Joint Modeling of Quality of Life and Survival Using a Bayesian Approach in a Retrospective Time Scale

Improving patients' quality of life (QoL) is one of the primary goals of palliative care clinical trials. However, a significant challenge in this area is the "truncation by death problem," where QoL data cannot be observed after a patient dies, potentially introducing bias into statistical analyses. Understanding the impact of truncation by death when estimating the association between QoL and exposure or treatment is essential, especially when a relatively large proportion of subjects die during a study. To address this issue, we propose a Bayesian joint modeling framework that considers dependencies at both the individual and cluster levels while examining longitudinal QoL trajectories and survival outcomes simultaneously. This approach builds on existing joint modeling methods by incorporating cluster-level random effects. We model QoL on a retrospective scale relative to the time of death, while linking survival via both the subject and cluster-level random effects. The longitudinal sub-model also allows for flexible, non-linear QoL trajectories, which are modeled using penalized regression splines. For the survival sub-model, we use a proportional hazards frailty model with a Weibull baseline hazard. The model is estimated using a Bayesian framework, implemented via Markov Chain Monte Carlo (MCMC) sampling. To evaluate the performance of our method, we conducted a comprehensive simulation study including scenarios with different numbers of clusters. We also show results from applying this novel methodology to data from the Reducing End of Life Symptoms with Touch (REST) study.