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Introduction to Modelling: Principles of modelling TB Diagnostics

Alice Zwerling MSI June 22, 2018

uOttawa.ca

Faculté de médecine | Faculty of Medicine

École d’épidémiologie, de santé publique et de médecine preventive

School of Epidemiology, Public Health and Preventive Medicine

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Outline

• What is a model?

• Why do we model? • Key concepts in infectious disease modelling • Strengths and limitations

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What is a model?

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“…Models are symbolic representations of real life, evidently simplified drastically so as to be logically or mathematically tractable.”

Represent a real scenario

Simplification

Easy to manipulate

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Different TB models…

In vitro model

Mouse model

Statistical model Mathematical model

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A model is not a ……

And modellers are not …….

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Why do we model?

• To understand hypothetical impact of interventions (population level)

• To better understand important drivers of disease dynamics

• To identify and generate information about disease parameters that are not well understood

• To give decision makers information upon which to base decisions

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What Happens Without Models? The Dogmatic Approach

• “The new test must be better – it’s more sensitive!” – “How can an older, less sensitive test be better than a

modern, more sensitive one?” • “It’s active case finding, it must be better!”

– “How can a passive strategy possibly be better than an active one?”

• “It’s just too complicated.” – “So therefore I have an excuse to ignore data and choose

the test that I like best.”

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Lin. et al Bull WHO 2012

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Different Modelling Approaches: How to Choose

• The type of question being asked

• Data that are available to parameterize the model

• Familiarity of the analyst with different modeling techniques

• Complexity needed and time requirements for model development

• Ease and speed of simulation

Adapted from: Vynnycky and White, An introduction to Infectious Disease Modeling, OUP, 2010

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Do we want to incorporate transmission? Dynamic vs. Static models

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Dynamic models • ARI will always depend on the number of infectious

individuals in the population at a given point in time

• Can be used to assess the impact on transmission

• Susceptible-Infected-Recovered (SIR) model

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Transmission model

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Static models

• The ARI is not sensitive to the changing number of infectious cases in the population

• Does not account for ongoing transmission in a population

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Decision analysis model

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A note about transmission and decision analysis models • Decision analysis describes what happens to a cohort of

selected individuals – By design does not incorporate pop’n outside of cohort – Can be expanded (Markov models of entire population) but

ultimately is limited in evaluating transmission effects

• Transmission modelling has largely been developed outside the field of health economics – Can incorporate costs and cost-effectiveness, but not always

computationally easy to do so

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The Role of Transmission Modeling

• The targets of TB diagnosis are moving from individual (clinical) to population-level (public health) effectiveness. “sensitivity & specificity” “population incidence & mortality”

• Individual-level effectiveness ≠ population-level effectiveness. • Transmission models allow us to convert measureable data about

individual-level effects to the population level. – Sensitivity & specificity are easy to measure, impact on incidence &

mortality requires a community-randomized trial. – We cannot conduct a CRT for every decision.

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Modelling Tuberculosis: Conceptualize natural history

(SLIR Model)

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Modelling Tuberculosis: Conceptualize natural history 1. ARI 2. Re-infection & Protection? 3. Rapid progression versus reactivation 4. Infectiousness 5. Spontaneous cure 6. Relapse 7. Death

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Parametrize model

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ARI Diagnosis & Treatment LTBI Diagnosis &

Treatment ??

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Transmission Models of TB

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ARI Diagnosis & Treatment

Infectiousness

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Many TB models:

Resch SC, Salomon JA, Murray M, Weinstein MC (2006) Cost-Effectiveness of Treating Multidrug-Resistant Tuberculosis. PLoS Med 3(7): e241

Dye et al. (1998). Lancet Dec 12;352(9144):1886-91.

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Modelling TB: Select model inputs and outputs • Risk of moving from one disease state to another

• Need to have point estimates or ranges for key

parameters/model inputs – Rate of spontaneous cure – Rate of TB mortality – TB detection and treatment rate – Rate of rapid progression to disease

• Data availability!

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Key elements to the population-level effectiveness of diagnostics:

– Time to diagnosis – Proportion successfully treated

• Impact depends not only on where you end up, but where you

start. Important operational contexts include: – Sensitivity of existing diagnostics – Duration of patient delay – % with access to TB care – % initial default after diagnosis

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Do we want to incorporate chance? Deterministic & Stochastic Models

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Deterministic models

• All parameters are fixed, no random element

• Model predictions are fixed, same answer every time

• Describes what happens on average to whole population

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Stochastic models

• Incorporate chance into the model • Results vary with every run • Important in small populations or where chance might

play a role • Require many simulations (more computing power)

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Decision analysis can use either approach, Transmission modelling tends to use stochastic models

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Population vs. Individual models

Population models: • Divides population into

mutually exclusive groups • Homogeneity within groups,

but can be subdivided • Individual level factors are

averaged together, model shows changes in average characteristics of whole population

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Can be used in either Decision analysis or Transmission modelling

Population = 10, 000 60% Female Median age 35 yrs 10% HIV positive

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Population vs. Individual models

Individual based • Follows individuals • Characteristics of each

individual are tracked through time

• Can explore complex relationships, social/spatial interactions, heterogeneity

• May include approaches such as agent-based models, or queue model

27 Can be used in either Decision analysis or Transmission modelling

40 yr ♀

32 yr ♂

65 yr ♂ 67 yr ♂

19 yr ♂

28 yr ♀

38 yr ♀

28 yr ♀

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Strengths of Modelling approaches

• Can be flexible: can consider hypothetical situations or specific populations

• Can consider scenarios/populations for whom a trial is not ethical or feasible

• Can be used to generalize/extrapolate trial findings (time/pop’n) • Can be used for hypothesis generating • Can take advantage of average data (e.g. meta-analyses) • Low cost and faster (relative to empirical studies)

• Transmission models translate individual-level assumptions into

population-level effects.

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Limitations of Modelling approaches

• Models cannot tell the future – The future is molded by unpredictable events. – Comparisons are usually more useful than precise

point estimates. • Models cannot work magic with limited data & assumptions

– Models can use different sets of assumptions to make different projections, but cannot tell which projections are the right ones.

• Models cannot make decisions for people – Decision-making is a political process; models seek only to

bring evidence into that process, and highlight where assumptions are being made.

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Acknowledgements

• McGill University

– Olivia Oxlade

• Johns Hopkins University – David Dowdy

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Reproduced from xkcd.com