A Linear Regression Model With A Continuous Interval-censored Covariate

In medical studies, interval-censored data are often encountered because the exact time of our interested event can not be observed but it is known to lie in an interval. There have been many studies for the analysis of interval-censored data. Though, to our knowledge, virtually all such methods consider situations where a response variable is subject to interval censoring. One exception is given by Gomez et al. [7]. Motivated by a study of an AIDS clinical trial, they considered a linear regression model with a discrete interval-censored explanatory variable in 2003. However, their approach can not be extended to the situation where the interval-censored explanatory variable is continuous.In this paper we introduce two kinds of methods for the analysis of a linear regression model with a continuous interval-censored explanatory variable. First, the unbiased transformation method was adopted for the analysis of this model and estimators of regression coefficients were proved to be unbiased, consistent and asymptotic normally distributed. Second, the MCMC method was used to obtain Bayesian estimation of parameters in the model and the procedure for the Gibbs sampling in this model was derived. In the simulation study, we compared three kinds of methods and the unbiased transformation method and the MCMC method had their advantages in different situations. At last, the two methods were used for the analysis of a dataset from an AIDS clinical trial.