Joint modeling of multivariate longitudinal data and the dropout process in a competing risk setting: application to...

Joint modeling of longitudinal and survival data has been increasingly considered in clinical trials, notably in cancer and AIDS. In critically ill patients admitted to an intensive care unit (ICU), such models also appear to be of interest in the investigation of the effect of treatment on severity scores due to the likely association between the longitudinal score and the dropout process, either caused by deaths or live discharges from the ICU. However, in this competing risk setting, only cause-specific hazard sub-models for the multiple failure types data have been used.

We propose a joint model that consists of a linear mixed effects submodel for the longitudinal outcome, and a proportional subdistribution hazards submodel for the competing risks survival data, linked together by latent random effects. We use Markov chain Monte Carlo technique of Gibbs sampling to estimate the joint posterior distribution of the unknown parameters of the model. The proposed method is studied and compared to joint model with cause-specific hazards submodel in simulations and applied to a data set that consisted of repeated measurements of severity score and time of discharge and death for 1,401 ICU patients.

Time by treatment interaction was observed on the evolution of the mean SOFA score when ignoring potentially informative dropouts due to ICU deaths and live discharges from the ICU. In contrast, this was no longer significant when modeling the cause-specific hazards of informative dropouts. Such a time by treatment interaction persisted together with an evidence of treatment effect on the hazard of death when modeling dropout processes through the use of the Fine and Gray model for sub-distribution hazards.

In the joint modeling of competing risks with longitudinal response, differences in the handling of competing risk outcomes appear to translate into the estimated difference in treatment effect on the longitudinal outcome. Such a modeling strategy should be carefully defined prior to analysis.