Trend test in dose-response has been a central problem in medicine. This paper treats the problem of comparing umbrella pattern treatment effects. Under an ordered m x r x k table, this article considers testing the hypothesis that all multinomial populations are conditional independence against the alternative that they are in an umbrella trend. For this hypothesis test problem, this article introduces a model-free test method by using likelihood ratio test statistic and gives the asymptotic distribution of the test statistic. Simulation study is conducted to compare the empirical power perfo...
