Assessing importance of biomarkers: A Bayesian joint modelling approach of longitudinal and survival data with semi-competing risks

Abstract

Longitudinal biomarkers such as patient-reported outcomes (PROs) and quality of life (QOL) are routinely collected in cancer clinical trials or other studies. Joint modelling 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 ((Formula presented.)) and a Cox proportional hazards model with time-varying covariates for the overall survival time ((Formula presented.)) to account for (Formula presented.) and treatment switching. Under the semi-competing risks framework, the disease progression is the non-terminal 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 (Formula presented.) DIC as well as (Formula presented.) LPML to determine the importance and contribution of the longitudinal data to the model fit of the (Formula presented.) and (Formula presented.) data.