Prescott, Gordon J. and Garthwaite, Paul H.
(2005).
Bayesian analysis of misclassified binary data from a matched case-control study with a validation sub-study.
*Statistics in Medicine*, 24(3) pp. 379–401.

## Abstract

Bayesian methods are proposed for analysing matched case-control studies in which a binary exposure variable is sometimes measured with error, but whose correct values have been validated for a random sample of the matched case-control sets. Three models are considered. Model 1 makes few assumptions other than randomness and independence between matched sets, while Models 2 and 3 are logistic models, with Model 3 making additional distributional assumptions about the variation between matched sets. With Models 1 and 2 the data are examined in two stages. The first stage analyses data from the validation sample and is easy to perform; the second stage analyses the main body of data and requires MCMC methods. All relevant information is transferred between the stages by using the posterior distributions from the first stage as the prior distributions for the second stage. With Model 3, a hierarchical structure is used to model the relationship between the exposure probabilities of the matched sets, which gives the potential to extract more information from the data. All the methods that are proposed are generalized to studies in which there is more than one control for each case. The Bayesian methods and a maximum likelihood method are applied to a data set for which the exposure of every patient was measured using both an imperfect measure that is subject to misclassification, and a much better measure whose classifications may be treated as correct. To test methods, the latter information was suppressed for all but a random sample of matched sets.

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