Checking the marginal Cox model for correlated failure time data

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Abstract
Correlated failure time data arise frequently in scientific investigations because there exists natural or artificial clustering of study subjects such that failure times within the same cluster are correlated. It is convenient and useful to perform regression analysis by formulating the marginal distributions of the correlated failure times with the Cox proportional hazards model. In this paper, we develop a class of graphical and numerical techniques for checking the adequacy of the marginal Cox model. The proposed methods are derived from cumulative sums of martingale-based residuals over the failure time and/or covariates. The distributions of these stochastic processes under the assumed model can be approximated through simulating certain zero-mean Gaussian processes. Each observed residual pattern can then be compared objectively with a number of realisations from the approximating process. An illustration with the Diabetic Retinopathy Study is provided.

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