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Comput Stat Data Anal. 2014 Jun 1;74:39-51.

Sample size determination for paired right-censored data based on the difference of Kaplan-Meier estimates.

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Department of Statistics, National Cheng Kung University, Tainan 70101, Taiwan.
Department of Applied Mathematics, National Chiayi University, Chiayi 60004, Taiwan.
Center for Quantitative Sciences, Vanderbilt University, Nashville, TN 37232, USA.


Sample size determination is essential to planning clinical trials. Jung (2008) established a sample size calculation formula for paired right-censored data based on the logrank test, which has been well-studied for comparing independent survival outcomes. An alternative to rank-based methods for independent right-censored data, advocated by Pepe and Fleming (1989), tests for differences between integrated weighted Kaplan-Meier estimates and is more sensitive to the magnitude of difference in survival times between groups. In this paper, we employ the concept of the Pepe-Fleming method to determine an adequate sample size by calculating differences between Kaplan-Meier estimators considering pair-wise correlation. We specify a positive stable frailty model for the joint distribution of paired survival times. We evaluate the performance of the proposed method by simulation studies and investigate the impacts of the accrual times, follow-up times, loss to follow-up rate, and sensitivity of power under misspecification of the model. The results show that ignoring the pair-wise correlation results in overestimating the required sample size. Furthermore, the proposed method is applied to two real-world studies, and the R code for sample size calculation is made available to users.


Kaplan-Meier statistic; Logrank test; hazard function; paired observation; positive stable frailty model

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