A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses

Estimates of HIV prevalence are important for policy to establish the health status of a country’s population and to evaluate the effectiveness of population-based interventions and campaigns. However, participation rates in testing for surveillance conducted as part of household surveys, on which many of these estimates are based, can be low. HIV positive individuals may be less likely to participate because they fear disclosure, in which case estimates obtained using conventional approaches to deal with missing data, such as imputation-based methods, will be biased. We develop a Heckman-type simultaneous equation approach that accounts for nonignorable selection, but unlike previous implementations, allows for spatial dependence and does not impose a homogenous selection process on all respondents. In addition, our framework addresses the issue of separation, where for instance some factors are severely unbalanced and highly predictive of the response, which would ordinarily prevent model convergence. Estimation is carried out within a penalized likelihood framework where smoothing is achieved using a parameterization of the smoothing criterion, which makes estimation more stable and efficient. We provide the software for straightforward implementation of the proposed approach, and apply our methodology to estimating national and sub-national HIV prevalence in Swaziland, Zimbabwe, and Zambia. Supplementary materials for this article are available online.