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A Role for Mathematical Models in Program Science
- 1. A Role forMathematical Models in Program Science Sharmistha Mishra April 30, 2015
- 2. The “Science” ofProgram 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)
- 3. Program Science • “collaborationand 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
- 4. The “Science” ofProgram 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
- 5. Key Program Questions Epidemicappraisal 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 & Evaluation Future Data Collection Consolidation Phase Blanchard and Aral. STI. 2011; Becker et al. submitted. 2015
- 6. Evidence Empirical “Classical “ researchstudies Clinical Diagnostic Prognostic Therapeutic Biology PK/PD Immunology Behaviour Epidemiology Surveillance Program Indicator Cost Socio- political Knowledge Syntheses Individual-level & System-level
- 7. Evidence Empirical “Classical “ researchstudies Clinical Diagnostic Prognostic Therapeutic Biology PK/PD Immunology Behaviour Epidemiology Surveillance Program Indicator Cost Socio- political Knowledge Syntheses Population-level =“More is different” Becker et al. submitted. 2015
- 8. Evidence Empirical “Classical “ researchstudies Clinical Diagnostic Prognostic Therapeutic Biology PK/PD Immunology Behaviour Epidemiology Surveillance Program Indicator Cost Socio- political Knowledge Syntheses Mathematical Models (Transmission Dynamics)
- 9. Individual & system-level characteristics population-level Model = simplified version of reality Pickles et al. Lancet Glob Health. 2013
- 10. Simplified reality Simplified version of reality Statisticalmodels Decision-tree models Cohort models Simulated “static” populations Mechanistic and dynamic models
- 11. 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
- 12.
- 13. Key Program Questions Epidemicappraisal Key population = relative size, distribution, contribution to transmission dynamics? Strategic Planning Phase
- 14. Epidemic appraisal • Theoverall 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?
- 15. How big cana 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
- 16. Key Program Questions Epidemicappraisal Key population = relative size, distribution, contribution to transmission dynamics? Population impact already achieved? Strategic Planning Phase Blanchard and Aral. STI. 2011
- 17. FSW HIV prevalence (Belgaum,south India) Existing condom-based targeted intervention Existing ART program Mishra et al. AIDS. 2013.
- 18. What if... No condom-basedtargeted intervention No ART program
- 19. What if... No condom-basedtargeted intervention No ART program No condom-based targeted intervention Poor ART program (3-5% ART coverage)
- 20. What if... Existing ARTprogram alone (13-15% coverage by 2010) No condom-based targeted intervention No ART program
- 21. Existing condom-based targetedintervention has had a larger impact than existing ART program to date No condom-based targeted intervention No ART program Existing ART program alone Existing condom-based targeted Intervention alone
- 22. % HIV infectionsaverted 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.
- 23. Key Program Questions Mixof interventions components Population impact of maintaining existing program? Implementation Phase Blanchard and Aral. STI. 2011
- 24. Life-years saved overnext 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
- 25. Preventive potential ofART largest early in India’s HIV epidemics 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 1990 1995 2000 2005 2010 % Year % due to increased life-expectancy % due to HIV prevention % of life-years saved over 10 years
- 26. Key Program Questions Mixof interventions components Population impact of maintaining existing program? Prioritization? Efficiency? Implementation Phase Blanchard and Aral. STI. 2011
- 27. 0 0.5 11.5 2 2.5 0 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 access all HIV+ DALYsaverted(thousands,3%discount Additional Cost, millions $US, 3% discount Cumulative impact over 10 years vs. maintain existing access & eligibility ICER<3*GDP Strategy on efficieny frontier Dominated 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.
- 28. Key Program Questions Optimalmanagement Optimal coverage? Duration or phases of programs? Consolidation Phase Blanchard and Aral. STI. 2011
- 29. 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 0 20 40 60 80 1 year 5 years 10 years 20 years #ofHIVinfections averted PreP for 20 years Low-risk group Clients FSWs 0 20 40 60 80 1 year 5 years 10 years 20 years #ofHIVinfections averted 5 years of PreP
- 30. Key Program Questions Optimalmanagement Optimal coverage? Duration or phases of programs? Monitoring & Evaluation Future Data Collection Consolidation Phase Blanchard and Aral. STI. 2011
- 31. 0 0.5 11.5 2 2.5 0 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 access all HIV+ DALYsaverted(thousands,3%discount Additional Cost, millions $US, 3% discount Cumulative impact over 10 years vs. maintain existing access & eligibility ICER<3*GDP Strategy on efficieny frontier Dominated 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.
- 32. 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 <$20,000 USD 0 20 40 60 80 100 120 Partialexpectedvalueofperfectinformation(thousands US$) Intervention , utilities, or cost parameter Decision: ≤500 vs. all HIV+ (prioritized to FSWs) ART efficacy (adherence) Reduction in HIV-attributable mortality ART discontinuation and re-initiation rates Relative value of additional information Mishra et al. In preparation. 2015.
- 33. A role forProgram Science in Mathematical Modelling?
- 34. PS generates data 1)Model validation 2) Model re-calibration 3) Model modification ...models = “moving target”...
- 35. 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
- 36. Harness data atdifferent 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
- 37. Strengthen how weconduct and report uncertainty 7) Models designed to meet the needs of decision-makers (program implementers) “absence of data” ignore the mechanism models to “impute” data test 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)
- 38. Summary • Mathematical Modelscould 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
Editor's Notes
- #2 Thank you. In the next 15 minutes, I’m going to try and show how mathematical models could play an important and diverse role in the “Science” component of Program Science.
- #3 Showing examples of how models could be useful tools in Program Science And conversely, how Program Science could advance the field of Mathematical Modelling And I’ll draw on examples from HIV modeling work for Program Science in india and SSA
- #28 Probabilistic sensitivity analyses: % = fraction of simulations where the first strategy was more cost-effective than the subsequent strategy (at 1 GDP = willingness to pay threshold)
- #32 Probabilistic sensitivity analyses: % = fraction of simulations where the first strategy was more cost-effective than the subsequent strategy (at 1 GDP = willingness to pay threshold)