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Biostatistics. 2013 Jul;14(3):409-21. doi: 10.1093/biostatistics/kxs057. Epub 2013 Jan 10.

A logrank test-based method for sizing clinical trials with two co-primary time-to-event endpoints.

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  • 1Department of Mathematical Sciences, Hirosaki University Graduate School of Science and Technology, 3 Bunkyocho, Hirosaki, Aomori 036-8561, Japan.


We discuss sample size determination for clinical trials evaluating the joint effects of an intervention on two potentially correlated co-primary time-to-event endpoints. For illustration, we consider the most common case, a comparison of two randomized groups, and use typical copula families to model the bivariate endpoints. A correlation structure of the bivariate logrank statistic is specified to account for the correlation among the endpoints, although the between-group comparison is performed using the univariate logrank statistic. We propose methods to calculate the required sample size to compare the two groups and evaluate the performance of the methods and the behavior of required sample sizes via simulation.


Bivariate dependence; Censored data; Copula model; Logrank statistic; Power

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