Test for increasing convex order in multivariate response

Trend test based on cross-classified data in dose-response has been a central problem in medicine. Most of existing test methods are known to only fit to binary response variables. However, the approaches for binary response tables may suffer from the lack of a clear choice for dichotomization. For multivariate response with ordered categories, some studies have been done for simple stochastic order, likelihood ratio order and so on. However, methods of statistical inference on increasing convex order for more than two multinomial populations have not been fully developed. For testing the increasing convex order alternative, this article provides a model-free test method which can be used in the case of two-way tables and stratified data. Two real examples will be used to illustrate how to apply our test method.