Efficient Estimation of Semiparametric Transformation Model with Interval-Censored Data in Two-Phase Cohort Studies

Interval sampling and two-phase sampling have both been advocated for studying rare failure outcomes. With few exceptions focusing on specific designs such as the case-cohort design, they are often studied separately in the statistical literature and require different estimation procedures. We consider efficient estimation of interval-censored data collected in a two-phase sampling design using a localized nonparametric likelihood. An expectation maximization algorithm is proposed by exploiting multiple layers of data augmentation that handle transformation function, interval-censoring, and two-phase sampling structure simultaneously. We study the asymptotic properties of the estimators and conduct inference using profile likelihood. We illustrate the performance of the proposed estimator by simulations and an HIV vaccine trial.