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Sample Size Calculation for Rank Tests Comparing K Survival Distributions

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Abstract

Rank tests, such as logrank or Wilcoxon rank sum tests, have been popularly used to compare survival distributions of two or more groups in the presence of right censoring. However, there has been little research on sample size calculation methods for rank tests to compare more than two groups. An existing method is based on a crude approximation, which tends to underestimate sample size, i.e., the calculated sample size has lower power than projected. In this paper we propose an asymptotically correct method and an approximate method for sample size calculation. The proposed methods are compared to other methods through simulation studies.

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References

  • O. O. Aalen, “Nonparametric inference for a family of counting processes,” Annals of Statistics vol. 6 pp. 701–726, 1978.

    Google Scholar 

  • S. Ahnn and S. J. Anderson, “Sample size determination for comparing more than two survival distributions,” Statistics in Medicine vol. 14 pp. 2273–2282, 1995.

    Google Scholar 

  • P. K. Andersen, O. Borgan, R. D. Gill, and N. Kidding, “Linear nonparametric tests for comparison of counting processes with application to censored survival data (with discussion),” International Statistical Review vol. 50 pp. 219–258, 1982.

    Google Scholar 

  • T. R. Fleming and D. P. Harrington, Counting Processes and Survival Analysis, Wiley: New York, 1991.

    Google Scholar 

  • E. A. Gehan, “A generalized Wilcoxon test for comparing arbitrarily single censored samples,” Biometrika vol. 52 pp. 203–223, 1965.

    Google Scholar 

  • S. L. George and M. M. Desu, “Planning the size and duration of a trial studying the time to some critical event,” Journal of Chronic Disease vol. 27 pp. 15–24, 1973.

    Google Scholar 

  • D. P. Harrington and T. R. Fleming, “A class of rank test procedures for censored survival data,” Biometrika vol. 69 pp. 133–143, 1982.

    Google Scholar 

  • G. E. Haynam, Z. Govindarajulu, and F. C. Leone, Tables of the Cumulative Non-Central Chi-Square Distribution. Case Statistical Laboratory, Publication No. 104, 1962.

  • E. L. Kaplan and P. Meier, “Nonparametric estimator from incomplete observations,” Journal of the American Statistical Association vol. 53 pp. 457–481, 1958.

    Google Scholar 

  • J. M. Lachin, “Introduction to sample size determination and power analysis for clinical trials,” Controlled Clinical Trials vol. 2 pp. 93–113, 1981.

    Google Scholar 

  • E. Lakatos, “Sample sizes based on the log-rank statistic in complex clinical trials,” Biometrics vol. 64 pp. 156–160, 1977.

    Google Scholar 

  • R. W. Makuch and R. M. Simon, “Sample size requirements for comparing time-to-failure among k treatment groups,” Journal of Chronic Disease vol. 35 pp. 861–867, 1982.

    Google Scholar 

  • R. Natarajan, B. W. Turnbull, E. H. Slate, and L. C. Clark, “A computer program for sample size and power calculations in the design of multi-arm and factorial clinical trials with survival time endpoints,” Computer Methods and Programs in Biomedicine vol. 49 pp. 137–147, 1996.

    Google Scholar 

  • W. Nelson, “Hazard plotting for incomplete failure data,” Journal of Quality Technology vol. 1 pp. 27–52, 1969.

    Google Scholar 

  • B. S. Pasternack and H. S. Gilbert, “Planning the duration of long-term survival time studies designed for accrual by cohorts,” Journal of Chronic Disease vol. 24 pp. 13–24, 1971.

    Google Scholar 

  • R. Peto and J. Peto, “Asymptotically efficient rank invariant test procedures (with discussion),” Journal of the Royal Statistical Society, Series A vol. 135 pp. 185–206, 1972.

    Google Scholar 

  • R. L. Prentice, “Linear rank tests with right censored data,” Biometrika vol. 65 pp. 167–179, 1978.

    Google Scholar 

  • W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing, Cambridge University Press: New York, 1980.

    Google Scholar 

  • D. A. Schoenfeld, “Sample size formula for the proportional hazards regression model,” Biometrics vol. 39 pp. 499–503, 1983.

    Google Scholar 

  • E. V. Slud, “Analysis of factorial survival experiments,” Biometrics vol. 50 pp. 25–38, 1994.

    Google Scholar 

  • R. E. Tarone and J. Ware, “On distribution-free tests for equality of survival distributions,” Biometrika vol. 64 pp. 156–160, 1977.

    Google Scholar 

  • N. A. Yateman and A. M. Skene, “Sample size for proportional hazards survival studies with arbitrary patient entry and loss to follow-up distributions,” Statistics in Medicine vol. 11 pp. 1103–1113, 1992.

    Google Scholar 

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Jung, SH., Hui, S. Sample Size Calculation for Rank Tests Comparing K Survival Distributions. Lifetime Data Anal 8, 361–373 (2002). https://doi.org/10.1023/A:1020518905233

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