Pairwise dependence diagnostics for clustered failure-time data

Frailty and copula models specify a parametric dependence structure for multivariate failure-time data. Estimation of some joint quantities can be highly sensitive to the assumed parametric form, and hence model fit is an important issue. This paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models. The approach is based on the cumulative sum of residuals that are calculated in bivariate time. The residuals reflect the difference between the observed and expected bivariate association structures. The proposed model-checking process is interpretable with a limiting distribution which can be approximated using the bootstrap. Simulations and a data example illustrate the practical application of the method.