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Biometrika Advance Access originally published online on July 17, 2009
Biometrika 2009 96(3):591-600; doi:10.1093/biomet/asp032
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© 2009 Biometrika Trust

Article

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

Yi-Hau Chen

Institute of Statistical Science, Academia Sinica, Taipei 11529, Taiwan; yhchen{at}stat.sinica.edu.tw

Received for publication 1 May 2008. Revision received 1 December 2008.
  Abstract

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 EM-type algorithm. The weighting idea is further extended to semiparametric transformation models with mismeasured covariates.

Key Words: Counting process • Errors in variables • Martingale residual • Proportional hazards model • Proportional odds model • Survival analysis


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