Novel Confidence Interval Estimations For Differences And Ratios Of Proportions For Correlated Binary Data

Background:Correlated binary data arise in many statistical contexts,and confidence intervals(CIs)of the differences and ratios in proportions are used and reported in the analysis of those data.Various confidence interval(CI)estimators have been developed for differences in proportions resulted from correlated binary data.However,the width(CW)of the mostly recommended Tango's score Cl tends to be wide,and the computing burden of exact methods recommended for small-sample data are intensive.The recently proposed rank-based nonparametric method by treating proportion as special areas under receiver operating characteristic(AUC)provided a new way to construct the CI for proportion difference on paired data,while the complex computation limits its application in practice.As for the CI estimates for proportions ratios,inconsistent results have been provided between different simulations studies.There is a need for a new simulation study to give a comparison of the existing CIs.In this study,we also provide three new way to construct MOVER Wilson score CIs for proportions ratios.Objective:We adopt the U-statistics approach for comparing two or more correlated AUCs to develop new normal approximated and t approximated nonparametric methods for the differences in proportions.For the proportions ratios,new MOVER CIs are constructed based on different correlation estimation methods of the binary data.Methods:In this study,we adopt the U-statistics approach of DeLong et.al for comparing two or more correlated AUCs to develop a new nonparametric method.The method of structural components is used to estimate the covariance of the correlated proportions.The constructed CI has a simple analytic form and a new estimate of the degree of freedom.Base on the continuity correction of the ?estimation of the correlation coefficient and by treating paired 2x2 data as multinomial data,three new MOVER Wilson score methods for ratios of paired proportions are developed.Simulation studies are conducted to investigate the performance of the new CI estimators on coverage probabilities(CPs),confidence interval widths(CWs),and mesial and distal noncoverage probabilities(MNCPs and DNCPs).Results:New nonparametric methods utilizing the U-statistics approach for comparing two or more correlated AUCs are constructed,and three new MOVER MOVER Wilson score methods for ratios of paired proportions are developed.The new t approximated nonparametric CI has a simple analytic form with a new estimate of the degrees of freedom of n-1.It demonstrates good coverage properties and has shorter CWs than that of Tango.This new CI with the new estimate of degrees of freedom also leads to CPs that are an improvement on the rank-based nonparametric CI.Comparing with the approximate exact unconditional method,the nonparametric CI demonstrates good coverage properties even in small samples,and yet they are very easy to implement computationally.The MOVER Wilson score methods base on? continuity correction and multinomial approximation and the score-based methods outperform than the other methods on CPs,CWs,and NCPs.Among them,the MOVER Wilson score methods base on ? continuity correction perform the best with good CPS and shorter CWs.Conclusion:The simplified t approximated nonparametric CI for proportions differences proposed in this study is an appealing choice in practice for its ease of use and good performance,and the MOVER Wilson score methods base on ? continuity correction is to recommend for the CI construction of proportions ratios.