Statistical Inference Of Risk Differences In Stratified Design With Correlated Bilateral Data And Applications

In otolaryngologic(or ophthalmologic)studies,correlated bilateral data can arise from studies involving paired body organs or body parts in the same subjects.In order to avoid the confounding effects caused by some different factors,we usually need to take these factors as stratified variables,and consider the statistical inference of the success rate of surgery(drug treatment)under the stratified design.We herein propose seven statistics for testing the homogeneity of risk differences(RD)in stratified design with correlated bilateral data,which are weighted-leastsquares(WLS),the Mantel-Haenszel(MH)estimator,the WLS method in combination with tanh-1(x)transformation,and the test statistics based on their log-transformation and the modified score test statistic.Then,based on the various homogeneity test procedures proposed in this paper,under the assumption of the independence model,we propose the sample size calculation formula or sample size approximation algorithm,they are the sample size formula based on WLS statistic,sample size formula based on MantelHaenszel-estimate-based statistic,sample size formula based on WLS Statistics with inverse hyperbolic tangent transformation and sample size approximation algorithm based on score statistic.We evaluate the performance of the test statistics in terms of empirical type I error rates and powers.Simulation results show that test procedures that fail to take into account the correlation between responses from paired body organs could lead to inflated type I errors,while all seven test procedures based on the dependence model perform well in studies with generally and are recommended for practical applications.It is noteworthy that the four of the tests perform well in general,with the tests based on the WLS method and tanh-1(x)transformation always perform satisfactory even under small sample size designs.Sample size formulae based on the modified score test,the weighted-least-square statistic and the tanh-1(x)transformation of weighted-least-square statistic are found to be satisfactory.Therefore,they are recommended for practical applications.Finally,the methods are illustrated with two examples from the literature.