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We present a method to fit a mixed effects Cox model with interval‐censored data. Our proposal is based on a multiple imputation approach that uses the truncated Weibull distribution to replace the interval‐censored data by imputed survival times and then uses established mixed effects Cox methods for right‐censored data. Interval‐censored data were encountered in a database corresponding to a recompilation of retrospective data from eight analytical treatment interruption (ATI) studies in 158 human immunodeficiency virus (HIV) positive combination antiretroviral treatment (cART) suppressed individuals. The main variable of interest is the time to viral rebound, which is defined as the increase of serum viral load (VL) to detectable levels in a patient with previously undetectable VL, as a consequence of the interruption of cART. Another aspect of interest of the analysis is to consider the fact that the data come from different studies based on different grounds and that we have several assessments on the same patient. In order to handle this extra variability, we frame the problem into a mixed effects Cox model that considers a random intercept per subject as well as correlated random intercept and slope for pre‐cART VL per study. Our procedure has been implemented in R using two packages: truncdist and coxme, and can be applied to any data set that presents both interval‐censored survival times and a grouped data structure that could be treated as a random effect in a regression model. The properties of the parameter estimators obtained with our proposed method are addressed through a simulation study. [ABSTRACT FROM AUTHOR]