A semiparametric hierarchical method for a regression model with an interval-censored covariate

Bayesian framework is proposed for analysing regression models in which one of the covariates is interval-censored. Such a situation was encountered in an AIDS clinical trial in which the goal was to examine the association between delays in initiating a new treatment after Indinavir failure and the subsequent viral load level of patients at the time of enrolment into the new treatment. The new method uses a mixture of Dirichlet processes allowing all the components in the model to be specified parametrically, except for the distribution of the interval-censored covariate, which is treated non-parametrically. The paper explains the proposed method for the linear regression model in detail. The performance of the method is assessed by simulations and illustrated using the AIDS clinical trial.