Practical Guidelines for Goodness-of-Fit Testing for Right-Censored Data

Abstract

In survival studies, right censoring often prevents the observation of subjects' complete outcomes, complicating inference about the underlying distribution. Evaluating whether a given distribution adequately fits right-censored data is therefore essential. However, guidance on the relative performance of available goodness-of-fit tests under different data conditions remains limited. In this work, we present a comparative assessment of three classical goodness-of-fit tests adapted for right-censored data: Kolmogorov-Smirnov, Anderson-Darling, and Cramér-von Mises. Through an extensive simulation study, we investigate how factors such as the proportion of right-censored observations, sample size, and distributional symmetry influence the statistical power of each test. All procedures were implemented using the R package GofCens, and power estimates were obtained from extensive replicated simulations. The results identify the settings in which each test exhibits superior performance, providing practical, evidence-based recommendations for test selection in survival analysis. These recommendations are summarized as user-oriented guidelines and complemented by a concise graphical cheat sheet, enabling practitioners to quickly identify the most suitable test for their specific application.