Bayesian evidence synthesis for a transmission dynamic model for HIV among men who have sex with men

Abstract

Understanding infectious disease dynamics and the effect on prevalence and incidence is crucial for public health policies. Disease incidence and prevalence are typically not observed directly and increasingly are estimated through the synthesis of indirect information from multiple data sources. We demonstrate how an evidence synthesis approach to the estimation of human immunodeficiency virus (HIV) prevalence in England and Wales can be extended to infer the underlying HIV incidence. Diverse time series of data can be used to obtain yearly "snapshots" (with associated uncertainty) of the proportion of the population in 4 compartments: not at risk, susceptible, HIV positive but undiagnosed, and diagnosed HIV positive. A multistate model for the infection and diagnosis processes is then formulated by expressing the changes in these proportions by a system of differential equations. By parameterizing incidence in terms of prevalence and contact rates, HIV transmission is further modeled. Use of additional data or prior information on demographics, risk behavior change and contact parameters allows simultaneous estimation of the transition rates, compartment prevalences, contact rates, and transmission probabilities.

Fig. 1.

Schematic DAG for the prevalence model.

Fig. 2.

Markov multistate model describing the male population of England and Wales in terms of risk group (non-MSM E, MSM) and HIV infection states: Susceptible, Undiagnosed, and Diagnosed.

Fig. 3.

Schematic DAG of the combined prevalence and incidence models. Squares/rectangles denote nodes that are observed data and circles denote stochastic nodes. Double circles denote nodes with prior distributions, whether diffuse or informative. Solid lines denote distributional dependencies, whereas dashed lines denote functional relationships. Panel (a) gives the initial state of the system at time t₁, while Panel (b) represents the system at subsequent timepoints t₂,…,t_K. Data informing the prevalence part of the model are shown at the bottom of the DAG, while data informing the transition rates in the combined model, namely the data of Section 3.1 and Table 2 of the supplementary material available at Biostatistics online, are shown in the top right-hand corner of Panel (b).

Fig. 4.

Posterior distributions from the combined model of incidence (a) and diagnosis (b) rates, and posterior distributions of proportion who are MSM (c), by model: prevalence (grey) and combined (black). Note that these distributions are plotted at the year-end break points only, but the rates are in fact piecewise constant.

Fig. 5.

Posterior distributions from the 2 combined models: base (grey), and transmission (black).