Semiparametric estimation of the accelerated failure time model with partly interval-censored data

Partly interval-censored (PIC) data arise when some failure times are exactly observed while others are only known to lie within certain intervals. In this article, we consider efficient semiparametric estimation of the accelerated failure time (AFT) model with PIC data. We first generalize the Buckley-James estimator for right-censored data to PIC data. Then, we develop a one-step estimator by deriving and estimating the efficient score for the regression parameters. We show that under mild regularity conditions the generalized Buckley-James estimator is consistent and asymptotically normal and the one-step estimator is consistent and asymptotically normal with a covariance matrix that attains the semiparametric efficiency bound. We conduct extensive simulation studies to examine the performance of the proposed estimators in finite samples and apply our methods to data derived from an AIDS study.