A joint model for longitudinal outcomes with potential ceiling and floor effects and survival times, with applications to analysis of quality of life data from a cancer clinical trial

Longitudinal data on patient-reported outcomes (PROs), such as quality of life of patients, are frequently collected in clinical trials and other medical studies. Joint analysis of these data with survival times may improve the accuracy of statistical inferences, especially when PRO measurements may be missing after the death of patients. Classical linear mixed models are often used as the models for the longitudinal measurements in a joint analysis, but it may not be suitable for longitudinal PRO measurements with potential ceiling and floor effects caused by a large portion of patients who report either a maximum or minimum score. In this paper, we introduce a new joint model that uses a longitudinal Tobit model for the longitudinal outcomes with potential ceiling arid floor effects arid a Cox proportional hazard model for survival time with a random effect connecting these two models. An estimation procedure based on the partial likelihood and Laplace approximation is developed to estimate the parameters in both models, and a random weighting method is proposed to calculate the variances of these parameter estimators. Performances of the proposed procedures are evaluated through simulation studies and an application to the analysis of quality of life data from a clinical trial.