TESTS OF INDEPENDENCE, TREATMENT HETEROGENEITY, AND DOSE-RELATED TREND WITH EXCHANGEABLE BINARY DATA

Existing methods of testing for treatment effects for clustered binary data include the beta-binomial, quasilikelihood, and GEE procedures. All of these methods revolve around the mean response and the second-o rder correlation. However, these two parameters alone do not fully det ermine the effect of treatment. This article develops nonparametric li kelihood ratio procedures to test for independence, heterogeneity, and dose-related trend in dose-response studies involving exchangeable bi nary data. The hypotheses of independence, heterogeneity, and trend ar e expressed in terms of joint probabilities of similar responses among cluster mates. Constrained maximum likelihood estimates of these prob abilities are computed and used to construct test statistics. Unlike t he test statistics for independence and heterogeneity, the asymptotic distribution of the likelihood ratio test for trend is not exactly a c hi-square. However, an upper bound of its p value is obtained by using a chi-squared distribution. A set of clustered binary data from the S hell Toxicology Laboratory, on the developmental effect of a chemical agent on banded Dutch rabbits, is used to illustrate the various test procedures. The same dataset is used to compare the proposed trend tes t with some existing trend tests, such as those based on a beta-binomi al model, generalized estimating equations, and survey sampling method s.