A parametric independence test for clustered binary data

This paper proposes an independence test for a set of clustered binary observations, such as might be encountered in developmental toxicity studies. An exchangeable binary model is employed, under an assumption of exchangeability among cluster elements, to model probability of positive response. With a Weibull form assumed for response, the independence test is equivalent to testing whether a parameter value is unity. This Weibull form also allows for parametric tests for a covariate-response relationship and for covariate effects on correlation. The procedure is illustrated using data obtained from a developmental toxicity study.