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An important problem in the analysis of preclinical and clinical data is the construction of test procedures to detect treatment related trend when data points are clusters of observations. Such tests have considerable applications in variety of areas, including teratology, and ophthalmological and otolaryngological studies. An essential component of the construction of such a test is a definition of trend that captures the effect of treatment on the cluster as a whole. One would want this definition to be intuitively interpretable, and the corresponding procedures to be mathematically tractable. In this paper, we construct a test of trend with clustered binary data, assuming exchangeability. We show that a meaningful trend test can be derived under stochastic and uniform stochastic orderings. As application of the new procedure, we analyze a set of developmental toxicity data on the effect of diethylhexyl phthalate (DEHP).
(This is joint work with Olusegun George, University of Memphis)