Comparison of case-deletion diagnostic methods for Cox regression

Case-deletion diagnostics are a routine component of regression analysis since they identify unusual observations that substantially affect parameter estimates. The exact approach is to compute the change in each regression parameter by dropping that individual and refitting the model. Repeating a Cox regression for the removal of each individual is very time consuming and therefore not done in practice. The two methods commonly used to approximate the exact case-deletion change for Cox regression are the empirical influence function approach and the covariate-vector augmentation approach. This paper reports the results of a simulation study on how well these methods estimate the exact change in a parameter estimate when deleting a known outlier or a known non-outlier. Additionally, we investigate how well these methods correctly identify outliers and non-outliers. The covariate augmentation approach clearly outperformed the influence function approach in these simulations.