Several Asymptotic Tests And Interval Estimations Of Correlation Coefficient For Stratified Bilateral Correlated Data

In randomized clinical trials,there exist some kind of correlation between responses from paired body parts of patients(e.g.,eyes,ears,arms)to a treatment or medicine.The paper is aiming at further research of the correlation coefficient in stratified bilateral data,and provides many theoretical value and clinical diagnosis suggestions.The main structure is described as follows:research background,model construction,testing methods,confidence interval methods,simulation studies and two real examples.When a patient in study contributes two such paired measurements,the overall outcomes can be recorded as non-response,one-response and double-response.In our research,the patient is divided into several strata according to ages,body parts and so on.Patients in each stratum are randomly divided into two treatment groups.Suppose that the correlation coefficients are the same in one stratum,but different from the others.This assumption provides theoretical support for studies of correlated stratified bilateral data.In this regards,three test statistics(Likelihood ratio test,Score test and Wald-type test)are used to test the equivalent of correlation coefficient from two different groups at first.Later,homogeneity test and common are derived under the assumption of equal correlation coefficient.Al1 methods are compared by Monte Carlo Simulation,according to their empirical type ? error(TIE)and powers.As a result,all three tests can effectively converge to robust area when sample size increases.Score test is better over most situation,while Wald-type test is not recommended especially in homogeneity test.Based on common test,confidence interval estimation is a better way to evaluate correlation coefficient.Six methods(MLE based Wald-type confidence interval,profile likelihood confidence interval,MLE based Score confidence interval,two weighted naive MLE based Wald-type confidence interval and pooled MLE based Wald-type confidence interval)are proposed and compared according to their empirical coverage probability(ECP)and mean interval width(MIW).As a result,five methods have robust ECP except profile likelihood confidence interval,and Score test is recommended for its proper MIW.Two real examples are given to illustrate the proposed methods:children's otitis media with effusion and the bovine collagen clinical trial.Two cases stratify with different age and body parts separately.The results of hypothesis tests and confidence intervals are similar to those in simulation studies.