Assessing Importance of Biomarkers: a Bayesian Joint Modeling Approach of Longitudinal and Survival Data with Semicompeting Risks

Longitudinal biomarkers such as patient-reported outcomes (PROs) and quality of life (QOL) are routinely collected in cancer clinical trials or other studies. Joint modeling of PRO/QOL and survival data can provide a comparative assessment of patient-reported changes in specific symptoms or global measures that correspond to changes in survival. Motivated by a head and neck cancer clinical trial, we develop a class of trajectory-based models for longitudinal and survival data with disease progression. Specifically, we propose a class of mixed effects regression models for longitudinal measures, a cure rate model for the disease progression time (T _P ), and a Cox proportional hazards model with time-varying covariates for the overall survival time (T _D ) to account for T _P and treatment switching. Under the semi-competing risks framework, the disease progression is the nonterminal event, the occurrence of which is subject to a terminal event of death. The properties of the proposed models are examined in detail. Within the Bayesian paradigm, we derive the decompositions of the deviance information criterion (DIC) and the logarithm of the pseudo marginal likelihood (LPML) to assess the fit of the longitudinal component of the model and the fit of each survival component, separately. We further develop ΔDIC as well as ΔLPML to determine the importance and contribution of the longitudinal data to the model fit of the T _P and T _D data.