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

type="main" xml:id="rssc12080-abs-0001"> The goal of the paper is to predict the additional amount of antiretroviral treatment that would be required to implement a policy of treating all human immunodeficiency virus (HIV) infected people at the 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 cell 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 cell counts. The inferential target of interest is the population level mean time to reaching the CD4 cell-based treatment threshold in this group of subjects. To address the challenges arising from the fact that these subjects’ 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 cell counts were measured over time. We use a multiple-imputation framework to combine across the different sources of data, and we discuss how the methods compensate for the length-biased sampling that is inherent in cross-sectional screening procedures, such as household surveys. We comment on how the results bear on analyses of costs of implementation of treatment-for-prevention use of antiretroviral drugs in HIV prevention interventions.