Efficient estimation for semiparametric cure models with interval-censored data

This paper is concerned with the analysis of interval-censored survival data in the presence of a non-negligible cure fraction using semiparametric non-mixture cure models. We propose a spline-based sieve estimation method which overcomes numerical difficulties encountered in the existing semiparametric maximum likelihood estimation for the unknown nonparametric component in models. This method is easy to implement using the sequential quadratic programming technique. Under certain regularity conditions, we show the consistency, asymptotic normality and semiparametric efficiency of the proposed estimators for parameters. For the nonparametric component, our estimator has an explicit convergence rate, higher than that conjectured by Liu and Shen (2009) [16]. We conduct extensive simulation studies to evaluate the finite-sample performance of the method proposed. The results suggest that our method produces generally more efficient estimators than the existing method. The application of the method is illustrated with data from a study of smoking cessation.