Catch-up Scheduling for Childhood Immunization

Transcription

1 Catch-up Scheduling for Childhood Immunization Faramroze Engineer 1 Pinar Keskinocak 2 Larry Pickering 3 1 University of Newcastle 2 Georgia Institute of Technology 3 Centers of Disease Control and Prevention ISYE 4803 Fall 2009 Outline The catch-up scheduling problem Current paradigm The need for an automated tool Problem description A Dynamic Programming (DP) algorithm Usage and dissemination Summary and ongoing work Catch-up Scheduling for Childhood immunization 1

2 Problem Description: The Recommended Schedule Catch-up Scheduling for Childhood immunization Problem Description: The Catch-up Guidelines Catch-up Scheduling for Childhood immunization 2

3 Problem Description: Untimely Vaccination Statistics from Luman et al : Only 9% of children received all recommended vaccines at the recommended ages. 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 Catch-up Scheduling for Childhood immunization Problem Description: Causes of Untimely Vaccination Reasons often cited for incorrect and untimely vaccination: parental negligence and misinformation incomplete or incorrect schedules constructed by health professionals due to: 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. 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, 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). Catch-up Scheduling for Childhood immunization 6/28 3

4 Problem Description: The Remedy Aim Provide a freely available and easy to use automated tool for constructing catch-up schedules aimed at providers and caretakers Immediate benefits: Eliminate human error. Speedup process. Improve public access to vital information. Long-term benefits: Alleviate missed opportunities. Improve timely vaccination rates. Improve awareness and parental participation. Catch-up Scheduling for Childhood immunization 7/28 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. Feasibility requirements: 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, 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. Catch-up Scheduling for Childhood immunization 8/28 4

5 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. 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. Example (Contraindicating PCV) The second dose of PCV is deemed final if the first dose is administered after age 12 months or the current age is months. In either case, the third and fourth doses are unnecessary.. Catch-up Scheduling for Childhood immunization 9/28 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. 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. Catch-up Scheduling for Childhood immunization 10/28 5

6 The Catch-up Scheduling Problem & Machine Scheduling Machine scheduling Catch-up Scheduling Similarities Jobs Vaccine doses Release and due dates Window for each dose Number of processors Number of simultaneous administrations i ti 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. Multilevel objective: makespan, tardiness etc.) 1. Maximize completable vaccination 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 Proposition The catch-up scheduling gproblem remains NP-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 is polynomially solvable without live vaccines and without any limit on the number of simultaneous administrations. Catch-up Scheduling for Childhood immunization 11/28 The Tool Child s vaccination history. INPUT SCHEDULER OUTPUT Vaccine Modeling Language (VML). Algorithms to construct schedule. Charts containing schedule for all remaining doses. Catch-up Scheduling for Childhood immunization 12/28 6

7 The Tool (User Input and Interface) Catch-up Scheduling for Childhood immunization 13/28 The Tool (Vaccine Modeling Language) Example (VML for PCV) ID Name Live? Num. Doses Num. Dose Constraints 5 PCV No 4 6 Dose Min Age Max Age Max Age Prev. Dose Rec. Gap to Rec. Age 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 Current Age Age of Prev Dose Min Gap Next Dose Prev Dose Between Final Dose? Min Max Min Max Dose <24m 0 <12m 4w No _ 12m _ 8w Yes m 59m 0 _ 8w Yes <12m 0 _ 4w No m _ 0 _ 8w Yes _ 0 _ 8w Yes Catch-up Scheduling for Childhood immunization 14/28 7

8 Optimization Models (Integer Programming) - Decision variables: x t = 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. min and max age requirements Penalize deviation from discretionary objectives such - Minimize i i Linear Objective Function: F f(x,y) as: Delay in administering doses - Subject to Linear Constraints: Deviation form recommended Constraint 1: h 1 (x,y) < b 1 gaps Constraint 2: h 2 (x,y) < b 2 Number of Doctor visits Constraint 3: h 3 (x,y) < b 3 : : : : : : : Constraint k: h k (x,y) < b k Min gap constraints Premature series termination constraints Max age of prev dose Prev dose deemed final Prev dose skipped and may not be replaced Catchup Scheduling for Childhood Immunization 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) } Decision variables: x t = 1 if a doctor s visit is scheduled on day t; 0 otherwise. y (v,k,t) = 1 if the k th dose of vaccine v is administered on day t; 0 otherwise. Constraints: C1. Administer each dose at-most once: Catchup Scheduling for Childhood Immunization 8

9 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 input Rows r = 1,...,R(v) Decision variables: x t = 1 if a doctor s visit is scheduled on day t and 0 otherwise. y (v,k,t) = 1 if the k th dose of vaccine v is administered on day t and 0 otherwise. Constraints: C3. Regulating gap between doses: Engineer Catchup Scheduling for Childhood Immunization Optimization Models (Integer Programming) Parameters: τ = time horizon V = set of vaccines n(v) = number of doses of vaccine v V Decision variables: x t = 1 if a doctor s visit is scheduled on day t and 0 otherwise. y (v,k,t) = 1 if the k th dose of vaccine v is administered on day t and 0 otherwise. Constraints: C4. Scheduling doctor visits: Engineer Catchup Scheduling for Childhood Immunization 9

10 Optimization Models (Integer Programming) Parameters: τ = time horizon V = set of vaccines n(v) = number of doses of vaccine v V Decision variables: x t = 1 if a doctor s visit is scheduled on day t and 0 otherwise. y (v,k,t) = 1 if the k th dose of vaccine v is administered on day t and 0 otherwise. Constraints: C5. Limiting number of simultaneous administrations: Engineer Catchup Scheduling for Childhood Immunization Optimization Models (Integer Programming) Parameters: τ = time horizon V = set of vaccines n(v) = number of doses of vaccine v V Decision variables: x t = 1 if a doctor s visit is scheduled on day t and 0 otherwise. y (v,k,t) = 1 if the k th dose of vaccine v is administered on day t and 0 otherwise. Objective Function: Large reward for administering dose Penalize delay in administering dose Penalize deviation from recommended gap Engineer Catchup Scheduling for Childhood Immunization 10

11 A DP Algorithm Day t S 0 Partial (initial) Schedule Schedule vaccine A Schedule vaccine B Schedule vaccine A & B Day t + 1 No vaccine scheduled Day t + 2 Day t + 3 Catch-up Scheduling for Childhood immunization 21/28 A DP Algorithm Day t Day t + 1 S 0 Partial (initial) Schedule S 1 S 2 S 3 S 4 Schedule vaccine A Schedule vaccine B Schedule vaccine A & B No vaccine scheduled Day t + 2 Day t + 3 Catch-up Scheduling for Childhood immunization 22/28 11

12 A DP Algorithm Day t Day t + 1 S 0 Partial (initial) Schedule S 1 S 2 S 3 S 4 Schedule vaccine A Schedule vaccine B Schedule vaccine A & B No vaccine scheduled Day t + 2 Day t + 3 Catch-up Scheduling for Childhood immunization 23/28 A DP Algorithm Day t Day t + 1 S 0 Partial (initial) Schedule S 1 S 2 S 3 S 4 Schedule vaccine A Schedule vaccine B Schedule vaccine A & B No vaccine scheduled Day t + 2 S 5 S 6 S 7 S 8 S 5 S 6 S 7 S 8 Day t + 3 Catch-up Scheduling for Childhood immunization 24/28 12

13 A DP Algorithm Day t Day t + 1 S 0 Partial (initial) Schedule S 1 S 2 S 3 S 4 Schedule vaccine A Schedule vaccine B Schedule vaccine A & B No vaccine scheduled Day t + 2 S 5 S 6 S 7 S 8 S 5 S 6 S 7 S 8 S 9 S 10 S 11 S 12 S 13 S 14 S 15 S 16 Day t + 3 S 29 S 30 S 31 S 32 S17 S 18 S 19 S 20 S 21 S 22 S 23 S 24 S 25 S 26 S 27 S 28 Catch-up Scheduling for Childhood immunization 25/28 A DP Algorithm d i Scheduled dose S X A B C d 1 d 2 d 3 d 1 d 2 d 1 Time Dominance criteria Schedule S X dominates S Y if: 1. The number of doses administered in S X is no less than S Y for each vaccine, 2. The timing of each critical dose S Y A B C d 1 d 2 d 1 d 2 d 1 Time Today administered in S Y is no earlier than in S X, and 3. The total delay in administering doses in common is less in S X. Proposition If S X dominates S Y then any completion of S Y cannot be better than the best completion of S X and thus, S Y is unwarranted. Catch-up Scheduling for Childhood immunization 26/28 13

14 A DP Algorithm S X S Y Min-Gap between doses d i Scheduled dose Delay in administering dose d j Dose to be scheduled A B C A B d 1 d 2 d 3 Dominance criteria Schedule S X dominates S Y if: d 1 d 2 d 3 1. The number of doses administered in d 1 d 2 Time d 1 d 2 d 1 d 2 C d 2 d 1 Time Today d 3 d 3 S X is no less than S Y for each vaccine, 2. The timing of each critical dose administered in S Y is no earlier than in S X, and 3. The total delay in administering doses in common is less in S X. Proposition If S X dominates S Y then any completion of S Y cannot be better than the best completion of S X and thus, S Y is unwarranted. Catch-up Scheduling for Childhood immunization 27/28 A DP Algorithm S X S Y Min-Gap between doses d i Scheduled dose Delay in administering dose d j Dose to be scheduled A d 1 d 2 d 3 B d 1 d 2 C A B d 1 Time d 1 d 2 d 1 d 2 d 1 d 3 d 2 C d 2 Time Today critical dose d 3 d 3 Dominance criteria Schedule S X dominates S Y if: 1. The number of doses administered in S X is no less than S Y for each vaccine, 2. The timing of each critical dose administered in S Y is no earlier than in S X, and 3. The total delay in administering doses in common is less in S X. Proposition If S X dominates S Y then any completion of S Y cannot be better than the best completion of S X and thus, S Y is unwarranted. Catch-up Scheduling for Childhood immunization 28/28 14

15 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. Catch-up Scheduling for Childhood immunization 29/28 The Tool (Output Charts) 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. Catch-up Scheduling for Childhood immunization 30/28 15

16 The Tool (Output Charts) Scenario 2 A 1 year old child who is presumed not received any vaccination to date. Catch-up Scheduling for Childhood immunization The Tool (Output Charts) Scenario 2 cont. A 1 year old child who is presumed not received any vaccination to date. Catch-up Scheduling for Childhood immunization 16

17 Usage and Dissemination 36,000+ downloads since June 2008 Referenced in AAP Red Book Tested by CDC and AAP Used by physicians at CHOA Catch-up Scheduling for Childhood immunization Summary and Ongoing Work Prototype Handover to CDC/AAP for piloting and validation Disseminate through www 36,000+ downloads since June 08 Guide rule makers in stating rules for new vaccines Combination vaccines 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 17