Efficient estimation of a semiparametric time-varying coefficient model for interval-censored failure time data

Survival models allowing temporal dynamic covariate effects for interval-censored data are underdeveloped. This paper introduces a spline-based sieve maximum likelihood estimation of a semiparametric model with time-varying coefficients for interval-censored data. We establish the consistency, minimax optimal convergence rate and asymptotic normality of estimators under regularity conditions. In particular, the estimator of time-independent coefficient is semiparametric efficient. Intensive simulation studies are carried out to demonstrate the finite-sample performance. The proposed estimation procedure is illustrated with the data from the Chinese Longitudinal Healthy Longevity Survey (CLHLS).