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Suppose I have 1000 patients enrolled in a trial (assuming 1:1 randomization to Treatment and Control arms), and my objective is to estimate the number of events (e.g., overall survival) needed to have a test of power at least 0.8 under the assumption of alpha=0.05. I wonder if there are formulas there to use, and/or R package that performs such power/sample size analyses. Thank you!

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  • $\begingroup$ You also need to take the estimated effect of the treatment into consideration. $\endgroup$
    – JonB
    Sep 20 '15 at 19:46
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    $\begingroup$ This approach is a bit backward from standard practice. Usually the size of the study is the result of power calculations based on event probabilities, estimated treatment effects, and the participant accrual pattern. Here one is starting already with a sample size of 1000. What is the purpose of the proposed calculation, if the sample size is already known? $\endgroup$
    – EdM
    Sep 20 '15 at 23:37
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There are ways of calculating this, but not implemented in R as far as I know. A good read would be Therenay & Grambsch's book (the reference for the survival package), chapter 3.3 "Sample size". If you don't have access to this book, it references the following 3 papers:

  • D. A. Schoenfeld. Sample-size formula for the proportional-hazards regression model. Biometries, 39:499-503, 1983.
  • D. Schoenfeld. The asymptotic properties of nonparametrie tests for comparing survival distributions. Biometrika, 68:316-319, 1981.
  • D. Berstein and S. W. Lagakos. SampIe size and power determination for stratified clinical trials. J Stat. Comput. Simul., 8:65-73, 1978.
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    $\begingroup$ The R Hmisc package's cpower and spower functions help a bit. $\endgroup$ Sep 23 '15 at 11:57

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