New residuals for Cox regression and their application to outlier screening

The identification of individuals who 'died far too early' or 'lived far too long' as compared to their survival probabilities from a Cox regression can lead to the detection of new prognostic factors. Methods to identify outliers are generally based on residuals. For Cox regression, only deviance residuals have been considered for this purpose, but we show that these residuals are not very suitable. Instead, we develop and propose two new types of residuals: the suggested log-odds and normal deviate residuals are simple and intuitively appealing and their theoretical properties and empirical performance make them very suitable for outlier identification. Finally, various practical aspects of screening for individuals with outlying survival times are discussed by means of a cancer study example.