Inference for a linear regression model with an interval-censored covariate

• Published in: Statistics in medicine 2003-02, Vol.22 (3), p.409-425
• Main Authors: Gómez, Guadalupe, Espinal, Anna, W. Lagakos, Stephen
• Format: Article
• Language: English
• Subjects: Adult; Biological and medical sciences; Computer Simulation; Computerized, statistical medical data processing and models in biomedicine; HIV - growth & development; HIV - metabolism; HIV Infections - drug therapy; HIV Infections - virology; HIV Protease Inhibitors - therapeutic use; Humans; Indinavir - therapeutic use; interval censoring; Likelihood Functions; Linear Models; Medical sciences; Medical statistics; Middle Aged; Multivariate Analysis; non-parametric estimation; Recurrence; self-consistency; Statistics as Topic - methods; Viral Load
• ISSN: 0277-6715; 1097-0258
• DOI: 10.1002/sim.1326

Interval‐censored observations of a response variable are a common occurrence in medical studies, and usually result when the response is the elapsed time until some event whose occurrence is periodically monitored. In this paper we consider a multivariate regression setting in which the explanatory variable is interval censored. Use of an ad hoc method of analysis for such data, such as taking the midpoint of the interval‐censored covariate and applying ordinary least‐squares, is not in general valid. We develop a likelihood approach, together with a two‐step conditional algorithm, to jointly estimate the regression coefficients as well as the marginal distribution of the covariate. The resulting estimators are asymptotically normal. The performance of the method is assessed via simulations, and illustrated using data from a recent HIV/AIDS clinical trial to assess the association between waiting time between indinavir failure and subsequent viral load at enrolment. Extensions of the procedure to other parametric distributions are discussed. Copyright © 2003 John Wiley & Sons, Ltd.