Shyamal Peddada, PhD

"Tests for multibariate stochastic ordering for ordred experimental groups with applications"

Abstract: In many applications, researchers are interested in testing hypotheses on two or more outcome variables when the experimental groups are ordered such as dose groups in dose-response studies, cancer stages in oncology, income levels in epidemiological and social studies etc.  Thus, the analysis of multivariate data over ordered experimental groups has broad applications, in toxicology, economics, finance, epidemiology, clinical trials and so on. In many instances, the data are non-normally distributed with shape of the distribution changing with population (or experimental groups).  Thus, the data are not likely to be multivariate normally distributed. Secondly, from an application point of view, often researchers are not only interested in determining whether the experimental groups are different from each other but whether they are “ordered” (in some sense) in the response vector.  Since the shape of the distribution may change over the experimental groups, it may not be sufficient or even meaningful to compare the mean vectors.  For example, even though the population means are identical the probability distributions could be very different. Consequently, standard multivariate methods such as the multivariate analysis of variance (MANOVA) may not suitable.   In this talk we describe some notions of stochastic ordering of multivariate random vectors and develop methodologies for testing such orders.  Resulting methodologies are illustrated using some examples from toxicology.