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I have a set of abnormal lab findings and a set of tenderness outcomes in a small sample of "cases" and "positive controls". We hypothesize there may be some lab findings which differentially affect cases and controls. For instance, abdominal tenderness may be associated with pain in the controls but not in cases, or vice versa. To assess marginal association within cases and controls individually, I have used Fisher's exact test to account for very low prevalence of certain abnormalities. The p-value from Fisher's exact test infers an association in the contingency table of exposure and outcome, and is very similar to inference about the odds ratio in a logistic regression model when minimal sample sizes are obtained.

Had I had sufficient sample sizes, what I would have been interested in was a test of modification of exposure/outcome (tenderness) by case/control status. This can be done by adjusting for an interaction in the logistic regression model. Is there any analogous test for $2 \times 2 \times 2$ contingency tables with small samples and 0 marginal cells?

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