrolithotomy,nephrolithotomy
Surgeon 13 Decompression 1)removal lumbar instrumentation l2-l5. plus
revision t10-l2 posterior decompression
instrumented fusion + transforaminal lumbar
interbody fusion,l4-5 posterior decompression
instrumented fusion + transforaminal lumbar
interbody fusion,l4-s1 posterior decompression
instrumented fusion + transforaminal lumbar
interbody fusion,posterior decompression
intrumented fusion + transforaminal lumbar
interbody fusion,posterior decompression
instrumented fusion,transforaminal lumbar
interbody fusion
Surgeon 13 Posterior Spinal Decompression bilateral l4-5 + right l5-s1 posterolateral
decompression,left l5-s1 posterolateral
decompression,l5-s1 posterolateral
decompression,posterolateral
decompression,posterior spinal decompression
Surgeon 14 Total Knee Arthroplasty Biomet
Vanguard
total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
87
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 14 Total Hip Arthroplasty Biomet total hip replacement,hip arthroplasty,total hip
arthroplasty,total hip arthroplasty-left,total hip
arthroplasty-right,total left hip
replacement,total right hip replacement,total
left hip arthroplasty,total right hip arthroplasty
Surgeon 15 Vaginal Hysterectomy vaginal hysterectomy
Surgeon 16 Arthrodesis Foot/Ankle right subtalar fusioln,right foot talonavicular
and subtalar fusion and navicular cuneform
joint fusioln,subtalar fusioln
Surgeon 17 TUR Bladder transurethral resection of bladder tumour,tur
bladder,transurethral resection of bladder
tumor,transurethral resection of the bladder
tumour,transurethral resection of the bladder
tumor
Surgeon 17 TUR Prostatectomy transurethral resection of prostate,tur
prostate,transurethral resection of the prostate
Surgeon 17 Nephrectomy Radical radical nephrectomy,nephrectomy radical
Surgeon 17 Prostatectomy Radical, Pelvic
Lymphadenectomy
radical prostatectomy pelvic lymphadenectomy
Surgeon 18 Total Knee Arthroplasty Oxford oxford,oxford knee replacment
Surgeon 18 Total Hip Arthroplasty Biomet
Uncemented
total hip replacement,hip arthroplasty,total hip
arthroplasty,total hip arthroplasty-left,total hip
arthroplasty-right,total left hip
88
replacement,total right hip replacement,total
left hip arthroplasty,total right hip arthroplasty
Surgeon 18 Total Knee Arthroplasty Biomet
Vanguard
total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 18 Unicompartmental Knee
Arthroplasty Oxford
left oxford knee replacement medial side,left
medial oxford knee replacement,left knee
medial oxford,fixed bearing left knee medial
oxford,medial oxford unicompartmental
arthroplasty right knee,right oxford knee
replacement medial side,oxford knee
replacement,oxford
hemiarthroplasty,unicompartmental oxford
Surgeon 19 Thyroidectomy w/Parathyroid
Reimplantation
parathyroid excision and re-
implantation,parathyroid
reimplantation,parathyroid excision and
reimplantation,thyroidectomy with parathyroid
reimplantation
Surgeon 19 Thyroidectomy total thyroidectomy and possible node
dissection,thyroidectomy
Surgeon 20 Total Knee Arthroplasty Biomet
Vanguard
total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 21 TUR Prostatectomy transurethral resection of prostate,tur
prostate,transurethral resection of the prostate
89
Surgeon 22 TUR Prostatectomy transurethral resection of prostate,tur
prostate,transurethral resection of the prostate
Surgeon 22 TUR Bladder Tumour/Tumour transurethral resection of bladder tumour,tur
bladder,transurethral resection of bladder
tumor,transurethral resection of the bladder
tumour,transurethral resection of the bladder
tumor
Surgeon 23 Total Knee Arthroplasty Oxford oxford,oxford knee replacment
Surgeon 23 Total Knee Arthroplasty Biomet
Vanguard
total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 24 Thyroidectomy total thyroidectomy and possible node
dissection,thyroidectomy
Surgeon 24 Laparoscopic Cholecystectomy laparoscopic cholecystectomy,open
cholecystectomy,possible open
cholecystectomy
Surgeon 24 Mastectomy Modified Radical
Sentinal Node Biopsy
left modified radical mastectomy,sentinel node
biopy,right sentinel lymph node
biopsy,mastectomy modified radical,radical
mastectomy modified,sentinel node
biopsy,sentinel lymph node biopsy
Surgeon 25 Endovascular Abdominal Aortic
Aneurysm Repair
endovascular abdominal aortic aneurysm
repair,eaaa,endovascular abdominal aortic
aneurysm
90
Surgeon 25 Abdominal Aortic Aneurysm
Repair
repair of abdominal aortic aneurysm,abdominal
aortic aneurysm repair,aaa
Surgeon 25 Carotid Artery Endarterectomy left carotid endarterectomy,carotid
endarterectomy,carotid artery endarterectomy
Surgeon 25 Aorto Bi-Femoral Bypass Graft aorto bi-femoral bypass graft,aortobifemoral
bypass,aorto bifemoral bypass
Surgeon 26 Total Knee Arthroplasty Biomet
Vanguard
total knee replacement,knee arthroplasty,total
knee arthroplasty,total knee arthroplasty-
right,total knee arthroplasty-left,total right knee
replacement,total left knee replacement
Surgeon 26 Total Hip Arthroplasty Biomet total hip replacement,hip arthroplasty,total hip
arthroplasty,total hip arthroplasty-left,total hip
arthroplasty-right,total left hip
replacement,total right hip replacement,total
left hip arthroplasty,total right hip arthroplasty
Surgeon 26 Total Knee Arthroplasty Oxford oxford,oxford knee replacment
91
Appendix D
Analysis of Urgent patients bed needs prediction
This Appendix provides analysis of the accuracy of prediction of Urgent patients bed needs only.
The prediction of Urgent patients bed needs for the 4-day prediction horizon is compared to the
actual bed needs. The analysis was performed for the period of October 4th, 2015 to November 3rd,
2015. The Generic Bed Planning Model by Liu, T.M. was used to predict the Urgent patients bed
needs, and the historical DAD data was used to compare the prediction to the actual number of
bed needs. Table D-1 summarizes the prediction error for the 4-day horizon. It can be seen that on
average the MAD is 3 beds on day 1, 5 beds on day 2, 5 beds on day 3, and 5 beds on day 4.
Table D-1: Prediction error due to Urgent patients only
Day 1 Day 2 Day 3 Day 4
MAD (# beds) 3 5 5 5
MAPE (%) 17.79% 31.65% 41.54% 102.89%
The results in table D-1 indicate that on average, the prediction error of Urgent patients bed needs
by end of day does not exceed 5 beds. This error range should be taken into consideration when
analyzing the accuracy prediction of the predictive tool that includes the error due to Urgent
patients bed needs, Elective patients bed needs, and the Current patients bed needs.
92