This article discusses regression analysis of interval-censored failure time data in the presence of a cure fraction and nonignorable missing covariates. To address the challenges caused by interval censoring, missing covariates and the existence of a cure subgroup, we propose a joint semiparametric modeling framework that simultaneously models the failure time of interest and the missing covariates. In particular, we present a class of semiparametric nonmixture cure models for the failure time and a semiparametric density ratio model for the missing covariates. A two-step likelihood-based estimation procedure is developed and the large sample properties of the resulting estimators are established. An extensive numerical study demonstrates the good performance of the proposed method in practical settings and the proposed approach is applied to an Alzheimer’s disease study that motivated this study.
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