GOODNESS-OF-FIT TESTS FOR THE GENERAL COX REGRESSION-MODEL

In this article, we extend the information matrix tests proposed by White (1982) for detecting parametric model misspecification to the partial likelihood setting with particular interest in the Cox semi-parametric regression model. First we identify two model-based consistent estimators for the inverse of the asymptotic covariance matrix of the maximum partial likelihood estimator in the Cox model. We then show that under the assumed model the difference between these two estimators is asymptotically normal with mean zero and with a covariance matrix which can be consistently estimated. Goodness-of-fit tests for the Cox model are constructed based on these asymptotic results. Extensive Monte Carlo studies indicate that the large-sample approximation is appropriate for practical use. In addition, we demonstrate that the proposed tests tend to be more powerful than other numerical methods in the literature. Two examples are provided for illustrations.