Test of homogeneity of binary data with explanatory variables

Apparent heterogeneity of the risk of a disease in different groups may be explained by subject-specific risk factors unequally distributed in these groups. We propose a score test of homogeneity that allows adjustment for known risk factors of the disease. The test is based on a random-effect logistic regression model and requires only simple computations in addition to a conventional logistic regression method. The score test is applied to the study of geographical heterogeneity of cognitive impairment in elderly using a sample of 3,318 subjects scattered in 75 parishes. It is shown that an apparent heterogeneity disappears when taking into account subject-specific risk factors. This test may also be useful for studying familial aggregation of a disease.