American Journal of Epidemiology Advance Access originally published online on November 3, 2005
American Journal of Epidemiology 2005 162(12):1225-1234; doi:10.1093/aje/kwi340
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Original Contribution |
Two-Stage Case-Control Studies: Precision of Parameter Estimates and Considerations in Selecting Sample Size
1 Department of Epidemiology, Biostatistics, and Occupational Health, McGill University, Montreal, Quebec, Canada
2 Division of Clinical Epidemiology, Royal Victoria Hospital, Montreal, Quebec, Canada
3 Population Health and Information, Alberta Cancer Board, Calgary, Alberta, Canada
4 Centre for Clinical Epidemiology and Community Studies, Jewish General Hospital, Montreal, Quebec, Canada
Correspondence to Dr. James A. Hanley, 1020 Pine Avenue West, Montreal, Quebec, H3A 1A2, Canada (e-mail: james.hanley{at}mcgill.ca).
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.
case-control studies; confounding factors (epidemiology); efficiency; multivariate analysis; sample size; two-stage sampling; variance inflation factor
Abbreviations: HRT, hormone replacement therapy; ln, natural logarithm; MI, myocardial infarction; or, empirical odds ratio: estimate of the odds ratio parameter OR; V, vasectomy
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