Consistency of the NPML Estimator in the Right-Censored Transformation Model

This paper studies the representation and large-sample consistency for nonparametric maximum likelihood estimators (NPMLEs) of an unknown baseline continuous cumulative-hazard-type function and parameter of group survival difference, based on right-censored two-sample survival data with marginal survival function assumed to follow a transformation model, a slight generalization of the class of frailty survival regression models. The paper’s main theoretical results are existence and unique a.s. limit, characterized variationally, for large data samples of the NPMLEof baseline nuisance function in an appropriately defined neighbourhood of the true function when the group difference parameter is fixed, leading to consistency of the NPMLE when the difference parameter is fixed at a consistent estimator of its true value. The joint NPMLE is also shown to be consistent. An algorithm for computing it numerically, based directly on likelihood equations in place of the expectation-maximization (EM) algorithm, is illustrated with real data.