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Improved Horvitz–Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology

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Abstract

The case-cohort study involves two-phase samplings: simple random sampling from an infinite superpopulation at phase one and stratified random sampling from a finite cohort at phase two. Standard analyses of case-cohort data involve solution of inverse probability weighted (IPW) estimating equations, with weights determined by the known phase two sampling fractions. The variance of parameter estimates in (semi)parametric models, including the Cox model, is the sum of two terms: (i) the model-based variance of the usual estimates that would be calculated if full data were available for the entire cohort; and (ii) the design-based variance from IPW estimation of the unknown cohort total of the efficient influence function (IF) contributions. This second variance component may be reduced by adjusting the sampling weights, either by calibration to known cohort totals of auxiliary variables correlated with the IF contributions or by their estimation using these same auxiliary variables. Both adjustment methods are implemented in the R survey package. We derive the limit laws of coefficients estimated using adjusted weights. The asymptotic results suggest practical methods for construction of auxiliary variables that are evaluated by simulation of case-cohort samples from the National Wilms Tumor Study and by log-linear modeling of case-cohort data from the Atherosclerosis Risk in Communities Study. Although not semiparametric efficient, estimators based on adjusted weights may come close to achieving full efficiency within the class of augmented IPW estimators.

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Authors and Affiliations

  1. Department of Biostatistics, University of Washington, Seattle, WA, USA

    Norman E. Breslow & Thomas Lumley

  2. Department of Medicine, Baylor College of Medicine, Houston, TX, USA

    Christie M. Ballantyne

  3. Department of Biostatistics, University of North Carolina, Chapel Hill, NC, USA

    Lloyd E. Chambless

  4. Department of Probability and Mathematical Statistics, Charles University, Prague, Czech Republic

    Michal Kulich

Authors
  1. Norman E. Breslow
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  2. Thomas Lumley
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  3. Christie M. Ballantyne
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  4. Lloyd E. Chambless
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  5. Michal Kulich
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Correspondence to Norman E. Breslow.

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Breslow, N.E., Lumley, T., Ballantyne, C.M. et al. Improved Horvitz–Thompson Estimation of Model Parameters from Two-phase Stratified Samples: Applications in Epidemiology. Stat Biosci 1, 32–49 (2009). https://doi.org/10.1007/s12561-009-9001-6

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  • DOI: https://doi.org/10.1007/s12561-009-9001-6

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