Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

  • Authors:

  • Haimeng Zhang;Larry Goldstein

  • Affiliations:

  • Department of Mathematics and Computer Science, Concordia College, Moorhead, MN;Department of Mathematics, University of Southern California, Los Angeles, CA

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2003

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Abstract

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d, setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.