Tests for interaction in epidemiologic studies: A review and a study of power

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Abstract
Tests for statistical interaction have come into increasing use in epidemiologic analysis, with most based on either an additive or multiplicative model for joint effects. Further procedures have been proposed for testing the goodness‐of‐fit and comparing the fit of the latter models. This paper reviews the relationships between the various tests and model comparison methods, and, for the special case of two dichotomous risk factors, presents asymptotic power functions for tests of additivity and multiplicativity. For a range of sample sizes and factor effects, the powers of the tests are computed using both the asymptotic power function and simulation studies. The powers of the tests are very low in several commonly encountered situations. In addition, convergence to the asymptotic distribution appears slow for some of the statistics. The results also indicate that likelihood comparison procedures can provide a useful adjunct to the classical hypothesis‐testing approach.