Joint modelling of bivariate longitudinal data with informative dropout and left-censoring, with application to the evolution of CD4+ cell count and HIV RNA viral load in response to treatment of HIV infection

Several methodological issues occur in the context of the longitudinal study of HIV markers evolution. Three of them are of particular importance: (i) correlation between CD4+ T lymphocytes (CD4+) and plasma HIV RNA; (ii) left-censoring of HIV RNA due to a lower quantification limit; (iii) and potential informative dropout. We propose a likelihood inference for a parametric joint model including a bivariate linear mixed model for the two markers and a lognormal survival model for the time to drop out. We apply the model to data from patients starting antiretroviral treatment in the CASCADE collaboration where all of the three issues needed to be addressed.