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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