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Biostatistics Advance Access published online on April 28, 2005
Biostatistics, doi:10.1093/biostatistics/kxi029
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.
Received December 19, 2003
Revised March 29, 2005
Accepted April 25, 2005

Article

Optimal design and efficiency of 2-phase case-control studies with error-prone and error-free exposure measures

R McNamee 1*

1 Biostatistics Group, School of Epidemiology and Health Sciences, University of Manchester, Oxford Rd, Manchester M13 9PT, England

* To whom correspondence should be addressed.
R McNamee, E-mail: rmcnamee{at}manchester.ac.uk


  Abstract

This paper addresses optimal design and efficiency of 2-phase case-control studies in which the first phase uses an error-prone exposure measure, Z, while the second phase measures true, dichotomous exposure, X, in a subset of subjects. Optimal design of a separate second phase, to be added to a pre-existing study, is also investigated. Differential mis-classification is assumed throughout. Results are also applicable to 2-phase cohort studies with error-prone and error-free measures of disease status but error-free exposure measures. While software based on the mean score method of Reilly and Pepe (1995) can find optimal designs given pilot data, the lack of simple formulae makes it difficult to generalise about efficiency compared to 1-phase studies based on X alone. Here, formulae for the optimal ratios of cases to controls and first to second phase sizes, and the optimal second phase stratified sampling fractions, given a fixed budget, are given. The maximum efficiency of 2-phase designs compared to a 1-phase design is deduced and is shown to be bounded from above by a function of the sensitivities and specificities of Z. The efficiency of ‘balanced’ separate second phase designs (Breslow & Cain 1988) - in which equal numbers of subjects are chosen from each first phase strata - compared to optimal design is deduced, enabling situations where balanced designs are nearly optimal to be identified.

Keywords: 2-phase studies; efficiency; case-control studies; exposure validation studies; measurement error; 2-stage studies; differential mis-classification.
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