Pairwise dependence diagnostics for clustered failure-time data

Frailty and copula models specify a parametric dependence structurefor multivariate failure-time data. Estimation of some jointquantities can be highly sensitive to the assumed parametricform, and hence model fit is an important issue. This paperlays out a general diagnostic framework for evaluating and selectingfrailty and copula models. The approach is based on the cumulativesum of residuals that are calculated in bivariate time. Theresiduals reflect the difference between the observed and expectedbivariate association structures. The proposed model-checkingprocess is interpretable with a limiting distribution whichcan be approximated using the bootstrap. Simulations and a dataexample illustrate the practical application of the method.     

Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data

Summary In many instances, a subject can experience both a nonterminal and terminal event where the terminal event (e.g., death) censors the nonterminal event (e.g., relapse) but not vice versa. Typically, the two events are correlated. This situation has been termed semicompeting risks (e.g., Fine, Jiang, and Chappell, 2001 , Biometrika 88, 907–939; Wang, 2003 , Journal of the Royal Statistical Society, Series B 65, 257–273), and analysis has been based on a joint survival function of two event times over the positive quadrant but with observation restricted to the upper wedge. Implicitly, this approach entertains the idea of latent failure times and leads to discussion of a marginal distribution of the nonterminal event that is not grounded in reality. We argue that, similar to models for competing risks, latent failure times should generally be avoided in modeling such data. We note that semicompeting risks have more classically been described as an illness–death model and this formulation avoids any reference to latent times. We consider an illness–death model with shared frailty, which in its most restrictive form is identical to the semicompeting risks model that has been proposed and analyzed, but that allows for many generalizations and the simple incorporation of covariates. Nonparametric maximum likelihood estimation is used for inference and resulting estimates for the correlation parameter are compared with other proposed approaches. Asymptotic properties, simulations studies, and application to a randomized clinical trial in nasopharyngeal cancer evaluate and illustrate the methods. A simple and fast algorithm is developed for its numerical implementation.