catch-up scheduling for childhood immunization...age. •8%of children received at least 1...

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Catch-up Scheduling for Childhood Immunization

Faramroze Engineer 1Pinar Keskinocak 2Larry Pickering 3

1 University of Newcastle2 Georgia Institute of Technology

3 Centers of Disease Control and Prevention

ISYE 4803 – Fall 2009

• The catch-up scheduling problemC t di

Outline

• Current paradigm

• The need for an automated tool

• Problem description

• A Dynamic Programming (DP) algorithm

• Usage and dissemination

Catch-up Scheduling for Childhood immunization

• Summary and ongoing work

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Problem Description: The Recommended Schedule


Problem Description: The Catch-up Guidelines


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Problem Description: Untimely Vaccination

• Only 9% of children received all recommended vaccines at the

recommended ages.

Statistics from Luman et al. 20021:

• 55% of children did not receive all recommended doses by 2 years of

age.

• 8% of children received at least 1 vaccination dose too early to be

considered valid.


More recent statistics from NIS 2 suggest only slight improvements.

1 E.T. Luman, M.M. Mc Cauley, S. Stokley, S.Y. Chu, and L.K. Pickering, Timeliness of Childhood Immunizations, American Journal of Preventive Medicine 110 (2002).

2 http://www.cdc.gov/vaccines/stats-surv

Problem Description: Causes of Untimely Vaccination

• parental negligence and misinformation

• incomplete or incorrect schedules constructed by health professionals due to:

Reasons often cited for incorrect and untimely vaccination:

3 P LaRussa S Chen P Sternfels L Cooper A Caesar M Ewing M Irigoyen and S Findley Impact of immunization

• insufficient knowledge and addition of new vaccines to the lineup, 3, 4

• problem complexity and tedious process of manual construction.

• missed opportunities for vaccination 5

• environmental and socioeconomic standings.

Catch-up Scheduling for Childhood immunization 6/28

3 P. LaRussa, S. Chen, P. Sternfels, L. Cooper, A. Caesar, M. Ewing, M. Irigoyen and S. Findley, Impact of immunization schedule changes on missed opportunities for vaccination, The 37th National Immunization Conference Chicago, IL, 2003.

4 N.J. Cohen, D.S. Lauderdale, P.B. Shete, J.B. Seal, and R.S. Daum, Physician knowledge of catch-up regimens and contraindications for childhood immunizations, Pediatrics 111 (2003).

5 P.G. Szilagyi, L.E. Rodewald, S.G. Humiston, R.F. Raubertas, L.A. Cove, C.B. Doane, P.H. Lind, M.S. Tobin,

K.L. Roghmann, and C.B. Hall, Missed opportunities for childhood vaccination in office practices and the effect on vaccination status, Pediatrics 91 (1993).

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Problem Description: The Remedy

Aim

Provide a freely available and easy to use automated tool forconstructing catch-up schedules aimed at providers and caretakers

• Eliminate human error.

• Speedup process

Immediate benefits:

• Alleviate missed opportunities.

• Improve timely vaccination rates

Long-term benefits:


• Speedup process.

• Improve public access to vital

information.

• Improve timely vaccination rates.

• Improve awareness and parental

participation.

The Catch-up Scheduling Problem

Paradigm

Given past vaccination history for a child, each remaining dose that can be feasibly administered and not contraindicated must be scheduled.

• minimum and maximum age requirement for each dose of each

vaccine.

• Gap between (not necessarily successive) doses of the same vaccine

must not violate the minimum allowed This gap may vary by vaccine

Feasibility requirements:


must not violate the minimum allowed. This gap may vary by vaccine,

dose, current age and/or age at which pervious dose is administered.

• “Live-virus” vaccines may be administered during the same visit or at

least 28 days apart.

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Paradigm


Possible contraindications:

• The previous dose is administered at an age that no longer warrants

further vaccination.

• The current age of the child no longer warrants further vaccination.

Catch-up Scheduling for Childhood immunization. 9/28

Example (Contraindicating PCV)The second dose of PCV is deemed final if the first dose is administered after age 12months or the current age is 24-59 months. In either case, the third and fourth dosesare unnecessary.


Paradigm


Discretionary measures:

• The aggressiveness of catch-up regime, i.e.

Administer when recommended

Vs

Administer as soon as feasibly possible


• The maximum number of simultaneous administrations.

• The number of doctor’s visits.

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The Catch-up Scheduling Problem & Machine Scheduling

Machine scheduling Catch-up SchedulingSimilarities

Jobs Vaccine doses

Release and due dates Window for each dose

Number of processors Number of simultaneous d i i t ti

Proposition

The catch-up scheduling problem remains administrations

Separation time between jobs Spacing between doses

(Chain) Precedence Doses must be given in sequence

Dissimilarities

Processing time Doses can be administered instantly

Typically single objective (i.e. makespan, tardiness etc.)

Multilevel objective:1. Maximize completable

p g pNP-hard:

1. without minimum gap between doses and live vaccines,

2. without any maximum age for a dose and without live vaccines, and

3. without a limit on the number of simultaneous administrations.

The catch-up scheduling problem ispolynomially solvable without live vaccines


p , ) pvaccination series.

2. Maximize number of administered doses.

3. Minimize total delay in administering doses.

Typically constant separation times or setup time depends only on previous job

Spacing may vary by age and age any previous dose is given

polynomially solvable without live vaccinesand without any limit on the number ofsimultaneous administrations.

The Tool

Child’s vaccination history.

OUTPUT

Charts containing schedule for all remaining doses

SCHEDULER

Algorithms to construct schedule

INPUT

Vaccine Modeling Language (VML).


for all remaining doses.construct schedule.

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The Tool (User Input and Interface)


Example (VML for PCV)

The Tool (Vaccine Modeling Language)

ID Name Live? Num. Doses Num. Dose Constraints

5 PCV No 4 6

Next Dose Prev DoseCurrent Age Age of Prev Dose Min Gap

Between Dose

Final Dose?Min Max Min Max

Dose Min Age Max AgeMax Age

Prev. DoseRec. Age Rec. Gap to

Next Dose

Min Max Min Max

1 6w 5y _ 2m 2m 4w 4w

2 10w 5y 2y 4m 4m 8w 8w

3 14w 5y 2y 6m 6m 6m 6m

4 12m 5y 2y 12m 15m _ _


DoseMin Max Min Max

2 1 0 <24m 0 <12m 4w No

2 1 0 _ 12m _ 8w Yes

2 1 24m 59m 0 _ 8w Yes

3 2 0 <12m 0 _ 4w No

3 2 12m _ 0 _ 8w Yes

4 3 0 _ 0 _ 8w Yes

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Optimization Models (Integer Programming)Optimization Models (Integer Programming)

Mi i i Li Obj ti F ti f( )

- Decision variables:xt = 1 if a doctor’s visit is scheduled on day t; 0 otherwise.

y(v,k,t) = 1 if the kth dose of vaccine v is administered on day t; 0 otherwise.

Penalize deviation from discretionary objectives such

min and max age requirements

- Subject to Linear Constraints:Constraint 1: h1(x,y) < b1

Constraint 2: h2(x,y) < b2

Constraint 3: h3(x,y) < b3

:

:

- Minimize Linear Objective Function: f(x,y) as:

• Delay in administering doses

• Deviation form recommended gaps

• Number of Doctor visits

Min gap constraints

Catchup Scheduling for Childhood Immunization

:

:

:

:

:

Constraint k: hk(x,y) < bk

Premature series termination constraints

• Max age of prev dose

• Prev dose deemed final

• Prev dose skipped and may not be replaced

Optimization Models (Integer Programming)Optimization Models (Integer Programming)Parameters:τ = time horizon

V = set of vaccines

n(v) = number of doses of vaccine v ∈ V

τ(v k) = {t τ : minAge(v k) ≤ t ≤ maxAge(v k) }τ(v, k) = {t τ : minAge(v, k) ≤ t ≤ maxAge(v, k) }

Decision variables:xt = 1 if a doctor’s visit is scheduled on day t; 0 otherwise.

y(v,k,t) = 1 if the kth dose of vaccine v is administered on day t; 0 otherwise.

Constraints:

C1. Administer each dose at-most once:

Catchup Scheduling for Childhood Immunization

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Optimization Models (Integer Programming)Optimization Models (Integer Programming)Parameters:τ = time horizon, V = set of vaccines, n(v) = number of doses of vaccine v ∈ V

R(v) = the number of rows from the second part of the VML inputRows r = 1, . . . ,R(v)

Decision variables:Decision variables:xt = 1 if a doctor’s visit is scheduled on day t and 0 otherwise.

y(v,k,t) = 1 if the kth dose of vaccine v is administered on day t and 0 otherwise.

Constraints:

C3. Regulating gap between doses:

Catchup Scheduling for Childhood ImmunizationEngineer


V = set of vaccines




Constraints:

C4. Scheduling doctor visits:


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V = set of vaccines




Constraints:

C5. Limiting number of simultaneous administrations:



V = set of vaccines




Objective Function:Large reward for

administering dosePenalize delay in

administering dose


Penalize deviation from recommended gap

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A DP Algorithm

S0

Day t + 1

Day tSchedule vaccine ASchedule vaccine BSchedule vaccine A & BNo vaccine scheduled

Partial (initial) Schedule

Day t + 2


Day t + 3

A DP Algorithm

S0

Day t + 1


S1 S3 S4S2


Day t + 2


Day t + 3

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A DP Algorithm

S0

Day t + 1


S1 S3 S4S2


Day t + 2


Day t + 3

A DP Algorithm

S0

Day t + 1


S1 S3 S4S2


Day t + 2 S5 S6 S7 S8 S5 S6 S7 S8


Day t + 3

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A DP Algorithm

S0

Day t + 1


S1 S3 S4S2


Day t + 2

S9 S10 S11 S12

S13 S14 S15 S16

S5 S6 S7 S8 S5 S6 S7 S8


Day t + 3 S29 S30 S31 S32 S17 S18 S19 S20

S21 S22 S23 S24

S25 S26 S27 S28

A DP Algorithm

Dominance criteria

Schedule SX dominates SY if:

1 The number of doses administered in

d1 d2 d3

d1 d2

A

B

SX

di Scheduled dose

1. The number of doses administered in

SX is no less than SY for each vaccine,

2. The timing of each critical dose

administered in SY is no earlier than in

SX, and

3. The total delay in administering doses in

d1

Time

C

d1 d2

d1 d2

d1

A

B

C

SY


Proposition

If SX dominates SY then any completion of SY cannot be better than the best completion of SX and thus, SY is unwarranted.

common is less in SX.Today

d1

Time

C

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A DP Algorithm

Dominance criteria



d1 d2 d3

d1 d2

A

B

SX

d3

Min-Gap between dosesDelay in administering dose

di Scheduled doseDose to be scheduleddj





SX, and


d1

Time

C

d1 d2

d1 d2

d1

A

B

C

SY

d2

d3

d3

d2


Proposition


common is less in SX.Today

d1

Time

C d2

A DP Algorithm

d1 d2 d3

d1 d2

A

B

SX

d3

Min-Gap between dosesDelay in administering dose

Dominance criteria



di Scheduled doseDose to be scheduleddj

d1

Time

C

d1 d2

d1 d2

d1

A

B

C

SY

d2

d3

d3

d2





SX, and


critical dose


Today

d1

Time

C d2

Proposition


common is less in SX.

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The Tool (Output Charts)

Scenario 1

A 4 month old child who has received 1 dose of HepB at birth and one each of DTaP, Hib and PCV at 2 months of age.


Scenario 1… cont.

A 4 month old child who has received 1 dose of HepB at birth and one each of DTaP, Hib and PCV at 2 months of age.



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Scenario 2

A 1 year old child who is presumed not received any vaccination to date.



Scenario 2… cont.

A 1 year old child who is presumed not received any vaccination to date.


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Usage and Dissemination

www.cdc.gov/vaccines/recs/scheduler/catchup.htm


• 36,000+ downloads since June 2008

• Referenced in AAP Red Book

• Tested by CDC and AAP

• Used by physicians at CHOA

Summary and Ongoing Work

• Prototype• Handover to CDC/AAP for piloting

and validation • Disseminate through wwwDisseminate through www …

36,000+ downloads since June 08

• Guide rule makers in stating rules for new vaccines

• Combination vaccines• Adolescent and adult vaccination


• Adolescent and adult vaccination• Schedules for immunosuppressed

children (children with diabetes, HIV, undergoing therapy, etc.)

• Extend to other countries

catch-up scheduling for childhood immunization...age. •8%of children received at least 1...

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