New residuals for Cox regression and their application to outlier screening

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