Summary
The problem of studying the relationship between a specific disease and the exposure to a risk factor, which may cause its development, is considered. The paper deals with the choice of sample size when the odds ratio is the measure of association used and the purpose is to perform a case-control study. In the Bayesian framework the interest focuses on three different ways of obtaining a log-normal approximation to the exact posterior density of the odds ratio. A simple criterion based on the study of the variability of the posterior distribution is used to compare the effects of the three approximations on the chosen sample size. Another method, exploiting an approximated evaluation of the expected length of the HPD regions, is used in order to make a comparison with a frequentist procedure based on the precision of the estimate of the odds ratio. The comparison regards above all the optimal allocation of the subjects among cases and controls. Some hints for choosing the hyperparameters of prior distributions are discussed and a sensitivity analysis is also performed.
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Sambucini, V. Sample size determination for inferences on the odds ratio. J. Ital. Statist. Soc. 9, 219–243 (2000). https://doi.org/10.1007/BF03178967
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DOI: https://doi.org/10.1007/BF03178967