  The primary goal of public health efforts to control HIV epidemics is to
diagnose and treat people with HIV infection as soon as possible after
seroconversion. The timing of initiation of antiretroviral therapy (ART)
treatment after HIV diagnosis is, therefore, a critical population-level
indicator that can be used to measure the effectiveness of public health
programs and policies at local and national levels. However, population-based
data on ART initiation are unavailable because ART initiation and prescription
are typically measured indirectly by public health departments (e.g., with
viral suppression as a proxy). In this paper, we present a random change-point
model to infer the time of ART initiation utilizing routinely reported
individual-level HIV viral load from an HIV surveillance system. To deal with
the left-censoring and the nonlinear trajectory of viral load data, we
formulate a flexible segmented nonlinear mixed effects model and propose a
Stochastic version of EM (StEM) algorithm, coupled with a Gibbs sampler for the
inference. We apply the method to a random subset of HIV surveillance data to
infer the timing of ART initiation since diagnosis and to gain additional
insights into the viral load dynamics. Simulation studies are also performed to
evaluate the properties of the proposed method.
