# Inferring the Timing of Antiretroviral Therapy by Zero-Inflated Random Change Point Models Using Longitudinal Data Subject to Left-Censoring

## TL;DR

This paper introduces a statistical model to estimate when people with HIV start antiretroviral therapy using viral load data.

## Contribution

A novel zero-inflated random change point model is proposed for ART timing inference with left-censored data.

## Key findings

- The model effectively estimates ART initiation timing using longitudinal HIV viral load data.
- Simulation studies confirm the method's performance in handling left-censored data.
- The method was successfully applied to real-world HIV data.

## Abstract

We propose a new random change point model that utilizes routinely recorded individual-level HIV viral load data to estimate the timing of antiretroviral therapy (ART) initiation in people living with HIV. The change point distribution is assumed to follow a zero-inflated exponential distribution for the longitudinal data, which is also subject to left-censoring, and the underlying data-generating mechanism is a nonlinear mixed-effects model. We extend the Stochastic EM (StEM) algorithm by combining a Gibbs sampler with a Metropolis–Hastings sampling. We apply the method to real HIV data to infer the timing of ART initiation since diagnosis. Additionally, we conduct simulation studies to assess the performance of our proposed method.