Construction Of Confidence Interval For Proportion Differences Based On Stratified Combined Unilateral And Bilateral Data

In biomedical statistical research,the data obtained from treatment of a pair of body organs or body parts of an individual has both unilateral data and bilateral data,and the bilateral data is often highly correlated.Not only must that,in practical applications,the influence of confounding effects also should be considered.The usual method is to treat these factors as stratified variables.Therefore,it is an important research to consider the construction of the confidence intervals(CIs)of the proportion differences based on stratified combined unilateral and bilateral data.First,this article considers the construction of the simultaneous CIs of the proportion differences and the CIs of the common proportion differences based on stratified combined unilateral and bilateral data.Based on the independence model in stratified designs(i.e.,intraclass correlation data model),seven simultaneous CIs for proportion differences are proposed,including Wald simultaneous CIs,simultaneous CI based on inverse hyperbolic tangent transformation,Score simultaneous CI,simultaneous CI for likelihood ratios and two Bootstrap simultaneous CIs for proportion differences.Based on the assumption of homogeneity for the common proportion difference,eight approximate CIs for the common proportion difference are presented,i.e.,Score CI,likelihood ratio CI,CI based on Cochran test statistic,Weighted-Least-Square(WLS)CI,two CIs based on Mantel-Haenszel(MH)estimates and two CIs based on Bootstrap resampling.For the above method of construction of simultaneous CIs and CIs of the common proportion difference,the statistical properties of CIs can be evaluated by simulation study of their empirical coverage probability(ECP),empirical coverage width(ECW)and the ratio of mesial non-coverage probability to the non-coverage probability(RMNCP).Simulation results show that a Wald simultaneous CI,simultaneous CI based on inverse hyperbolic tangent transformation,Score simultaneous CI and bootstrap percentile simultaneous CI perform well and hence be recommended for applications.For CIs of the common proportion difference,Score CI and CI based on Cochran statistic for the common proportion difference behave well even under small sample sizes,other CIs produce good performance when sample size is not small.Finally,the proposed CIs construction method is applied to real data to verify the effectiveness of the proposed methods.Then,consider the approximate sample size formulas for comparing the cure rates of two treatments based on combined unilateral and bilateral data.Under controlling the width of a CI for the proportion difference at a specified width with a pre-specified confidence level,the approximate formulas of the sample sizes based on the Wald CI,the Score CI and the likelihood ratio CI are given.The accuracy of various sample sizes formulas is studied by simulation,that is,ECP and ECW of estimation CIs are simulated under the estimated sample sizes.Simulation results show that sample sizes based on Wald,Score and likelihood ratio CIs are accurate and hence be recommended in practical applications.Real data set from an otolaryngology study is used to illustrate the proposed methods.