Group-sequential logrank methods for trial designs using bivariate non-competing event-time outcomes

  • Tomoyuki SugimotoEmail author
  • Toshimitsu Hamasaki
  • Scott R. Evans
  • Susan Halabi


We discuss the multivariate (2L-variate) correlation structure and the asymptotic distribution for the group-sequential weighted logrank statistics formulated when monitoring two correlated event-time outcomes in clinical trials. The asymptotic distribution and the variance–covariance for the 2L-variate weighted logrank statistic are derived as available in various group-sequential trial designs. These methods are used to determine a group-sequential testing procedure based on calendar times or information fractions. We apply the theoretical results to a group-sequential method for monitoring a clinical trial with early stopping for efficacy when the trial is designed to evaluate the joint effect on two correlated event-time outcomes. We illustrate the method with application to a clinical trial and describe how to calculate the required sample sizes and numbers of events.


Bivariate dependence Error-spending method Independent censoring Logrank statistic Non-fatal events Normal approximation 



We thank one reviewer and the Associate Editor for their comments. Research reported in this publication was supported by JSPS KAKENHI Grant Numbers JP17K00054 and JP17K00069, the Project Promoting Clinical Trials for Development of New Drugs (18lk0201061h0002/18lk0201061h0202) from the Japan Agency for Medical Research and Development (AMED) and the National Institute of Allergy and Infectious Diseases of the National Institutes of Health under Award Number UM1AI068634. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.


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Authors and Affiliations

  1. 1.Graduate School of Data ScienceShiga UniversityHikoneJapan
  2. 2.Department of Data ScienceNational Cerebral and Cardiovascular CenterSuitaJapan
  3. 3.Epidemiology and Biostatistics and the Center for BiostatisticsGeorge Washington UniversityRockvilleUSA
  4. 4.Department of Biostatistics and BioinformaticsDuke University School of MedicineDurhamUSA

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