Flexible epidemiological model for estimates and short-term projections in generalised HIV/AIDS epidemics

Abstract

Objective: UNAIDS and country analysts use a simple infectious disease model, embedded in the Estimation and Projection Package (EPP), to generate annual updates on the global HIV/AIDS epidemic. Our objective was to develop modifications to the current model that improve fit to recently observed prevalence trends across countries.

Methods: Our proposed alternative to the current EPP approach simplifies the model structure and explicitly models changes in average infection risk over time, operationalised using penalised B-splines in a Bayesian framework. We also present an alternative approach to initiating the epidemic that improves standardisation and efficiency, and add an informative prior distribution for changes in infection risk beyond the last data point that enhances the plausibility of short-term extrapolations.

Results: The spline-based model produces better fits than the current model to observed prevalence trends in settings that have recently experienced levelling or rising prevalence following a steep decline, such as Uganda and urban Rwanda. The model also predicts a deceleration of the decline in prevalence for countries with recent experience of steady declines, such as Kenya and Zimbabwe. Estimates and projections from our alternative model are comparable to those from the current model where the latter performs well.

Conclusions: A more flexible epidemiological model that accommodates changing infection risk over time can provide better estimates and short-term projections of HIV/AIDS incidence, prevalence and mortality than the current EPP model. The alternative model specification can be incorporated easily into existing analytical tools that are used to produce updates on the global HIV/AIDS epidemic.

Figure 1

Example of a spline-based curve for infection risks over time (solid line) using third degree B-splines comprised of seven evenly-spaced basis functions (dashed curves labelled 1 through 7). The spline curve is a linear combination of the basis functions and their coefficients (labelled β₁ through β₇).

Figure 2

Median prevalence with 95% credible intervals (in black) for the spline-based model for r, with the best fit from the EPP 2009 Reference Group model added for comparison (in blue) for nine selected settings. Observed prevalence data for antenatal clinic sites to which the models are fit are plotted in various colours.

Figure 3

Posterior predicted prevalence versus observed prevalence across all antenatal clinic sites for urban and rural Uganda, along with posterior predicted site-level prevalence for four selected antenatal clinics (red indicates observed site prevalence, black indicates median and 95% prediction intervals for predicted site prevalence).

Figure 4

Median prevalence with 95% credible intervals for the spline-based model with (in black) and without (in blue) a prior for the future behaviour of r for six selected settings. Observed prevalence data for antenatal clinic sites to which the models are fit are plotted in various colours.

Figure 5

Median prevalence with 95% credible intervals for out-of-sample prevalence predictions for the spline-based model (in blue), with median fit for the full-sample results added for comparison (in black), for four selected settings. Data for the last 3 years of observation were excluded for generating out-of-sample predictions (denoted by the vertical dashed line).

Figure 6

Plots of r, incidence and mortality for urban Uganda and urban Rwanda from the spline-based model. Unique curves from the posterior are plotted in grey, along with the median and 95% credible intervals.