A multiple imputation approach for flexible modelling of interval-censored data with missing and censored covariates

This paper discusses regression analysis of interval-censored failure time data that commonly occur in biomedical studies among others. For the situation, the failure event of interest is known only to occur within an interval instead of being observed exactly. In addition to interval censoring on the failure time of interest, sometimes covariates may be missing or suffer censoring, which can bring extra theoretical and computational challenges for the regression analysis. To deal with such data, we propose a novel multiple imputation approach with the use of the rejection sampling under a class of semiparametric transformation models. The proposed method is flexible and can lead to more efficient estimation than the existing methods, and the resulting estimators are shown to be consistent and asymptotically normal. An extensive simulation study is conducted and demonstrates that the proposed approach works well in practice. Finally, we apply the proposed approach to a set of real data on Alzheimer's disease that motivated this study.