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Information in the sample covariate distribution in prevalent cohorts

Authors

  • Richard J. Cook,

    Corresponding author
    1. Department of Statistics and Actuarial Science, University of Waterloo, 200 University Avenue West, Waterloo, Ont., Canada N2L 3G1
    • Department of Statistics and Actuarial Science, Faculty of Mathematics, University of Waterloo, 200 University Avenue West, Waterloo, Ont., Canada N2L 3G1
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  • Pierre-Jérôme Bergeron

    1. Mathematics and Statistics Ottawa, University of Ottawa, Ont., Canada
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Errata

This article is corrected by:

  1. Errata: Information in the sample covariate distribution in prevalent cohorts: Addendum Volume 30, Issue 26, 3166, Article first published online: 17 August 2011

Abstract

Methods of estimation and inference about survival distributions based on length-biased samples are well-established. Comparatively little attention has been given to the assessment of covariate effects in the context of length-biased samples, but prevalent cohort studies often have this objective. We show that, like the survival distribution, the covariate distribution from a prevalent cohort study is length-biased, and that this distribution may contain parametric information about covariate effects on the survival time. As a result, a likelihood based on the joint distribution of the survival time and the covariates yields estimates of covariate effects which are at least as efficient as estimates arising from a traditional likelihood which conditions on covariate values in the length-biased sample. We also investigate the empirical bias of estimators arising from a joint likelihood when the population covariate distribution is misspecified. The asymptotic relative efficiencies and empirical biases under model misspecification are assessed for both proportional hazards and accelerated failure time models. The various methods considered are applied in an illustrative analysis of risk factors for death following onset of dementia using data collected in the Canadian Study of Health and Aging. Copyright © 2011 John Wiley & Sons, Ltd.

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