Assessing model fit in joint models of longitudinal and survival data with applications to cancer clinical trials

Joint models for longitudinal and survival data now have a long history of being used in clinical trials or other studies in which the goal is to assess a treatment effect while accounting for longitudinal assessments such as patient-reported outcomes or tumor response. Compared to using survival data alone, the joint modeling of survival and longitudinal data allows for estimation of direct and indirect treatment effects, thereby resulting in improved efficacy assessment. Although global fit indices such as AIC or BIC can be used to rank joint models, these measures do not provide separate assessments of each component of the joint model. In this paper, we develop a novel decomposition of AIC and BIC (i.e., AIC = AICLong + AICSurv|Long and BIC = BICLong + BICSurv|Long) that allows us 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. Based on this decomposition, we then propose ΔAICSurv and ΔBICSurv to determine the importance and contribution of the longitudinal data to the model fit of the survival data. Moreover, this decomposition, along with ΔAICSurv and ΔBICSurv, is also quite useful in comparing, for example, trajectory-based joint models and shared parameter joint models and deciding which type of model best fits the survival data. We examine a detailed case study in mesothelioma to apply our proposed methodology along with an extensive set of simulation studies.