Bernoulli

  • Bernoulli
  • Volume 15, Number 2 (2009), 569-597.

Efficiency of the maximum partial likelihood estimator for nested case control sampling

Larry Goldstein and Haimeng Zhang

Full-text: Open access

Abstract

In making inference on the relation between failure and exposure histories in the Cox semiparametric model, the maximum partial likelihood estimator (MPLE) of the finite dimensional odds parameter, and the Breslow estimator of the baseline survival function, are known to achieve full efficiency when data is available for all time on all cohort members, even when the covariates are time dependent. When cohort sizes become too large for the collection of complete data, sampling schemes such as nested case control sampling must be used and, under various models, there exist estimators based on the same information as the MPLE having smaller asymptotic variance.

Though the MPLE is therefore not efficient under sampling in general, it approaches efficiency in highly stratified situations, or instances where the covariate values are increasingly less dependent upon the past, when the covariate distribution, not depending on the real parameter of interest, is unknown and there is no censoring. In particular, in such situations, when using the nested case control sampling design, both the MPLE and the Breslow estimator of the baseline survival function achieve the information lower bound both in the distributional and the minimax senses in the limit as the number of cohort members tends to infinity.

Article information

Source
Bernoulli, Volume 15, Number 2 (2009), 569-597.

Dates
First available in Project Euclid: 4 May 2009

Permanent link to this document
https://projecteuclid.org/euclid.bj/1241444903

Digital Object Identifier
doi:10.3150/08-BEJ162

Mathematical Reviews number (MathSciNet)
MR2543875

Zentralblatt MATH identifier
1200.62122

Keywords
highly stratified information bound semi-parametric models

Citation

Goldstein, Larry; Zhang, Haimeng. Efficiency of the maximum partial likelihood estimator for nested case control sampling. Bernoulli 15 (2009), no. 2, 569--597. doi:10.3150/08-BEJ162. https://projecteuclid.org/euclid.bj/1241444903


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