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Activity Number: 349 - Lifetime Data Science Student Awards
Type: Topic-Contributed
Date/Time: Thursday, August 12, 2021 : 10:00 AM to 11:50 AM
Sponsor: Lifetime Data Science Section
Abstract #317126
Title: Efficiency of the Breslow Estimator in Semiparametric Transformation Models
Author(s): Theresa Devasia* and Alexander Tsodikov
Companies: University of Michigan and University of Michigan
Keywords: semiparametric transformation model; Breslow estimator; nonparametric maximum likelihood estimation; weighted Breslow; proportional odds model; efficiency

Semiparametric transformation models for failure time data consist of a parametric regression component and an unspecified cumulative baseline hazard. The nonparametric maximum likelihood estimator (NPMLE) of the cumulative baseline hazard can be summarized in terms of weights introduced into a Breslow-type estimator (Weighted Breslow). At any given time point, the weights invoke an integral over the future of the cumulative baseline hazard, which presents theoretical and computational challenges. A simpler non-MLE Breslow-type estimator (Breslow) was derived earlier from a martingale estimating equation (MEE) setting observed and expected counts of failures equal, conditional on the past history. Despite much successful theoretical and computational development, the simpler Breslow estimator continues to be commonly used as a compromise between simplicity and perceived loss of full efficiency. In this paper we show that these two estimators are asymptotically equivalent. We also study the equivalence of these estimators using simulations and real data on prostate cancer survival.

Authors who are presenting talks have a * after their name.

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