Statistical Inference For Proportion Ratios Based On Stratified Combined Unilateral And Bilateral Data

In otolaryngologic(or ophthalmologic)studies,the treatment data from the paired organs or body parts are usually both unilateral and bilateral data,and there exists high intraclass correlation.In order to avoid the confounding effects caused by some factors,we usually need to take these factors as stratified variables.Therefore,it is an important issue to consider the statistical inference of the cure rates of the two treatments based on the stratified combined unilateral and correlated bilateral series.First,we propose seven statistics for testing the homogeneity of proportion ratios in stratified design with combined unilateral and bilateral data,i.e.,the weighted-least-squares(WLS)test statistic,the Mantel-Haenszel(MH)test statistic,the WLS statistics with the log-transformation,the corresponding log-transformation tests of these statistics and the modified score test statistic.The large-sample asymptotic test procedures and Bootstrap-resampling test procedures based on these test statistics are considered for the homogeneity testing.Based on the proposed test statistics,the approximate sample size formulas which are required to achieve the pre-specified power at the nominal level are derived and evaluated.Simulation studies are conducted to examine the performance of various test statistics in terms of empirical type I error rates and empirical powers.Simulation results show that all test procedures based on the dependence model perform well for moderate and large sample sizes,the modified score test statistic performs satisfactory even under small sample sizes.It is worth noting that test procedures based on Bootstrap-resampling method usually can well control its empirical type I error rates around the nominal level,and hence be recommended in practical applications.Sample size formulas based on the proposed tests are generally accurate.Real example is used to illustrate the proposed methods.Second,based on the pooled data under the assumption of homogeneity,the equivalence test for the cure rates of two treatments is considered.Confidence intervals for proportion ratio,including Wald CI,the modified Wald CI based on Agresti-Coull method,the log-transformation-based CI,the CI based on likelihood ratio test and the Bootstrap-resampling CI are developed for the equivalence test.All CIs are evaluated by simulation studies in term of the empirical coverage probability(ECP),empirical coverage width(ECW),and the left and right non-coverage probabilities(LNCP,RNCP).Simulation results show that the modified Wald CI based on Agresti-Coull method,the log-transformation-based CI and Bootstrap resampling CI perform satisfactory in the sense that their ECPs are close to the confidence level even under small sample size designs.Furthermore,the latter two confidence intervals also have satisfactory interval location in the sense that they have symmetric left and right non-coverage probabilities.A real data set from an otolaryngologic study is used to illustrate the proposed methods.