Confidence intervals construction for difference of two means with incomplete correlated data.

Hui-Qiong Li,Nian-Sheng Tang,Jie-Yi Yi

doi:10.1186/s12874-016-0125-3

Hui-Qiong Li, Nian-Sheng Tang + Show 1 more

Open Access

https://doi.org/10.1186/s12874-016-0125-3

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Abstract

BackgroundIncomplete 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.MethodsLarge sample method, hybrid method, simple Bootstrap-resampling method based on the maximum likelihood estimates (B1) and Ekbohm’s unbiased estimator (B2), and percentile Bootstrap-resampling method based on the maximum likelihood estimates (B3) and Ekbohm’s unbiased estimator (B4) 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.ResultsEmpirical results show that the Bootstrap-resampling-based CIs B1, B2, B4 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].ConclusionsIf one would like a CI with the shortest interval width, the Bootstrap-resampling-based CIs B1 is the optimal choice.

Highlights

Incomplete data often arise in various clinical trials such as crossover trials, equivalence trials, and pre and post-test comparative studies
Inspired by [16–19], we develop several confidence interval (CI) for the difference of two means with incomplete correlated data under the missing completely at random (MCAR) assumption based on the large sample method, hybrid method and Bootstrap-resampling method
To investigate the performance of the proposed CIs under the assumption σ12 = σ22 = σ 2, we calculate the corresponding results for T3, T4, T5, hybrid CIs, Bootstrapresampling-based CIs when σ 2 = 4 and (n, n1, n2) = (5, 5, 2), which are given in Tables 9, 10 and 11

Summary

Introduction

Incomplete data often arise in various clinical trials such as crossover trials, equivalence trials, and pre and post-test comparative studies. Incomplete data often arise in various research fields such as crossover trials, equivalence trials, and pre and post-test comparative studies. 212) designed a crossover clinical trial to measure the onset of action of two doses of formoterol solution aerosol: 12 ug and 24 ug. For the above crossover clinical trial, our main interest is to test the equivalence between 12 ug and 24 ug formoterol solution aerosols with respect to the FEV1 value. To this end, we can construct a (1 − α)100 % confidence interval for the

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