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J Biopharm Stat. 2018;28(4):589-611. doi: 10.1080/10543406.2017.1372775. Epub 2017 Dec 1.

Sample size determination for the current strategy in oncology Phase 3 trials that tests progression-free survival and overall survival in a two-stage design framework.

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a Center for Research and Administration and Support , National Cancer Center , Chiba , Japan.
b Department of Information and Computer Technology, Graduate School of Engineering , Tokyo University of Science , Tokyo , Japan.
c Department of Biostatistics and Bioinformatics , The University of Tokyo , Tokyo , Japan.


The selection of progression-free survival (PFS) or overall survival (OS) as the most suitable primary endpoint (PE) in oncology Phase 3 trials is currently under intense debate. Because of substantial limitations in the single use of PFS (or OS) as the PE, trial designs that include PFS and OS as co-primary endpoints are attracting increasing interest. In this article, we report on the formulation of determining the sample size for a trial that sequentially tests PFS and OS by treating them as co-PEs. Using a three-component model of OS, the proposed method overcomes the drawbacks of an existing method that requires unreasonable assumption of the exponential distribution for OS, although the hazard function is nonconstant because effective subsequent therapy has prolonged postprogression survival in recent oncology trials. Alternative estimation method of hazard ratio for OS under a three-component mode is also discussed by checking the appropriateness of assuming proportionality of hazards for OS. In order to examine the performance of our proposed method, we performed three numerical studies using both simulated and actual data of cancer Phase 3 trials. We find that the proposed method preserves a prespecified target value of power with a feasible increment of trial scale.


copula; correlated endpoint; overall survival; progression-free survival; sample size

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