Modelling HIV prevention: strengths and limitations of different modelling approaches

Transcription

1 Modelling HIV prevention: strengths and limitations of different modelling approaches Leigh Johnson Centre for Infectious Disease Epidemiology and Research

2 Background Models of HIV differ greatly in their level of complexity, structure and assumptions. There is no right model for all research questions. Rather, the appropriateness of a model depends on the research question it aims to address. This presentation aims to describe the different types of model and their strengths and limitations.

3 From population averages to cohort-based, to individual-based The simplest models are based on population averages : all HIV-negative individuals are assumed to have the same rate of HIV acquisition. Cohort-based models: the population is divided into cohorts of individuals with similar characteristics, and within each cohort all individuals are assumed to have the same rate of HIV acquisition. Individual-based/microsimulation models: characteristics are determined separately for each individual in the population (a.k.a. agent-based modelling). Cohort-based models and models based on population averages are often described as compartmental.

4 Heterogeneity in HIV acquisition risk Individual-based models are best placed to represent heterogeneity in HIV acquisition risk, though cohort-based approaches may also be acceptable. This is important because the simulated impact of HIV prevention programmes is sensitive to the assumed level of heterogeneity in HIV acquisition risk: higher assumed heterogeneity is associated with smaller intervention impact. e.g. We simulated the historic impact of changes in condom use and ART rollout in South Africa, and assessed the correlation between the combined intervention impact and the modelled heterogeneity in HIV acquisition risk.

5 The association between heterogeneity in susceptibility and intervention impact 3.6 Coefficient of variation in incidence % 35% 40% 45% 50% 55% 60% % reduction in incidence due to intervention More heterogeneity Source: Johnson et al (2012)

6 Metapopulation models Metapopulation models are often used to represent geographical heterogeneity. The population is divided into a number of geographic subpopulations (e.g. different cities or districts). Individuals are assumed to have contact mostly with other individuals in the same sub-population, though some individuals have contacts outside of their own sub-population, which creates opportunity for disease spread. Also known as patch models. Source: Mishra et al (2011)

7 Metapopulation model structure Source: Chen et al (2009)

8 Advantages of metapopulation models Important for understanding why HIV incidence and prevalence differs between regions. Useful for characterizing low-prevalence sub-populations according to whether their infections are mostly imported or are mostly locally acquired. Important for modelling geographically-targeted HIV prevention programmes.

9 Stochastic vs deterministic models Stochastic models allow events (e.g. acquisition of infection, death) to be simulated by random processes. Deterministic models work with expected numbers of events in cohorts of individuals. Individual-based models are usually stochastic, while compartmental models are usually deterministic. Stochastic models generate different results every time they are run, because different random values are generated each time the model is run. Deterministic models generate the same result every time they are run (provided input parameters remain the same).

10 Advantages and disadvantages Advantages of stochastic models Important in understanding the role of random variation in determining the uncertainty around epidemic outcomes. Individual-based models (which are usually stochastic) are generally considered more realistic than deterministic models. Important in modelling probabilities of disease extinction. Disadvantages of stochastic models Slower to run. Models usually need to be run several times to generate a distribution of possible outcomes (long run times). Model results are less predictable than in deterministic models and hence stochastic models are more difficult to check and validate.

11 Frequency-dependent models versus pair models Frequency-dependent models assume that the rate of HIV acquisition is proportional to the frequency of HIV in specified model compartments (also known as mean-field or mixing models). Pair models classify individuals according to both their own HIV status and their partner s HIV status, so that the rate of HIV acquisition depends only on whether their current partner is infected. Network models are pair models that allow for concurrent partnerships.

12 Differences in times to transmission Pair model Frequency-dependent model 1. Person A transmits STI to person B 1. Person B acquires STI from risk pool A B 2. Relationship between A and B ends B A B 3. B forms new relationship with C 2. B is at risk of transmitting infection to any susceptible person in risk pool B C 4. B transmits infection to C B B C Source: Johnson & Geffen (2016)

13 Advantages of pair/network models Important when simulating interventions that target partners of index cases, e.g. PrEP for individuals in sero-discordant relationships, assisted partner notification. Better for understanding the role of behavioural factors such as concurrency. Generally considered more realistic. Johnson & Geffen (2016) compared a network model and a frequencydependent model that were identical in structure and found that the simulated impact of interventions targeted to high-risk groups was much greater in the network model than in the frequency-dependent model.

14 Dynamic vs static models In dynamic models of infectious disease transmission, the incidence of infection depends on the prevalence of infection and therefore can change over time as the prevalence in the population changes. In static models, the incidence of infection is assumed to be independent of prevalence, or is constant. This independence assumption is usually only justified when considering very short-term projections, or when modelling infectious diseases that do not change in prevalence over time. Static models are often used in cost-effectiveness analyses. Source: Mishra et al (2011)

15 The basic reproductive number (R 0 ) This is defined as the average number of secondary cases of infection generated by one primary case in a susceptible population. This is a measure of the infectiousness of a disease: If R 0 >1, the disease will spread and there will be an epidemic. If R 0 <1, the disease will die out. Hence much disease modelling work has focused on how effective/widely implemented prevention strategies need to be in order to reduce R 0 below 1. Source: Anderson & May (1992)

16 Steady-state prevalence Non-linearities in dynamic models Example: Suppose we have a chronic infectious disease with R 0 = 4. We simulate the effect of vaccination at different coverage levels (r) on the long-term ( steady-state ) prevalence of the disease. 80% 70% 60% 50% 40% 30% 20% 10% 0% At r 0.75, we have herd immunity (everyone protected). At r < 0.75, there is a non-linear relationship between r and the prevalence of disease. 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95% 100% Vaccination proportion

17 Disadvantages of static models They cannot represent the non-linearities referred to previously. For this reason, they are only appropriate when evaluating a) Very short-term impacts, b) Impacts of interventions that are expected to be small at a population level (i.e. minimal feedback), or c) Non-communicable diseases Not capable of explaining observed time trends in HIV prevalence or AIDS mortality.

18 Mechanistic vs phenomenological models Mechanistic models relate HIV incidence to specific assumed behaviours and interventions. Phenomenological models simulate HIV incidence based on mathematical functions, where the function parameters are not related to real-world variables. e.g. The Epidemic Projection Package (EPP), used by UNAIDS to estimate trends in HIV incidence, uses cubic splines to represent changes in HIV transmission risk over time. Disadvantages of phenomenological approach: Not appropriate to modelling the impact of HIV prevention. Not able to explain why HIV incidence rates are changing.

19 References Anderson RM, May RM. Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press; 1992 Chen MI, Ghani AC, Edmunds WJ. A metapopulation modelling framework for gonorrhoea and other sexually transmitted infections in heterosexual populations. Journal of the Royal Society Interface 2009, 6: El-Sayed AM, Scarborough P, Seemann L, Galea S. Social network analysis and agent-based modeling in social epidemiology. Epidemiologic Perspectives and Innovations 2012; 9:1. Johnson LF, Geffen N. A comparison of two mathematical modeling frameworks for evaluating sexually transmitted infection epidemiology. Sexually Transmitted Diseases 2016; 43(3): Johnson LF, Hallett TB, Rehle TM, Dorrington RE. The effect of changes in condom usage and antiretroviral treatment coverage on HIV incidence in South Africa: a model-based analysis. Journal of the Royal Society Interface 2012; 9(72): Mishra S, Fisman DN, Boily MC. The ABC of terms used in mathematical models of infectious diseases. Journal of Epidemiology and Community Health 2011, 65:87-94.