Checking the Cox Proportional Hazards Model with Interval-Censored Data

This article presents a general framework for checking the adequacy of the Cox proportional hazards model with interval-censored data, which arise when the event of interest is known only to occur over a random time interval. Specifically, we construct certain stochastic processes that are informative about various aspects of the model, that is, the functional forms of covariates, the exponential link function and the proportional hazards assumption. We establish their weak convergence to zero-mean Gaussian processes under the assumed model through empirical process theory. We then approximate the limiting distributions by Monte Carlo simulation and develop graphical and numerical procedures to check model assumptions and improve goodness of fit. We evaluate the performance of the proposed methods through extensive simulation studies and provide an application to the Atherosclerosis Risk in Communities Study. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.