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Abstract:
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Motivated from a clinical trial in head and neck cancer, we develop a class of shared parameter joint models for longitudinal and survival data with treatment switches. Specifically, we propose a class of mixed effects regression models for longitudinal measures, a cure rate model for the treatment switch (TS) time, and a time-varying covariates model for the overall survival (OS) time to account for switch time. The properties of the proposed models are examined in details. In addition, we derive the decomposition of the logarithm of the pseudo marginal likelihood (LPML) (i.e., LPML =LPML$_{\mbox{Long}}$ + LPML$_{\mbox{Surv}|\mbox{Long}}$) to assess the fit of each component of the joint model, and in particular to assess the fit of the longitudinal component of the model and the survival component separately and further use ?LPML to determine the importance and contribution of the longitudinal data to the model fit of the survival data. Moreover, efficient Markov chain Monte Carlo sampling algorithms are developed to carry out posterior computation. We apply the proposed methodology to the motivating clinical trial.
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