Li Hui-Qiong, Tang Nian-Sheng, Yi Jie-Yi
Department of Statistics, Yunnan University, No.2 Cuihu North Road, Kunming, 650091, China.
School of Statistics, Beijing Normal University, No. 19 XinJieKouWai St., HaiDian District, Beijing, China.
BMC Med Res Methodol. 2016 Mar 11;16:31. doi: 10.1186/s12874-016-0125-3.
Incomplete data often arise in various clinical trials such as crossover trials, equivalence trials, and pre and post-test comparative studies. Various methods have been developed to construct confidence interval (CI) of risk difference or risk ratio for incomplete paired binary data. But, there is little works done on incomplete continuous correlated data. To this end, this manuscript aims to develop several approaches to construct CI of the difference of two means for incomplete continuous correlated data.
Large sample method, hybrid method, simple Bootstrap-resampling method based on the maximum likelihood estimates (B 1) and Ekbohm's unbiased estimator (B 2), and percentile Bootstrap-resampling method based on the maximum likelihood estimates (B 3) and Ekbohm's unbiased estimator (B 4) are presented to construct CI of the difference of two means for incomplete continuous correlated data. Simulation studies are conducted to evaluate the performance of the proposed CIs in terms of empirical coverage probability, expected interval width, and mesial and distal non-coverage probabilities.
Empirical results show that the Bootstrap-resampling-based CIs B 1, B 2, B 4 behave satisfactorily for small to moderate sample sizes in the sense that their coverage probabilities could be well controlled around the pre-specified nominal confidence level and the ratio of their mesial non-coverage probabilities to the non-coverage probabilities could be well controlled in the interval [0.4, 0.6].
If one would like a CI with the shortest interval width, the Bootstrap-resampling-based CIs B 1 is the optimal choice.
在各种临床试验中，如交叉试验、等效性试验以及前后测试比较研究中，常常会出现数据不完整的情况。针对不完整配对二元数据，已经开发出了多种方法来构建风险差异或风险比的置信区间（CI）。但是，对于不完整的连续相关数据，相关研究较少。为此，本手稿旨在开发几种方法来构建不完整连续相关数据的两个均值之差的置信区间。
提出了大样本法、混合法、基于最大似然估计的简单Bootstrap重采样法（B1）和埃克博姆无偏估计法（B2），以及基于最大似然估计的百分位数Bootstrap重采样法（B3）和埃克博姆无偏估计法（B4），用于构建不完整连续相关数据的两个均值之差的置信区间。进行了模拟研究，以评估所提出的置信区间在经验覆盖概率、预期区间宽度以及近端和远端未覆盖概率方面的性能。
实证结果表明，基于Bootstrap重采样的置信区间B1、B2、B4在小到中等样本量的情况下表现令人满意，因为它们的覆盖概率可以在预先指定的名义置信水平附近得到很好的控制，并且它们的近端未覆盖概率与未覆盖概率的比率可以在区间[0.4, 0.6]内得到很好的控制。
如果希望得到区间宽度最短的置信区间，基于Bootstrap重采样的置信区间B1是最佳选择。
