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

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.