1. Optimize What? Issues in Optimizing Public Health Resources through Mathematical Modeling. Michael L Washington, PhD Martin I Meltzer, PhD, MS Coordinating Center for Infectious Disease Centers for Disease Control and Prevention

2. Challenges Three concerns in public health modeling –Objective –Constraints (input or model) –Results Discuss briefly and then give examples

3. Objective Economic analyses Which analysis is most appropriate for the situation (outcome, perspective) Optimization a single function with a single outcome This can mean a lot of discussion.

4. Constraints The ability to create an accurate model –Data –Experts (epi, physians, PHA) Within the model –What are constraints –2 nd “objective” function in the constraint?

5. Results Mathematically – tend to have an unemotional/non-political solution Public health – maximizing “inclusiveness” or minimizing death (i.e., get to as many people as possible, and try to exclude none)

6. Two Examples Cost-effectiveness of vaccination again Lyme Disease (Meltzer et al. (1999). Emerging Infectious Diseases, 5(3):321-328) Optimization of a mass vaccination clinic (Washington, submitted to Medical Decision Making)

7. Example 1: Lyme Disease Disease –Most common tick-borne disease in the US and Europe –Typical symptoms: fever, headache, fatigue, and a characteristic skin rash –Untreated: joint, heart, and nervous system –Does not kill

8. Ixodes scapularis

10. White footed mouse White tailed deer Natural hosts and reservoirs of B. burgdoferi

11. Example 1: Lyme Disease Solution –Treatment: few weeks of antibiotics –Prevention Insect repellent, removing ticks promptly, landscaping, integrated pest management Have not dramatically reduce disease incidence Development of safe/efficacious vaccine –Do we have unlimited funds? –Is it cost-effective?

12. Lyme Disease Model Objective –Cost effectiveness (CE) of the vaccine (cost per case averted to the society) –Societal cost/benefit (CB) was not used Understand CE ($/Case) vs. CB ($) Usually, the biggest cost is death –Does not kill –Difficulties quantifying human life and suffering –No fancy modeling Humans are an accidental, dead-end hosts

13. Lyme Disease Model Constraints (in developing the model) Sensitivity analyses on 6 key inputs 1.Vaccination cost 2.Prob of contracting the disease (Delphi) 3.Early successful treatment cost 4.Prob of early diagnosis and treatment –3 & 4, 95% successful recovery if diagnosed early –Not popular with vaccine proponents 5.Prob of sequelae due to early infection 6.Prob of sequelae due to late dissemination infection (Delphi)

14. Model

15. Assumes 3 doses and 85% effectiveness Cost savings Net cost

16. Cost savings Net cost

17. Results Cost savings if target individuals with an annual risk of contracting disease was > 0.03 Recommend early detection and successful treatment for low risk (< 0.005/ year) The two highest risk states 0.0009 & 0.0005

18. Issues Difficult for some public health officials (and pharm) to accept (include everyone and the newest technology) A less “sexy” intervention – early diagnosis and treatment Not recommending wide-spread So, no need for more complex math models?

19. Example 2: Clinic Problem –A public health department physically simulated a mass influenza/ pneumococcal vaccination clinic Injectors, facilities, space, universal vaccination (extrapolate to drug distribution) –Anticipated vaccination 15,000 clients in 17 hours, only vaccinated 8,300 arrived –Could they have vaccinated 15,000 with current staff?

20. Clinic Solution –Run the physical model again Expense, timely, lack of client participation –Use an “expert” estimate 20,400 clients –20 vaccinators * 10 min/client * 6 clients/hr*17 hrs –Should be 2,040 Queuing theory (too simple) –Simulation

21. Clinic Objective (clinic’s perspective) Max numbers vaccinated per 17 hrs Constraints –Three client types (Medicare, Special Needs, and Cash) (explain on next slide) –Same human resources –All stations must be staffed –Must visit specific stations

22. Medicare and Special – Gov’t pays for vaccine

24. OriginalOptimized Arrival Intensity (%)8004080 to 160 Max Client Vaccinated13,1389,83913,039 14,817- 15,096 Special Flu Vaccination2211 Pnu Vaccination4422 Medicare Registration181215 Medicare/ Cash Flu Vaccination20 23 Cashier3344 Others* 9 Total Staff565054 * Special Flu Copy (1), Special Flu Registration (2), Pnu Registration(2), Medicare Copy (4)

25. Time in Clinic Medicare follows path similar to Special.

26. Issues Simulation targeted group with: –Little processing times –Few stations to visit –Largest numbers Alternative objective functions could have limited this disparity at the expense of efficiency What are some alternatives?

27. Issues Objective function –Increase revenue – focus on one group of clients –Decrease cost – vaccinate no one –Increase profit – we are the government –Increase societal benefit minus cost, including opportunity cost – depends upon the programming

28. Issues Constraints 2 nd objective function – Limit the optimization to where no one spends more than a specific amount of time in the clinic; however, this also decreases efficiency (max throughput)

29. Issues Result –Elderly suffer: small number and slow Still good to separate the elderly from others –High resource utilization means more staff are needed –Planners did a good job “Experts” estimates were incorrect

30. Other PH Issues Working alone Constrained by superiors –Do not trust or like results, easy to dismiss –Political, unsupportive, embarrassed Data collection is an after-thought “One-size/type of model” fits all? Develop a tool for others to use

31. Tools Maxi-Vac www.bt.cdc.gov/agent/smallpox/vaccination/maxi-vac/ FluAid and FluSurge www.cdc.gov/flu/pandemic/preparednesstools.htm Vaccine selection www.vaccineselection.com