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Z-estimation and stratified samples: application to survival models.

Norman E Breslow1, Jie Hu2, Jon A Wellner3

  • 1Department of Biostatistics, University of Washington, Seattle, WA, USA. norm@uw.edu.

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|January 16, 2015
PubMed
Summary

This study introduces a Z-estimation theorem for joint parameter estimation in probability models, particularly useful for censored survival data with complex sampling designs. The method provides consistent estimates, even with model misspecification.

Keywords:
Additive hazardsCalibration of sampling weightsModel misspecificationProportional hazardsSemiparametric modelsSurvey sampling

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Area of Science:

  • Statistics
  • Biostatistics
  • Survival Analysis

Background:

  • Joint estimation of Euclidean and non-Euclidean parameters is challenging in probability models.
  • Stratified sampling designs and unpredictable inverse probability weights complicate standard survival data analysis.
  • Martingale theory is often insufficient for complex weighting schemes in survival data.

Purpose of the Study:

  • To present an infinite dimensional Z-estimation theorem for joint parameter estimation.
  • To adapt the theorem for stratified sampling designs in survival data analysis.
  • To address challenges posed by unpredictable weights in estimating parameters for censored survival data.

Main Methods:

  • Utilizes an infinite dimensional Z-estimation theorem.
  • Applies to Cox proportional and Lin-Ying additive hazards models.
  • Employs weighted likelihood and estimating equations for parameter estimation.
  • Incorporates weight calibration using all available subject information.

Main Results:

  • Provides a systematic approach for joint estimation of parameters in probability models.
  • Successfully adapts to stratified sampling designs.
  • Offers consistent estimates for regression coefficients and baseline hazard functions.
  • Enables estimation of individual survival probabilities.

Conclusions:

  • The Z-estimation theorem offers a robust method for joint parameter estimation in complex survival data.
  • The approach yields consistent population parameter estimates, robust to model misspecification.
  • Weight calibration enhances estimation efficiency compared to standard methods.