Bivariate longitudinal model for the analysis of the evolution of HIV RNA and CD4 cell count in HIV infection taking into account left censoring of HIV RNA measures.

We present a bivariate linear mixed model taking into account censored measures of the response variable due to lower quantification limit of the assays. It allows an estimate of the correlation between the two response variables and takes into account this correlation for the estimation of other model parameters. This model was applied in a large cohort study (APROCO Cohort) to study the evolution under antiretroviral treatment of the two major biomarkers of the progression of Human Immunodeficiency Virus (HIV) infection: plasma HIV RNA and CD4+ T lymphocytes cell count. In a sample of 929 patients who started an highly active antiretroviral therapy, we illustrate the superiority in terms of likelihood of a bivariate model compared to two univariate models and the impact of taking into account the left-censoring of HIV-RNA. Moreover, interpretation of the model parameters allows confirmation of correlation between these two markers throughout the whole follow-up and the continuous decrease of plasma HIV RNA on average. Despite some limitations (distribution assumption, ignorance of missingness process), such a model appeared to be very useful to correctly describe the current evolution of important biomarkers in HIV infection.