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