Assessment of Fit in Longitudinal Data for Joint Models with Applications to Cancer Clinical Trials

Joint models for longitudinal and survival data have now become increasingly popular in clinical trials or other studies for assessing a treatment effect while accounting for longitudinal measures such as patient-reported outcomes or tumor response. Most studies in the existing literature primarily focus on reducing the bias and improving efficiency in the estimate of the treatment effect in the joint modeling of survival and longitudinal data. Global fit indices such as Akaike information criterion (AIC) or Bayesian information criterion (BIC) can be used to assess the overall fit of the joint model. However, these indices do not provide separate assessments of each component of the joint model. In this chapter, we develop new model assessment criteria using a novel decomposition of AIC and BIC (i.e., AIC = AIC\(_\textrm{Surv}\) + AIC\(_\textrm{Long} | \textrm{Surv}\) and BIC = BIC\(_\textrm{Surv}\) + BIC\(_\textrm{Long} | \textrm{Surv}\)) to assess the contribution of the survival data to the model fit of the longitudinal data. We apply the proposed methodology to the analysis of a real dataset from a cancer clinical trial in mesothelioma.