Inference in generalized linear regression models with a censored covariate

The problem of estimating the parameters in a generalized linear model when a covariate is subject to censoring is studied. A new method based on an estimating function approach is proposed. The method does not assume a parametric form for the distribution of the response given the regressors and is computationally simple. In the linear regression case, the proposed approach implies the use of mean imputation of the censored regressor. The use of flexible parametric models for the distribution of the covariate is employed. When survival time is considered as the covariate subject to censoring, the use of the generalized gamma distribution is explored, since it is considered as a platform distribution covering a wide variety of hazard rate shapes.