Influence diagnostics for the Cox proportional hazards regression model: method, simulation and applications

Abstract

This article investigates the performance of several residuals for the Cox proportional hazards regression model to diagnose the influential observations. The standardized and adjusted forms of residuals are proposed for Cox proportional hazards regression model. In addition, Cook’s distance is proposed for both standardized and adjusted residuals. The assessment of different residuals for the identification of influential observations is made through the Monte Carlo simulation. A real dataset of bone marrow transplant Leukaemia is analyzed to show the benefit of the proposed methods. Simulation and application results show that the standardized and adjusted residuals based on the Cox–Snell method perform best for the detection of influential points. Furthermore, the standardized, and adjusted Martingale and deviance residuals work better when the sample size is large.