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American Journal of Epidemiology Advance Access published online on November 3, 2005
American Journal of Epidemiology, doi:10.1093/aje/kwi340
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American Journal of Epidemiology Copyright © 2005 by the Johns Hopkins Bloomberg School of Public Health All rights reserved; printed in U.S.A.
Received December 21, 2004
Accepted July 7, 2005

ORIGINAL CONTRIBUTIONS

Two-Stage Case-Control Studies: Precision of Parameter Estimates and Considerations in Selecting Sample Size

James A. Hanley 1*, Ilona Csizmadi 2, and Jean-Paul Collet 3

1 Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, Quebec, Canada; Division of Clinical Epidemiology, Royal Victoria Hospital, Montreal, Quebec, Canada
2 Population Health and Information, Alberta Cancer Board, Calgary, Alberta, Canada
3 Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, Quebec, Canada; Centre for Clinical Epidemiology and Community Studies, Jewish General Hospital, Montreal, Quebec, Canada

* To whom correspondence should be addressed.
James A. Hanley, E-mail: james.hanley{at}mcgill.ca


  Abstract

A two-stage case-control design, in which exposure and outcome are determined for a large sample but covariates are measured on only a subsample, may be much less expensive than a one-stage design of comparable power. However, the methods available to plan the sizes of the stage 1 and stage 2 samples, or to project the precision/power provided by a given configuration, are limited to the case of a binary exposure and a single binary confounder. The authors propose a rearrangement of the components in the variance of the estimator of the log-odds ratio. This formulation makes it possible to plan sample sizes/precision by including variance inflation factors to deal with several confounding factors. A practical variance bound is derived for two-stage case-control studies, where confounding variables are binary, while an empirical investigation is used to anticipate the additional sample size requirements when these variables are quantitative. Two methods are suggested for sample size planning based on a quantitative, rather than binary, exposure.

Keywords: case-control studies; confounding factors (epidemiology); efficiency; multivariate analysis; sample size; two-stage sampling; variance inflation factor.
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