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Comparison of empirical and dynamic models for HIV viral load rebound after treatment interruption

Ante Bing, Yuchen Hu, Melanie Prague, Alison L. Hill, Jonathan Z. Li, Ronald J. Bosch, Victor DeGruttola and Rui Wang ORCID logo



To compare empirical and mechanistic modeling approaches for describing HIV-1 RNA viral load trajectories after antiretroviral treatment interruption and for identifying factors that predict features of viral rebound process.


We apply and compare two modeling approaches in analysis of data from 346 participants in six AIDS Clinical Trial Group studies. From each separate analysis, we identify predictors for viral set points and delay in rebound. Our empirical model postulates a parametric functional form whose parameters represent different features of the viral rebound process, such as rate of rise and viral load set point. The viral dynamics model augments standard HIV dynamics models–a class of mathematical models based on differential equations describing biological mechanisms–by including reactivation of latently infected cells and adaptive immune response. We use Monolix, which makes use of a Stochastic Approximation of the Expectation–Maximization algorithm, to fit non-linear mixed effects models incorporating observations that were below the assay limit of quantification.


Among the 346 participants, the median age at treatment interruption was 42. Ninety-three percent of participants were male and sixty-five percent, white non-Hispanic. Both models provided a reasonable fit to the data and can accommodate atypical viral load trajectories. The median set points obtained from two approaches were similar: 4.44 log10 copies/mL from the empirical model and 4.59 log10 copies/mL from the viral dynamics model. Both models revealed that higher nadir CD4 cell counts and ART initiation during acute/recent phase were associated with lower viral set points and identified receiving a non-nucleoside reverse transcriptase inhibitor (NNRTI)-based pre-ATI regimen as a predictor for a delay in rebound.


Although based on different sets of assumptions, both models lead to similar conclusions regarding features of viral rebound process.

Corresponding author: Rui Wang, Department of Population Medicine, Harvard Pilgrim Health Care Institute and Harvard Medical School and Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, MA, 02215, USA, E-mail:

Bing and Hu contributed equally to this work.

Funding source: amfAR, The Foundation for AIDS Research

Award Identifier / Grant number: 109856-65-RGRL

Funding source: National Institute of Allergy and Infectious Diseases

Award Identifier / Grant number: P01 AI131365; P01 AI131385; R01 AI136947; R37 AI051164; UM1 AI068634; UM1 AI068636

Funding source: The Inria Associate team

Award Identifier / Grant number: project DYNAMHIC


We thank the participants, staff, and principal investigators of the ACTG studies 371, A5024, A5068, A5130, A5187, and A5197.

  1. Research funding: We gratefully acknowledge grants from National Institute of Allergy and Infectious Diseases P01 AI131385, P01 AI131365, R37 AI051164, and R01 AI136947, UM1 AI068634, UM1 AI068636, and an amfAR Impact Grant 109856-65-RGRL from the Foundation for AIDS Research, and the Inria Associate team, project DYNAMHIC.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: Authors state no conflict of interest.


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Received: 2019-11-15
Accepted: 2020-06-30
Published Online: 2020-08-21

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