Theoretical and applied issues arising from the joint modelling of longitudinal response processes and time to competing events

The statistical analysis of observational data arising from HIV/AIDS research is generally faced with complexities that arise from both the longitudinal and survival features of the data.This thesis proposes a methodology for modelling the joint variation over time of the two main biomarkers of the progression of disease and of the survival processes of a set of competing events. Modelling two longitudinal response processes as a bivariate linear mixed effects model, with knots at relevant times, will account for the dependence between two biomarkers by random effects while overcoming the problem of irregularly measured data and of the possible measurement errors. Furthermore modelling the informative withdrawals from the study as dependent competing risks, by estimating the so called cumulative incidence functions whithin a proportional hazards model, will allow for an unbiased estimate of the markers' processes. At the same time the parameters that specify the association between the markers processes and the survival processes will allow to model the effect of the biomarkers, adjusted for other covariates, on the competing events. The essential feature of joint modelling is that the parameters which describe the longitudinal response processes and those which describe the failure risks, as a function of the longitudinal processes, are estimated simultaneously, making a more efficient use of data.