Tests for homogeneity of effect in an epidemiologic investigation

A test for homogeneity of the effect of a factor in inducing disease in the various strata of a population should relate to the scaling in which homogeneity is anticipated. Popularity, it is the multiplicative effect on the odds ratio in which homogeneity is anticipated. An asymptotic test by M. Zelen (Biometrika 58:129-137, 1971) for homogeneity in this scaling is indicated to be invalid. Further, a test by J. L. Fleiss (Statistical Methods for Rates and Proportions. NY, Wiley, 1973) for homogeneity of the standardized difference is shown to be the same as the Zelen test, to be invalid in any case, and not to correspond to any scaling. The examples given include one in which results of two studies are apparently inhomogeneous by the test even though they give effectively identical results. It is advised that tests for homogeneity be conducted with care, and that thought be given to how effects might be made homogeneous rather than to trying to demonstrate the existence of heterogeneity.