A Role for Mathematical Models in Program Science

A Role for Mathematical Models in Program Science

Sharmistha Mishra

April 30, 2015

The “Science” of Program Science

1) How Mathematical Models could be useful tools in Program Science

2) How Program Science could advance the field of Mathematical Modelling

Examples / Focus: HIV (India, Sub-Saharan Africa)

Program Science

• “collaboration and integration between programs and science to improve the ways programs are designed, implemented and evaluated to accelerate and increase health impact”

Blanchard and Aral. STI. 2011

population

The “Science” of Program Science

Key program/community questions or observations

Clear Research Questions and Hypotheses

Program planning , implementation, management

Best (Feasible) Tools

Becker et al. In preparation. 2013

Key Program Questions

Epidemic appraisal

Key population = relative size, distribution, contribution to transmission dynamics?

Population impact already achieved?

Strategic Planning Phase

Mix of interventions components

Population impact of maintaining existing program?

Prioritization? Efficiency?

Implementation Phase

Optimal management

Duration or phases of programs?

Monitoring & EvaluationFuture Data Collection

Consolidation Phase

Blanchard and Aral. STI. 2011; Becker et al. submitted. 2015

Evidence

Empirical

“Classical “ research studies

Clinical

Diagnostic Prognostic

Therapeutic

Biology

PK/PDImmunology

Behaviour Epidemiology

Surveillance Program

Indicator Cost

Socio-political

Knowledge Syntheses

Individual-level & System-level

Evidence

Empirical


Clinical


Therapeutic

Biology

PK/PDImmunology



Indicator Cost

Socio-political

Knowledge Syntheses

Population-level =“More is different”Becker et al. submitted. 2015

Evidence

Empirical


Clinical


Therapeutic

Biology

PK/PDImmunology



Indicator Cost

Socio-political

Knowledge Syntheses

Mathematical Models (Transmission Dynamics)

Individual & system-level characteristics population-level

Model =simplified version of

reality

Pickles et al. Lancet Glob Health. 2013

Simplified reality

Simplified version of

reality

Statistical models

Decision-tree models

Cohort models

Simulated “static” populations

Mechanistic and dynamic models

Transmission dynamics models• Mechanistic

• Natural history of infection• Differences and changes in the epidemiological (behavioural or biological)

characteristics of individuals• Differences and changes at a system-level (health, structural, environmental)

or features that are “shared” by individuals • The mechanism of transmission

• Dynamic = feedback loop• Incidence Prevalence Incidence Prevalence• Every “case is a risk factor”

• Onward or indirect transmission (upstream or downstream infections); herd effects

Examples


Epidemic appraisal



Epidemic appraisal

• The overall HIV prevalence in my district is 3.3% but 1% of women are sex workers and their HIV prevalence is 38%

• Am I dealing with a generalized HIV epidemic (overall HIV prevalence >1%)?– don’t need to prioritize prevention for sex

workers?

How big can a concentrated HIV epidemic get?

• Concentrated epidemic– key population (sex workers)

• Simulated 10,000 HIV concentrated epidemics using data from West/Central Africa to reproduce range of “plausible” overall HIV prevalence trends* b/w 1995-2012

• 170,000 snap-shots of different concentrated epidemics

* Range in HIV prevalence over time from UNAIDS Boily et al. 2015


Epidemic appraisal


Population impact already achieved?



FSW HIV prevalence (Belgaum, south India)

Existing condom-based targeted interventionExisting ART program

Mishra et al. AIDS. 2013.

What if...

No condom-based targeted interventionNo ART program

What if...


No condom-based targeted interventionPoor ART program (3-5% ART coverage)

What if...

Existing ART program alone(13-15% coverage by 2010)


Existing condom-based targeted intervention has had a larger impact than existing ART program to date


Existing ART program alone

Existing condom-based targeted Intervention alone

% HIV infections averted up to Jan 2014

% HIV infections averted (total pop.)

Belgaum Mysore Shimoga

Existing ART alone 5-11%(2006-2014)

6-18%(2007-2014)

5-9%(2008-2014)

Existing condom-based TI alone

27-47%(2004-2014)

29-55%(2004-2014)

31-48%(2004-2014)

Existing ART + condom-based TI

30-50% 32-58% 33-55%

Incremental impact of the existing ART program to date: 2-3% infections averted

Mishra et al. AIDS. 2013.






Life-years saved over next 10 years due to infections prevented vs. mortality

District (by epidemic size)

Belgaum Mysore Shimoga

Life-years saved per person-year on ART

14-26 8-21 3-5

% of life-years saved due to infections averted

13.6%(5.3-34.9%)

11.9% (4.4-23.4%)

9.7%(2.3-19.1%)

Epidemic size

80-85% of life-years saved due to mortality benefit of ART @ individual-level

Preventive potential of ART largest early in India’s HIV epidemics

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

% due to HIV prevention% due to increased life-expectancy

Year

%

% of life-years saved over 10 years




Prioritization? Efficiency?



0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

500, FSWs

all HIV+, FSWs

access FSWs

access FSWs, all HIV+ FSWs

accessall HIV+

DA

LYs

aver

ted

(tho

usan

ds,

3% d

isco

unt

Additional Cost, millions $US, 3% discount

Cumulative impact over 10 yearsvs. maintain existing access & eligibility

ICER<3*GDP

Strategy on efficieny frontierDominated strategy

ICER>3*GDP

Most efficient next step?

Efficient next steps (expansion path)

$US per DALY averted(% discount)

≤500, FSWs 223 (190-345)

All HIV+ FSWs 271 (217-398)

↑access FSWs 539 (498-691)

↑access FSWs, all HIV+ FSWs

660 (510-818)

↑access, all HIV+ 6,249 (5,851-7,192)

Best fit from dynamical model & average across efficacy, costs, and utilities

Added health impact

Added cost

Eaton et al. 2014.


Optimal management

Optimal coverage? Duration or phases of programs?

Consolidation Phase


HIV pre-exposure prophylaxis (PreP) for FSWs in Mysore, India

• Impact plateaus after 5-10 years

• Impact of 5 years of PrEP achieves:– 80% impact of 10

years of PrEP– 66% impact of 20

years of PrEP

1 year 5 years 10 years 20 years0

20

40

60

80 PreP for 20 years

Low-risk group

Clients

FSWs

# o

f H

IV in

fec

tio

ns

a

ve

rte

d

1 year 5 years 10 years 20 years0

20

40

60

80

5 years of PreP

# o

f H

IV in

fec

tio

ns

a

ve

rte

d


Optimal management

Optimal coverage? Duration or phases of programs?

Monitoring & EvaluationFuture Data Collection

Consolidation Phase


0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

500, FSWs

all HIV+, FSWs

access FSWs

access FSWs, all HIV+ FSWs

accessall HIV+

DA

LYs

aver

ted

(tho

usan

ds,

3% d

isco

unt

Additional Cost, millions $US, 3% discount

Cumulative impact over 10 yearsvs. maintain existing access & eligibility

ICER<3*GDP

Strategy on efficieny frontierDominated strategy

ICER>3*GDP

Most efficient next step?

Efficient next steps (expansion path)

$US per DALY averted(% discount)

≤500, FSWs 223 (190-345)

All HIV+ FSWs 271 (217-398)

↑access FSWs 539 (498-691)

↑access FSWs, all HIV+ FSWs

660 (510-818)

↑access, all HIV+ 6,249 (5,851-7,192)

Best fit from dynamical model & average across efficacy, costs, and utilities

Added health impact

Added cost

62% @1 GDP

41% @1 GDP

Eaton et al. 2014.

Value of information

• What data should we collect to help us choose the most cost-effective strategy (willingness to pay = 1 GDP)? re-analyze

For parameters <$20,000 USD

ART effic

acy

Reduc

tion

in m

orta

lity

Discon

tinua

tion

rate

ART re-in

itiatio

n ra

te

Cost:

Reach

ing F

SWs

Cost:

pre-

ART car

e

Cost:

re-in

itiatio

n ART

0

20

40

60

80

100

120

Decision: ≤500 vs. all HIV+ (prioritized to FSWs)

Intervention , utilities, or cost parameter

Pa

rtia

l e

xp

ec

ted

va

lue

of

pe

rfe

ct

info

rma

tio

n (

t-h

ou

sa

nd

s U

S$

)

ART efficacy (adherence)

Reduction in HIV-attributablemortality

ART discontinuation and re-initiation rates

Relative value of additional information

Mishra et al. In preparation. 2015.

A role for Program Science in Mathematical Modelling?

PS generates data

1) Model validation2) Model re-calibration3) Model modification

...models = “moving target”...

Ask first, Choose later

4) PS first asks the question, then chooses the tools will require that we design and build new (novel) mathematical models

Harness data at different scales

5) PS generate and draw from data gathered at very different scales (cellular, host, population) will require that we build the next generation of mathematical models that make best use of different data-including qualitative data

6) Knowledge syntheses could (should) play a larger role in mathematical modelling projects

Strengthen how we conduct and report uncertainty

7) Models designed to meet the needs of decision-makers (program implementers) “absence of data” ignore the mechanism models to “impute” datatest the importance of the “missing” data or “structural” assumptions

8) To inform decisions, we should provide uncertainty bounds pushing transmission dynamics modelling to utilize applications from other fields (Bayesian statistics, Health Economics)

Summary

• Mathematical Models could be useful tools in Program Science– examine the influence of individual biology,

behaviour, and the environment dynamics of disease spread in the population

• Program Science could advance the field of Mathematical Modelling

Education

A Role for Mathematical Models in Program Science