Joint modeling of censored longitudinal and event time data

Censoring of a longitudinal outcome often occurs when data are collected in a biomedical study and where the interest is in the survival and or longitudinal experiences of a study population. In the setting considered herein, we encountered upper and lower censored data as the result of restrictions imposed on measurements from a kinetic model producing “biologically implausible” kidney clearances. The goal of this paper is to outline the use of a joint model to determine the association between a censored longitudinal outcome and a time to event endpoint. This paper extends Guo and Carlin's [6] paper to accommodate censored longitudinal data, in a commercially available software platform, by linking a mixed effects Tobit model to a suitable parametric survival distribution. Our simulation results showed that our joint Tobit model outperforms a joint model made up of the more naïve or “fill-in” method for the longitudinal component. In this case, the upper and/or lower limits of censoring are replaced by the limit of detection. We illustrated the use of this approach with example data from the hemodialysis (HEMO) study [3] and examined the association between doubly censored kidney clearance values and survival.