title: Sample Size Considerations in Clinical Trials when Comparing Two Interventions using Multiple Co-Primary Binary Relative Risk Contrasts.
abstract: The effects of interventions are multi-dimensional. Use of more than one primary endpoint offers an attractive design feature in clinical trials as they capture more complete characterization of the effects of an intervention and provide more informative intervention comparisons. For these reasons, multiple primary endpoints have become a common design feature in many disease areas such as oncology, infectious disease, and cardiovascular disease. More specifically in medical product development, multiple endpoints are utilized as co-primary to evaluate the effect of the new interventions. Although methodologies to address continuous co-primary endpoints are well-developed, methodologies for binary endpoints are limited. In this paper, we describe power and sample size determination for clinical trials with multiple correlated binary endpoints, when relative risks are evaluated as co-primary. We consider a scenario where the objective is to evaluate evidence for superiority of a test intervention compared with a control intervention, for all of the relative risks. We discuss the normal approximation methods for power and sample size calculations and evaluate how the required sample size, power and Type I error vary as a function of the correlations among the endpoints. Also we discuss a simple, but conservative procedure for appropriate sample size calculation. We then extend the methods allowing for interim monitoring using group-sequential methods.
authors.affiliation: Biostatistics Group, Center for Product Evaluation, Pharmaceuticals and Medical Devices Agency, Japan ; Department of Mathematical Health Science, Osaka University Graduate School of Medicine, Japan.
authors.forename: Yuki
authors.initials: Y
authors.lastname: Ando
authors.affiliation: Office of Biostatistics and Data Management, National Cerebral and Cardiovascular Center, Japan ; Department of Innovative Clinical Trials and Data Sciences, Osaka University Graduate School of Medicine, Japan ; Department of Mathematical Health Science, Osaka University Graduate School of Medicine, Japan.
authors.forename: Toshimitsu
authors.initials: T
authors.lastname: Hamasaki
authors.affiliation: Department of Biostatistics and the Center for Biostatistics in AIDS Research, Harvard School of Public Health, USA.
authors.forename: Scott R
authors.initials: SR
authors.lastname: Evans
authors.affiliation: Office of Biostatistics and Data Management, National Cerebral and Cardiovascular Center, Japan ; Department of Innovative Clinical Trials and Data Sciences, Osaka University Graduate School of Medicine, Japan.
authors.forename: Koko
authors.initials: K
authors.lastname: Asakura
authors.affiliation: Department of Mathematical Sciences, Graduate School of Science and Technology, Hirosaki University, Japan.
authors.forename: Tomoyuki
authors.initials: T
authors.lastname: Sugimoto
authors.affiliation: Department of Biostatistics, Kyoto University School of Public Health, Japan.
authors.forename: Takashi
authors.initials: T
authors.lastname: Sozu
authors.affiliation: Department of Mathematical Health Science, Osaka University Graduate School of Medicine, Japan.
authors.forename: Yuko
authors.initials: Y
authors.lastname: Ohno
keywords: Co-primary endpoints; Conjunctive power; Group-sequential designs; Monte-Carlo simulation; Normal approximation; Type I error