A specification test for univariate and multivariate proportional hazards models

This paper applies White's (1982, Econometrica 50, 1-25) information matrix (IM) test for correct model specification to proportional hazards models of univariate and multivariate censored survival data. Several alternative estimators of the test statistic are presented and their size performance examined. White also suggested an estimator of the parameter covariance matrix that was robust to certain forms of model misspecification. This has been subsequently proposed by others (e.g., Royall, 1986, International Statistical Review 54, 221-226) and applied by Huster, Brookmeyer, and Self (1989, Biometrics 45, 145-156) as part of an independence working model (IWM) approach to multivariate censored survival data. We illustrate how the IM test can be used for both univariate data and as part of the IWM approach to multivariate data.