Statistics for Infection Control PractitionersPresented By: Shana OHeron, MPH, CICInfection Prevention and Management Associates

Role of Statistics in Hospital EpidemiologyAid in organizing and summarizing dataPopulation characteristicsFrequency distributionsCalculation of infection rates

Make inferences about dataSuggest associationInfer causality

Communicate findingsPrepare reports for the ICCMonitor the impact of interventions

Study DesignObservational StudiesDraw inferences from patterns of exposureDescriptive or Analytic

Experimental StudiesProspectiveManipulation of variablesRandomization

Observational StudiesDescriptive StudiesIdentify population at riskCharacterize disease by person, place, timeEstimate disease frequency and generate ratesStudy Design: Cross-Sectional

Analytic StudiesDesigned to test etiologic hypothesesSuggest mechanisms of causationStudy Design: Case-Control, Cohort

Descriptive EpidemiologyDescriptive Statistics: techniques concerned with the organization, presentation, and summarization of data.Measures of central tendencyMeasures of dispersionUse of proportions, rates, ratios

Measures of Central TendencyMean- mathematical average of the values in a data set.

Median- the value falling in the middle of the data set.

Mode- most frequently occurring value in a data set.

Average Length of StayMean = The sum of each patients length of stay The number of patients

=12 + 9 + 3 + 5 + 7 + 6 + 13 + 8 + 4 + 15 + 6 = 88 = 8 days 11 11

Median = 3, 4, 5, 6, 6, 7, 8, 9, 12, 13, 15 = 7 daysMode = 6 days

Measures of DispersionRange- the difference between the smallest and largest values in a data set.

Standard Deviation- measure of dispersion that reflects the variability in values around the mean.

Variance- a measure of variability that is equal to the square of the standard deviation.

Dispersion in Procedure LengthRange = 2-7 hours note: mean=4.2

SD = (14.80) = 3.70 = 1.94 V = 3.70 4

Use of Proportions, Rates, and RatiosProportions- A fraction in which the numerator is part of the denominator.

Rates- A fraction in which the denominator involves a measure of time.

Ratios- A fraction in which there is not necessarily a relationship between the numerator and the denominator.

Prevalence ProportionPrevalence- proportion of persons with a particular disease within a given population at a given time.

Proportion of S. aureus Nosocomial Infections Resistant to Oxacillin (MRSA) Among Intensive Care Unit Patients,1989-2003*

*Source: NNIS System, data for 2003 are incomplete

Device-associated Infection RateCalculation of a Device-associated Infection RateStep 1: Decide upon the time period for your analysis. Step 2: Select the patient population for analysis. Step 3: Select the infections to be used in the numerator.Step 4: Determine the number of device-days which is used as the denominator of the rate. Device days: total number of days of exposure to the device by all patients in the selected population during the time period.

Device-associated Infection RateStep 5: Calculate the device-associated infection rate (per 1000 device-days) using the following formula: Number of device-associated infections x 1000Number of device-days

Example: Foley-Associated UTIs in the ICU# of Infections: 2Foley-days in ICU: 920

Rate: 2 x 1000 = 2.17 per 1000 Foley-days 920

NNIS Comparison

Control Charts

Data Entry

Company Name:West Houston Medical CenterPeriods

Days

Infection:Ventilator Associated PneumoniaWeeks

Months

Privacy Notice:Quarters

Years

PeriodVent Days# InfectionsNNIS

Q1 200050655.6

Q2 200051765.6Summary

Q3 200055715.6Total Patient Days8,826

Q4 20005060.05.6Total Infections36

Q1 200146715.6

Q2 200136715.6

Q3 200149915.6Setup Chart

Q4 20013730.05.6Type in Cell Name from Column A for Starting Period. For example: A12a8

Q1 200254025.6

Q2 200247915.6Enter the type of Period Length (ex: Week, Month, Quarter)Quarters

Q3 200254135.6

Q4 200262635.6Enter the Number of Periods:17

Q1 200356535.6

Q2 200347315.6

Q3 200358535.6

Q4 20035660.05.6

Q1 200465955.6

Instructions

Instructions for Using This Spreadsheet

IPMA Disclaimer

General Information

1.Fields in blue are designed for user input.

2.Users should not make any attempt to modify the "mechanics" of this spreadsheet tool

3.The spreadsheet is designed to hold up to 120 periods. If each periods represents a month, 10 years worth of data can be maintained

Specific Instructions

Step 1 - Enter/Revise Heading Information

1.Enter Company Name in the blue box

2.Enter Infection Type that is being analyzed

3.Enter Company Confidential disclaimer. Many companies have specific requirements for labeling the confidentiality of information. This field allows the user to label the data accordingly.

Step 2 - Enter/Revise Infection Data

1.Period Column - This is a free text field that enables you to label each period. Users can list periods as weeks, months, quarter or years for example. Users can label the data however you see fit. This data will appear on the graph exactly as entered.

2.Patient Days Column - Enter the corresponding number of patient days.

3.# of Infections Column - Enter the number of infections observed for the corresponding period.

4.Benchmark Column - Enter any benchmarks you use for the corresponding periods. These cells can be left blank

Step 3 - Setup Chart

1.Enter cell name (ex: A8) that contains the value representing the starting period

2.Select type of period from list (ex: Week, Month, Quarter)

3.Enter the number of periods that you want to show on the chart.

Step 4 - Press Graph Button to Recalculate Graph

NOTE: You must press a graph button to recalculate the graph

1.Press the button of the graph you want recalculated.

Calculations

Ventilator Associated PneumoniaTotal Patient Days8,826

Monthly 2001-2002Total Infections36

c1c2c3c4c5c6c7c8c9c10c11c12c13c14c15c16

Data Input

PeriodPatient Days# InfectionsBenchmarkSigmaDateInfection Rate-3 SigmaUbar3 Sigma-2 Sigma2 Sigma-1 Sigma1 Sigma

Q1 200050655.62.8391872131Q1 20009.881422924904.0788612.596419559209.7572323461.23967070676.9180451329

Q2 200051765.62.8088207014Q2 200011.605415860704.0788612.50532002409.69649932261.27003721846.8876786212

Q3 200055715.62.7060866031Q3 20001.795332136404.0788612.19711772909.49103112591.37277131676.7849445229

Q4 20005060.05.62.8391872131Q4 2000004.0788612.596419559209.7572323461.23967070676.9180451329

Q1 200146715.62.9553631138Q1 20012.141327623104.0788612.944947261209.98958414741.1234948067.0342210336

Q2 200136715.63.333774779Q2 20012.724795640304.0788614.0801822569010.74640747790.74508314077.4126326988

Q3 200149915.62.8590319983Q3 20012.00400801604.0788612.655953914809.79692191651.21982592146.9378899181

Q4 20013730.05.63.3068528731Q4 2001004.0788613.9994165391010.6925636660.77200504677.3857107929

Q1 200254025.62.7483523413Q1 20023.703703703704.0788612.323914943809.57556260251.33050557846.8272102611

Q2 200247915.62.9181091483Q2 20022.087682672204.0788612.833185364809.91507621651.16074877146.9969670681

Q3 200254135.62.7458110996Q3 20025.545286506504.0788612.316291218609.5704801191.33304682026.8246690194

Q4 200262635.62.5525962226Q4 20024.792332268404.0788611.736646587609.1840503651.52626169726.6314541424

Q1 200356535.62.686860167Q1 20035.309734513304.0788612.139438420909.45257825381.39199775286.7657180868

Q2 200347315.62.9365589158Q2 20032.114164904904.0788612.888534667209.95197575141.1422990047.0154168356

Q3 200358535.62.6405315186Q3 20035.128205128204.0788612.000452475409.35992095691.43832640126.7193894383

Q4 20035660.05.62.6844855663Q4 2003004.0788612.132314618809.44782905241.39437235356.7633434861

Q1 200465955.62.4878636891Q1 20047.587253414304.0788611.542448987109.0545852981.59099423076.5667216089

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Control Chart

9.88142292494.078857919809.7572323461.23967070676.91804513295.6

11.60541586074.078857919809.69649932261.27003721846.88767862125.6

1.79533213644.078857919809.49103112591.37277131676.78494452295.6

04.078857919809.7572323461.23967070676.91804513295.6

2.14132762314.078857919809.98958414741.1234948067.03422103365.6

2.72479564034.0788579198010.74640747790.74508314077.41263269885.6

2.0040080164.078857919809.79692191651.21982592146.93788991815.6

04.0788579198010.6925636660.77200504677.38571079295.6

3.70370370374.078857919809.57556260251.33050557846.82721026115.6

2.08768267224.078857919809.91507621651.16074877146.99696706815.6

5.54528650654.078857919809.5704801191.33304682026.82466901945.6

4.79233226844.078857919809.1840503651.52626169726.63145414245.6

5.30973451334.078857919809.45257825381.39199775286.76571808685.6

2.11416490494.078857919809.95197575141.1422990047.01541683565.6

5.12820512824.078857919809.35992095691.43832640126.71938943835.6

04.078857919809.44782905241.39437235356.76334348615.6

7.58725341434.078857919809.0545852981.59099423076.56672160895.6

Infection Rate

Ubar

-2 Sigma

2 Sigma

-1 Sigma

1 Sigma

Benchmark

Quarters

# of Infections/ 1000 Foley Days

Foley Catheter Associated UTIs in the ICU

MBD03D2018B.unknown

MBD0000FECC.unknown

Device Utilization RatioCalculation of Device Utilization (DU) Ratio Step 1: Decide upon the time period for your analysis. Step 2: Select the patient population for analysis. Step 3: Determine the number of device-days.Step 4: Determine the number of patient-days.Patient-days are the total number of days that patients are in the selected population during the time period.

Device Utilization RatioStep 5: Calculate the device-utilization ratio using the following formula: Number of device-days Number of patient-days

Example: Foley Utilization Ratio in the ICUFoley-days in ICU: 920Patient-days in ICU: 1176

Ratio: 920 = 0.78 1176

NNIS Comparison

What does this tell you?When examined together, the device-associated infection rate and device utilization ratio can be used to appropriately target preventative measures.Consistently high rates and ratios may signify a problem and further investigation is suggested.Potential overuse/improper use of deviceConsistently low rates and ratios may suggest underreporting of infection or the infrequent use or short duration of use of devices.

Analytic EpidemiologyInferential statistics: procedures used to make inferences about a population based on information from a sample of measurements from that population.

Hypothesis Testing StudiesNull Hypothesis (Ho): a hypothesis of no association between two variables.The hypothesis to be tested

Alternate Hypothesis (Ha): a hypothesis of association between two variables.

ErrorType I Error (): Probability of rejecting the null hypothesis when the null hypothesis is true.p-value =

Type II Error(): Probability of accepting the null hypothesis when the alternate hypothesis is true.Power = 1 -

Significance Testingp-value (): probability that the findings observed could have occurred due to chance alone.p-value = 0.05

Confidence Interval: a computed interval of values that, with a given probability, contains the true value of the population parameter.95% CI- 95% of the time the true value falls within this interval.

Significance of a p-valueIf p > .05, then the results are considered not statistically significant.

If .01 p < .05, then the results are significant.

If .001 p < .01, then the results are highly significant.

If p < .001, then the results are very highly significant.

Examples of SignificanceStudy A found that the patients average length of stay was associated with C. difficile colitis (p = .002). Highly Significant

Study B found that men were more likely to develop a BSI than women (P = .09) Not Significant

Normal Distribution

Properties of a Normal DistributionContinuous distributionBell shaped curveSymmetric around the mean

Study DesignCase-Control Study: a retrospective study that compares individuals with and without a disease in order to examine differences in exposures or risk factors for the disease.

Cohort Study: a prospective study that compares individuals with and without exposures or risk factors for a disease in order to examine differences in the development of disease.

Components of Study DesignPrecision (reliability)- the ability of a measuring instrument to give consistent results on repeated trials.

Validity (accuracy)- the ability of a measuring instrument to give a true measure.

Study PrecisionSample Size- a portion of the population under study that is representative of that population.Random Sampling: Simple, Stratified, Cluster, SequentialNonrandom Sampling: Convenience, Volunteer, Quota

Study ValiditySensitivity- percentage of people with a disease who test positive for the disease.

Specificity- percentage of people without a disease who test negative for the disease.

Predictive Value Positive- percentage of people who test positive for the disease who actually have the disease.

Predictive Value Negative- percentage of people who test negative for the disease who actually do not have the disease.

2x2 Table

Sensitivity True Positives = a/(a + c) All diseased persons

Sensitivity= 80(80+40)

Sensitivity=0.67

Specificity True negatives = d/(b + d) All non-diseased

Specificity= 860(20+860)

Specificity=0.98

Predictive Value EquationsPredictive Value Positive= true positives = a/(a + b) true + false positives

Predictive Value Negative = true negatives = d/(c + d) true + false negatives

Case-Control StudyMeasure of Association: Odds Ratio OR = (a*d)/(b*c)Significance Test: 95% CI

Case-Control StudyHo: C. difficile colitis is not associated with prolonged antimicrobial use.Ha: C. difficile colitis is associated with prolonged antimicrobial use.

OR= (332)*262) (164)*(230)

OR = 2.3

Case-Control Study95% CI of the Odds Ratio CI = e(OR) +- 1.96(1/A + 1/B + 1/C + 1/D)^0.5

OR=2.3CI = e(2.3) +- 1.96(1/332 + 1/164 + 1/230 + 1/262)^0.5CI = [1.78, 2.98]

SSI Rate ComparisonZ-test CalculationTest statistic (Z) based on normal distribution.

Chi-Square AnalysisTest statistic (X2) based on Chi-Square distribution.

Z-test CalculationRisk-Stratified Rate Comparison

Z-test Calculation

Z-test CalculationZ = 21.8*The critical values -1.6 and 1.6 correspond to a p-value of 0.05.

Chi-Square AnalysisComparing Dr. Xs surgical site infection rate to Dr. Ys surgical site infection rate.

Chi-Square AnalysisExpected Values

X2= 8.615

Chi-Square AnalysisX2 = 8.615df = 1

0.001< p < 0.01

Questions?Questions?

ReferencesRosner, B. (2000). Fundamentals of Biostatistics (5th ed). United States: Brooks/Cole. Friis, RH & Sellers, TA. (2004). Epidemiology for Public Health Practice (3rd ed). Sudbury: Jones and Bartlett Publishers, Inc.www.apic.orgwww.cdc.govhttp://www.slack.ser.man.ac.uk/theory/association_odds.html