Predicting time to threshold for initiating antiretroviral treatment to evaluate cost of treatment as prevention of human immunodeficiency virus.

The goal of this paper is to predict the additional amount of antiretroviral treatment that would be required to implement a policy of treating all HIV-infected people at time of detection of infection rather than at the time that their CD4 T-lymphocyte counts are observed to be below a threshold-the current standard of care. We describe a sampling-based inverse prediction method for predicting time from HIV infection to attainment of the CD4 threshold and apply it to a set of treatment-naive HIV-infected subjects in a village in Botswana who participated in a household survey that collected cross-sectional CD4 counts. The inferential target of interest is the population-level mean time to reaching CD4-based treatment threshold in this group of subjects. To address the challenges arising from the fact that these subject's dates of HIV infection are unknown, we make use of data from an auxiliary cohort study of subjects enrolled shortly after HIV infection in which CD4 counts were measured over time. We use a multiple imputation framework to combine across the different sources of data, and discuss how the methods compensate for the length-biased sampling inherent in cross-sectional screening procedures, such as household surveys. We comment on how the results bear upon analyses of costs of implementation of treatment-for-prevention use of antiretroviral drugs in HIV prevention interventions.