Optimize What? Issues in Optimizing Public Health
Resources through Mathematical Modeling.
Michael L Washington, PhDMartin I Meltzer, PhD, MS
Coordinating Center for Infectious DiseaseCenters for Disease Control and Prevention
Challenges
• Three concerns in public health modeling – Objective – Constraints (input or model)– Results
• Discuss briefly and then give examples
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.
Constraints
• The ability to create an accurate model– Data– Experts (epi, physians, PHA)
• Within the model– What are constraints– 2nd “objective” function in the
constraint?
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)
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)
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
Ixodes scapularis
Ixodes scapularis
White footed mouse
White tailed deer
Natural hosts and reservoirs of B. burgdoferi
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?
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
Lyme Disease Model
Constraints (in developing the model)Sensitivity analyses on 6 key inputs
1. Vaccination cost2. 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 infection6. Prob of sequelae due to late dissemination
infection (Delphi)
Vaccinate?YES
NOVaccinate?
Get LD?No
Yes
Early LD?Yes
No
Health outcome
No LDCardiacNeurologicArthriticCase resolved
Cardiac
Neurologic
Arthritic
Case resolved
No LD
Cardiac
Neurologic
Arthritic
Case resolved
Cardiac
Neurologic
Arthritic
Case resolved
Get LD?No
Yes
Early LD?Yes
No
Model
Results: Vaccine effectiveness
Vaccine effectiveness
Probability ofLyme disease: 0.03
Probability ofLyme disease: 0.005
70%80%
90%100%
($60)
($40)
($20)
$0
$20
70% 80% 90% 100%$ p
er c
ase
aver
ted
($'
000)
$50
$100
$200
Assumes 3 doses and 85% effectiveness
Cost savings
Net cost
Results: Cost effectiveness
Probability of Lyme Disease: 0.005
60% 70% 80%
($40)
($20)
$0
$ p
er c
ase
aver
ted
($'
000)
Probability of early diagnosis and treatment of Lyme disease
60% 70% 80%
Probability of Lyme Disease: 0.03
$50
$200
$100
60%
Cost savings
Net cost
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 states0.0009 & 0.0005
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?
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?
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
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
RN R
RN RN
R R R R R R
CASH
RNRN RNRN RNRN RNRN RNRN
R
Educational Display
Ed
Display
Work Station Vaccine PrepStaff Break
Area
Pneumonia VaccinationArea
C C
6%
24%
81%
19%
70%
19%81%
EnterExit
C C
C
Special
Cash
Medicare
C = CopierRN = ShotsR = Registration
Staff Sits Patient Stands or Sits
Key
Medicare Copy Station
Medicare Registration Station
Medicare and Cash Vaccination Station
Cashier
Waiting Area
Special CopyStation
Special RegistrationStation
Special FluVaccination Station
Pnu RegistrationStation
Pnu VaccinationStation
Medicare and Special – Gov’t pays for vaccine
Original Optimized
Arrival Intensity (%) 80 0 40 80 to 160
Max Client Vaccinated 13,138 9,839 13,03914,817-15,096
Special Flu Vaccination 2 2 1 1
Pnu Vaccination 4 4 2 2
Medicare Registration 18 12 15 15
Medicare/ Cash Flu Vaccination 20 20 23 23
Cashier 3 3 4 4
Others* 9
Total Staff 56 50 54 54* Special Flu Copy (1), Special Flu Registration (2), Pnu Registration(2), Medicare Copy (4)
Time in Clinic
0
50
100
150
200
250
300
350
0 20 40 60 80 100 120 140 160
Intensity of Arrival Increase (%)
Min
ute
s
Special
Cash
Special (Opt)
Cash (Opt)
Medicare follows path similar to Special.
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?
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
Issues
Constraints2nd 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)
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
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
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