Joint modeling quality of life and survival using a terminal decline model in palliative care studies

Palliative medicine is a relatively new specialty that focuses on preventing and relieving the suffering of patients facing life-threatening illness. For cancer patients, clinical trials have been carried out to compare concurrent palliative care with usual cancer care in terms of longitudinal measurements of quality of life (QOL) until death, and overall survival is usually treated as a secondary endpoint. It is known that QOL of patients with advanced cancer decreases as death approaches; however, in previous clinical trials, this association has generally not been taken into account when inferences about the effect of an intervention on QOL or survival have been made. We developed a new joint modeling approach, a terminal decline model, to study the trajectory of repeated measurements and survival in a recently completed palliative care study. This approach takes the association of survival and QOL into account by modeling QOL retrospectively from death. For those patients whose death times are censored, marginal likelihood is used to incorporate them into the analysis. Our approach has two submodels: a piecewise linear random intercept model with serial correlation and measurement error for the retrospective trajectory of QOL and a piecewise exponential model for the survival distribution. Maximum likelihood estimators of the parameters are obtained by maximizing the closed-form expression of log-likelihood function. An explicit expression of quality-adjusted life years can also be derived from our approach. We present a detailed data analysis of our previously reported palliative care randomized clinical trial.