A Unified Modeling Approach to Estimating HIV Prevalence in Sub-Saharan African Countries

Estimates of HIV prevalence are important for policy in order to establish the health status of a country's population, to evaluate the effectiveness of population-based interventions and campaigns, to identify the most at risk members of the population, and to target those most in need of treatment. However, data in low and middle income countries are often derived from HIV testing conducted as part of household surveys, where participation rates in testing can be low. Low participation rates may be attributed to HIV positive individuals being less likely to participate because they fear disclosure, in which case, estimates obtained using conventional approaches to deal with non-participation, such as imputation-based methods, will be biased. In addition, establishing which population sub-groups are most in need of intervention requires modeling of both spatial dependence and the predictors of HIV status, which is complicated by data censoring due to this non-participation. We develop a Heckman-type selection model framework which accounts for non-ignorable selection, but allows for heterogeneous selection behavior by incorporating a flexible linear predictor structure for modeling copula dependence. The utilization of penalized regression splines and Gaussian Markov random fields allows us to account for non-linear covariate effects and for geographic clustering of HIV. A ridge penalty avoids convergence failures, even when the parameters of the selection variable are not fully identified. We provide the software for straightforward implementation of this approach, and apply our methodology to estimating national and sub-national HIV prevalence in three sub-Saharan African countries.