chapter  5
Joint Models for Longitudinal Data and Continuous Event Times from Competing Risks
Pages 28

The joint models discussed in Chapter 4 assume that the event times are generated from a single failure type, so are not applicable to studies with multiple failure types or competing risks. Use the scleroderma lung study we have introduced in Chapter 1 as an example. Recall that the primary outcome is forced vital capacity (FVC, as % predicted) determined at 3-month intervals from baseline. The event of interest is time to treatment failure or death. The longitudinal and survival data are possibly correlated, which could introduce nonignorable non-response missing values for %FVC after event times. Dependence between the two endpoints is further complicated by informatively censored events due to dropout during follow-up. Note that both death and dropout could lead to nonignorable missing data in %FVC measurements. The joint model developed by Elashoff, Li, and Li (2008)[61], as described in Section 5.1, has the capacity to handle multiple failure types, or competing risks at the survival endpoint. Parameter estimation and inference of this model via a Bayesian approach can be found in Hu, Li, and Li (2009)[100]. A robust joint model with t-distributed random errors (Li, Elashoff, and Li, 2009[137]) is described in Section 5.2. Li et al. (2010)[138] developed a model for studies with ordinal longitudinal measurements and competing risks, and this approach is discussed in Section 5.3. Section 5.4 extends joint models with competing risks to the scenario where there exists heterogeneity in the random effects covariance across study subjects (Huang, Li, and Elashoff, 2010[103]; Huang, Li, Elashoff, and Pan, 2011[104])

5.1 Joint Analysis of Longitudinal Data and Competing Risks

5.1.1 The Model Formulation

Let Yi(t) be the longitudinal outcome measured at time t for subject i, where i = 1, 2, . . . , n, and n is the total number of subjects in study. Each subject may experience one of g distinct failure types or could be right censored during follow-up. Let Ci = (Ti, Di) denote the competing risks data on subject i, where Ti is the failure/censoring time, and Di takes a value in {0, 1, . . . , g}, with Di = 0 indicating a censored event and Di = k showing that subject i fails from the kth type of failure, k = 1, . . . , g. The censoring mechanism is assumed to be independent of event times.