Spline-based modelling of trends in the force of HIV infection, with application to the UNAIDS Estimation and Projection Package

Abstract

Objective: We previously developed a flexible specification of the UNAIDS Estimation and Projection Package (EPP) that relied on splines to generate time-varying values for the force of infection parameter. Here, we test the feasibility of this approach for concentrated HIV/AIDS epidemics with very sparse data and compare two methods for making short-term future projections with the spline-based model.

Methods: Penalised B-splines are used to model the average infection risk over time within the EPP 2011 modelling framework, which includes antiretroviral treatment effects and CD4 cell count progression, and is fit to sentinel surveillance prevalence data with a Bayesian algorithm. We compare two approaches for future projections: (1) an informative prior related to equilibrium prevalence and (2) a random walk formulation.

Results: The spline-based model produced plausible fits across a range of epidemics, which included 87 subpopulations from 14 countries with concentrated epidemics and 75 subpopulations from 33 countries with generalised epidemics. The equilibrium prior and random walk approaches to future projections yielded similar prevalence estimates, and both performed well in tests of out-of-sample predictive validity for prevalence. In contrast, in some cases the two approaches varied substantially in estimates of incidence, with the random walk formulation avoiding extreme changes in incidence.

Conclusions: A spline-based approach to allowing the force of infection parameter to vary over time within EPP 2011 is robust across a diverse array of epidemics, including concentrated ones with limited surveillance data. Future work on the EPP model should consider the impact that different modelling approaches have on estimates of HIV incidence.

Figure 1

Prevalence and incidence projections for specific risk groups in Argentina, as generated from spline-based force of infection models. ‘Equilibrium prior’ projections use an informative prior for r to make out-of-sample projections, whereas ‘Random walk’ projections impose minimal structure on future values for r. The data used in this analysis are meant to allow for illustrative model projections, and therefore our results should not be interpreted as being directly comparable to official estimates regularly published by countries and UNAIDS.

Figure 2

Average coverage of site-level 95% prediction intervals for final year of out-of-sample projections in 69 generalised epidemics, comparing two approaches to making future projections from a spline-based force of infection model: (1) an informative prior related to equilibrium prevalence and (2) a random walk formulation. When the two methods have different coverage for a given subepidemic, they are connected with a vertical line.

Figure 3

Prevalence, incidence and force of infection parameter (r) projections for two generalised epidemics in sub-Saharan Africa, as generated from spline-based force of infection models. ‘Equilibrium prior’ projections use an informative prior for r to make out-of-sample projections, whereas ‘Random walk’ projections impose minimal structure on future values for r. The data used in this analysis are meant to allow for illustrative model projections, and therefore our results should not be interpreted as being directly comparable to official estimates regularly published by countries and UNAIDS.

Figure 4

Ratios of projected incidence and prevalence for final year of out-of-sample projections in 69 generalised epidemics, comparing the random walk (numerator of ratio) to equilibrium prior (denominator of ratio) approaches to making future projections with a spline-based force of infection model.