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Inferring the Timing of Antiretroviral Therapy by Zero-Inflated Random Change Point Models Using Longitudinal Data

Hongbin Zhang1,2, McKaylee Robertson2, Sarah L Braunstein3

  • 1Department of Biostatistics, College of Public Health, University of Kentucky, Lexington, KY 40506, USA.

Algorithms
|March 30, 2026
PubMed
Summary

We developed a new statistical model using HIV viral load data to pinpoint when individuals started antiretroviral therapy (ART). This method helps understand ART initiation timing for people living with HIV.

Keywords:
Gibbs samplerMetropolis–Hastings samplingStochastic EMantiretroviral therapycensored datanonlinear mixed-effects modelrandom change point modelzero-inflated exponential distribution

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Area of Science:

  • Biostatistics
  • Epidemiology
  • Infectious Disease Modeling

Background:

  • Accurate estimation of antiretroviral therapy (ART) initiation timing is crucial for managing HIV infection.
  • Routinely collected individual-level HIV viral load data offer a valuable resource for retrospective analysis.
  • Existing models may not fully capture the complexities of longitudinal viral load data and ART initiation.

Purpose of the Study:

  • To propose a novel random change point model for estimating ART initiation timing.
  • To incorporate zero-inflated exponential distribution and left-censoring into the model for longitudinal HIV viral load data.
  • To validate the model's performance using real HIV patient data and simulation studies.

Main Methods:

  • Development of a random change point model for longitudinal data.
  • Assumption of a zero-inflated exponential distribution for change point analysis.
  • Utilization of a nonlinear mixed-effects model for the data-generating mechanism.
  • Extension of the Stochastic EM (StEM) algorithm with Gibbs and Metropolis-Hastings sampling.

Main Results:

  • The proposed model successfully estimates the timing of ART initiation from HIV viral load data.
  • The method accounts for data characteristics such as left-censoring and zero-inflation.
  • Simulation studies demonstrate the model's robust performance in various scenarios.

Conclusions:

  • The new statistical model provides a reliable method for inferring ART initiation timing.
  • This approach enhances the utility of routinely collected HIV viral load data for epidemiological research.
  • The findings contribute to a better understanding of HIV treatment dynamics and patient management.