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Stat Med. 2014 Jul 30;33(17):2897-913. doi: 10.1002/sim.6154. Epub 2014 Mar 27.

Sample size determination in group-sequential clinical trials with two co-primary endpoints.

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Department of Biomedical Statistics, Osaka University Graduate School of Medicine, Osaka, Japan; Office of Biostatistics and Data Management, Research and Development Initiative Center, National Cerebral and Cardiovascular Center, Osaka, Japan.


We discuss sample size determination in group-sequential designs with two endpoints as co-primary. We derive the power and sample size within two decision-making frameworks. One is to claim the test intervention's benefit relative to control when superiority is achieved for the two endpoints at the same interim timepoint of the trial. The other is when superiority is achieved for the two endpoints at any interim timepoint, not necessarily simultaneously. We evaluate the behaviors of sample size and power with varying design elements and provide a real example to illustrate the proposed sample size methods. In addition, we discuss sample size recalculation based on observed data and evaluate the impact on the power and Type I error rate.


Cui-Hung-Wang statistics; Type I error; average sample number; co-primary endpoints; conditional power; group-sequential methods; maximum sample size; sample size recalculation

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