Multilevel models for longitudinal variables prognostic for survival.

The issue of modelling the joint distribution of survival time and of prognostic variables measured periodically has recently become of interest in the AIDS literature but is of relevance in other applications. The focus of this paper is on clinical trials where follow-up measurements of potentially prognostic variables are often collected but not routinely used. These measurements can be used to study the biological evolution of the disease of interest; in particular the effect of an active treatment can be examined by comparing the time profiles of patients in the active and placebo group. It is proposed to use multilevel regression analysis to model the individual repeated observations as function of time and, possibly, treatment. To address the problem of informative drop-out--which may arise if deaths (or any other censoring events) are related to the unobserved values of the prognostic variables--we analyse sequentially overlapping portions of the follow-up information. An example arising from a randomized clinical trial for the treatment of primary biliary cirrhosis is examined in detail.