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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×r×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 performed via the proposed method and others.Finally,two real data axe studied to illustrate the vahdity of the proposed method.
Trend test in dose-response has been a central problem in medicine.This paper treats the problem of comparing umbrella pattern treatment effects. Undered an ordered m × r × k table, this article considers testing the hypothesis that all multinomial populations are conditional 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 to compare the empirical power implemented via the proposed method and others .Finally, two real data axe studied to illustrate the vahdity of the proposed method.