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The primary goal of public health efforts to control HIV epidemics is todiagnose and treat people with HIV infection as soon as possible afterseroconversion. The timing of initiation of antiretroviral therapy (ART)treatment after HIV diagnosis is, therefore, a critical population-levelindicator that can be used to measure the effectiveness of public healthprograms and policies at local and national levels. However, population-baseddata on ART initiation are unavailable because ART initiation and prescriptionare typically measured indirectly by public health departments (e.g., withviral suppression as a proxy). In this paper, we present a random change-pointmodel to infer the time of ART initiation utilizing routinely reportedindividual-level HIV viral load from an HIV surveillance system. To deal withthe left-censoring and the nonlinear trajectory of viral load data, weformulate a flexible segmented nonlinear mixed effects model and propose aStochastic version of EM (StEM) algorithm, coupled with a Gibbs sampler for theinference. We apply the method to a random subset of HIV surveillance data toinfer the timing of ART initiation since diagnosis and to gain additionalinsights into the viral load dynamics. Simulation studies are also performed toevaluate the properties of the proposed method.

Inferring random change point from left-censored longitudinal data by  segmented mechanistic nonlinear models, with application in HIV surveillance  study