单双边混合数据下比例比的渐近置信区间构造

Asymptotic Confidence Interval Construction of Proportion Ratio Based on Combined Unilateral and Bilateral Data

研究了单双边混合试验设计下2种治疗的治愈率之比的渐近置信区间构造问题。基于非独立模型下的单双边混合数据提出了Wald置信区间,基于Agresti-Coull方法的修正Wald置信区间,基于对数变换的置信区间,基于似然比检验的置信区间以及Bootstrap重抽样置信区间,通过模拟研究了各种置信区间的经验覆盖概率,经验区间宽度以及左、右非覆盖概率。结果表明:基于Agresti-Coull方法的修正Wald置信区间,基于对数变换的置信区间和Bootstrap重抽样置信区间即使在小样本下的经验覆盖概率都很接近置信水平,大样本下所提出的各种置信区间都有很好的覆盖性质;同时,基于对数变换的置信区间和Bootstrap重抽样置信区间具有对称的左右非覆盖概率,因而具有良好的区间位置。最后,耳科临床数据进一步验证了所提出方法的有效性。

In this article,we consider the asymptotic confidence interval(CI)construction for the ratio of cure rates of two treatments based on combined unilateral and bilateral data.Based on the dependence model,the Wald CI,the modified Wald CI based on Agresti-Coull method,the logtransformation-based CI,the CI based on likelihood ratio test and the Bootstrap-resampling CI are proposed.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 logtransformation-based CI and Bootstrap-resampling CI perform satisfactory in the sense that their ECPs are very close to the confidence level even under small sample size designs.Furthermore,the latter two confidence intervals also have satisfactory interval location in term of symmetric left and right noncoverage probabilities.A real data set from an otolaryngologic study is used to illustrate the proposed methods.