Weighted Breslow-type and maximum likelihood estimation in semiparametric transformation models

A semiparametric transformation model comprises a parametric component for covariate effects and a nonparametric component for the baseline hazard/intensity. The Breslow-type estimator has been proposed for estimating the nonparametric component in some inefficient estimation procedures. We show that introducing weights into this estimator leads to nonparametric maximum likelihood estimation, with the weights depending on the martingale residuals. The weighted Breslow-type estimator suggests an iterative reweighting algorithm for nonparametric maximum likelihood estimation, which can be implemented by a weighted variant of the existing algorithms for inefficient estimation, and can be computationally more efficient than an <sc>em</sc>-type algorithm. The weighting idea is further extended to semiparametric transformation models with mismeasured covariates. Copyright 2009, Oxford University Press.