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Biom J. 2017 Jul;59(4):703-731. doi: 10.1002/bimj.201600026. Epub 2016 Oct 19.

Interim evaluation of efficacy or futility in group-sequential trials with multiple co-primary endpoints.

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Department of Data Science, National Cerebral and Cardiovascular Center, Suita, Osaka, 565-8565, Japan.
Department of Innovative Clinical Trials and Data Science, Osaka University Graduate School of Medicine, Suita, Osaka, Japan.
Center for Biostatistics in AIDS Research, Department of Biostatistics, Harvard T. H. Chan School of Public Heath, Boston, MA, 02115, USA.


We discuss group-sequential designs in superiority clinical trials with multiple co-primary endpoints, that is, when trials are designed to evaluate if the test intervention is superior to the control on all primary endpoints. We consider several decision-making frameworks for evaluating efficacy or futility, based on boundaries using group-sequential methodology. We incorporate the correlations among the endpoints into the calculations for futility boundaries and sample sizes as a function of other design parameters, including mean differences, the number of analyses, and efficacy boundaries. We investigate the operating characteristics of the proposed decision-making frameworks in terms of efficacy/futility boundaries, power, the Type I error rate, and sample sizes, while varying the number of analyses, the correlations among the endpoints, and the mean differences. We provide an example to illustrate the methods and discuss practical considerations when designing efficient group-sequential designs in clinical trials with co-primary endpoints.


Error-spending method; Futility; Multiple endpoints; Nonbinding boundary; Type I and Type II error adjustments

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