Asymptotic Method For Many-to-One Response Rates Of Correlated Paired Data

In medical research,such as ophthalmology and otorhinolaryngology,clinical data usually include bilateral measurements from paired organs(such as arms and ears),which often have certain differences relevance.If we ignore the correlation and confounding effect between the paired samples of independent individuals,the statistical inference may lead to wrong conclusions.In medicine,there are many kinds of treatment methods for a certain disease.According to the different treatment methods,the subjects are randomly divided into multiple groups to judge whether there are significant differences in the treatment effect of different treatments on the same disease.One group was set as the control group,the others as the control group,so as to form the judgment and comparison of multiple groups to one group.This paper is based on Donner model,assuming that the intra group correlation coefficient of each group is a fixed value,which reflects the correlation between paired correlation data.Under Donner model,the consistency and homogeneity of the comparison cases are tested by the progressive method.Before the test,we put forward three hypotheses about proportion ratio,namely global hypothesis,restrictive hypothesis and non restrictive hypothesis.Since there is no explicit solution to the maximum likelihood estimation of parameters,Fisher iteration method is used to solve the maximum likelihood estimation.The so-called consistency test is to test the non restrictive hypothesis that the proportion ratio δ from the second group to the G group is equal.According to the maximum likelihood estimation,the likelihood ratio,score and Wald statistics are constructed,and the expression of the statistics is given.At this time,the statistics obey the χ2 distribution with g-2 degree of freedom.The data fitting shows that score statistics and likelihood ratio statistics are more robust in the first type of error rate and efficacy,but score will be more robust.An example is given to illustrate the method of consistency test.Therefore,score statistic is worthy to be recommended as the consistency test statistic of paired related data.On the basis of consistency test,the restricted hypothesis of whether the proportional ratio is a specific constant is tested,that is,homogeneity test is carried out.According to the maximum likelihood estimation of the parameters under the restricted hypothesis,the likelihood ratio,score and Wald statistics are reconstructed,and the expressions of each statistic are obtained.At this time,the statistics obey the χ2 distribution with 1 degree of freedom,In terms of their performance in the first kind of error rate and efficacy,score statistic is the most robust and Wald statistic is the most aggressive.Then an example is given to illustrate the homogeneity test method.Finally,under the unrestricted assumption,the interval of proportional ratio is estimated.The SC and LC are obtained by Newton iterative method.WClinterval is the traditional confidence interval based on maximum likelihood estimation,and the weighted WC2 confidence interval is expanded beyond theWC1 confidence interval.Empirical coverage and confidence width are evaluated for each confidence interval.Finally,an example from a Massachusetts hospital is used to further demonstrate these methods.