We propose a Bayesian chi-squared model diagnostic for analysis of data subject to censoring. The test statistic has the form of Pearson's chi-squared test statistic and is easy to calculate from standard output of Markov chain Monte Carlo algorithms. The key innovation of this diagnostic is that is based only on observed failure times. Because it does not rely on the imputation of failure times for observations that have been censored, we show that it has higher power for detecting model departures than a comparable test based on the complete data. In a simulation study, we show that tests based on this diagnostic exhibit comparable power and better nominal Type I error rates than a commonly used alternative test proposed by Akritas (1988). An important advantage of the proposed diagnostic is that it applies to a broad class of censored data models, including generalized linear models and other models with non-identically distributed and non-additive error structures. We illustrate the proposed model diagnostic for testing the adequacy of two parametric survival models for Space Shuttle main engine failures.
Biostatistics | Clinical Trials | Statistical Methodology | Statistical Theory
Cao, Jing; Moosman, Ann; and Johnson, Valen E., "A Bayesian Chi-Squared Goodness-of-Fit Test for Censored Data Models" (May 2008). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 43.