A joint analysis of quality of life and survival using a random effect selection model

In studies of patients with advanced disease, longitudinal quality of life data may be truncated as a result of early death. Since survival and quality of life are likely to be related, modelling of the quality of life response needs to account for these different survival patterns. Here we discuss the application of a random effect selection model, in the form of a trivariate Normal model for the joint analysis of quality of life response (intercept and slope) and log survival time. Under certain assumptions this can give an unbiased description of the quality of life responses and valid inferences comparing treatment strategies in a clinical trial. It also indicates how quality of life and survival are related, by estimating the expected quality of life responses conditional on different survival times. Model parameters can be estimated using a restricted iterative generalized least-squares (RIGLS) procedure within standard software, extended to handle censoring of survival outcome using an EM algorithm. The model is applied to a physical quality of life score and survival data from a trial of treatment for patients with colorectal hepatic metastases. Survival differed between the treatment groups, and quality of life repsonse tended to be worse, both in initial level and change over time, for those patients who died earlier. The parameter estimates obtained agreed well with those from analysing the extended trial data set with complete survival information. Residual diagnostics used to check the necessary underlying assumptions of the model are exemplified. We conclude that such models can give an informative description of longitudinal responses when these are truncated by differential survival patterns.