Modelling HIV viral rebound using non-linear mixed effects models

Individuals infected with the human immunodeficiency virus type 1 (HIV-1) who initiate antiretroviral therapy typically experience a marked decline in concentrations of HIV-1 RNA in plasma. Often, however, viral rebound occurs within the first year of treatment and this rebound may be associated with resistance to antiretroviral therapy. For this reason, it is important to study the patterns of virological response of HIV-1 RNA to treatment. In particular, there is interest in the relationship between the lowest level of plasma HIV-1 RNA attained after initiation of therapy (nadir value) and the time until rebound. To investigate this question, we implement a simple and flexible non-linear mixed effects model for the trajectory of the HIV-1 RNA until rebound. This model is also consistent with biological insights into the effects of treatment. We also show how the problem of censoring of HIV-1 RNA values at the lower limit of assay quantification can be addressed using a multiple imputation scheme. The algorithm is simple to implement and is based on accessible software. Our application makes use of data from clinical trial 315 conducted by the AIDS Clinical Trials Group (ACTG 315). We find a strong relationship between HIV-1 RNA nadir and time to rebound, with potentially important consequences for the management of HIV-infected individuals.