Multiple Imputation for M-Regression With Censored Covariates

Abstract

We develop a new multiple imputation approach for M-regression models with censored covariates. Instead of specifying parametric likelihoods, our method imputes the censored covariates by their conditional quantiles given the observed data, where the conditional quantiles are estimated through fitting a censored quantile regression process. The resulting estimator is shown to be consistent and asymptotically normal, and it improves the estimation efficiency by using information from cases with censored covariates. Compared with existing methods, the proposed method is more flexible as it does not require stringent parametric assumptions on the distributions of either the regression errors or the covariates. The finite sample performance of the proposed method is assessed through a simulation study and the analysis of a c-reactive protein dataset in the 2007–2008 National Health and Nutrition Examination Survey. This article has supplementary material online.

KEY WORDS:

• Censored predictor
• Censored quantile regression
• Detection limit
• Imputation
• Linear regression
• M-estimator
• Nonignorable missingness

Acknowledgments

The research is partially supported by the NSF Award DMS-1007420 and the NSFC grant 11101254. The authors thank two anonymous reviewers, the associate editor, and the editor for constructive comments and helpful suggestions that led to a major improvement of the article.