Randomized Survival Probability Residual for Assessing Parametric Survival Models

Abstract

Traditional residuals for diagnosing accelerated failure time models in survival analysis, such as Cox-Snell, martingale and deviance residuals, have been widely used. However, ex- amining those residuals are often only made visually, which can be subjective. Therefore, lack of objective measure of examining model adequacy has been a long-standing issue that needs to be addressed for survival analysis. In this thesis, a new type of residual is proposed called Normal-transformed Randomized Survival Probability (NRSP) residual. A compre- hensive review of the traditional residuals including Cox Snell and deviance residuals is firstly presented highlighting their disadvantages for examining model adequacy. We then introduce NRSP residual. Simulation studies were conducted to compare the performance of NRSP residuals with the traditional residuals. Our simulation studies demonstrated that NRSP residuals are approximately normally distributed when the fitted model is correctly speci- fied, and has great statistical power in detecting model inadequacies. We also apply NRSP residuals to a real dataset to check the goodness-of-fit of three plausible models.