| 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 a variety of areas, including teratology, and ophthalmology and otolaryngology 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 test procedures to be mathematically tractable. In this dissertation, we construct tests of trend with clustered binary and multinomial data, assuming exchangeability. We show that meaningful trend tests can be derived under stochastic ordering and some of its generalizations. |
