Residual analysis in linear regression models with an interval‐censored covariate

Abstract

Abstract Residual analysis is a useful class of techniques for the evaluation of the goodness of a fitted model. Checking the underlying assumptions is important since most linear regression estimators require a correctly specified regression function and independent and identically distributed errors to be consistent. For uncensored data, the examination of the residuals of the fitted model is a standard tool for checking whether or not the underlying model assumptions hold. Such analysis has not been widely developed for censored data. Hillis ( Statistics in Medicine 1995; 14 :2023–2036) developed a residual plot for model checking when the response variable of a linear model is right‐censored, and Gómez et al . ( Statistics in Medicine 2003; 22 :409–425) proposed residuals in models with interval‐censored covariates. In this paper, we propose a new definition of residuals for linear models that incorporate interval‐censored covariates. This definition can be also applied when the response variable is interval‐censored. These new residuals are shown to perform better in model checking than other types of residuals in this context. We illustrate them with a data set from an AIDS clinical trial study. Copyright © 2004 John Wiley & Sons, Ltd.