Statistical Powers of Some Tests for Checking Homogeneity of Survival Distributions with Disjointed Ends in the Presence of Censoring

Main Article Content

Babalola Bayowa Teniola
Adeleke Raphael Ayantunji
Halid Omobolaji Yusuf
Olubiyi Adenike Olufunmilola
Ogunsakin Ropo Ebenezer
Adigun Kehinde Abimbola
Adejuwon Samuel Oluwaseun
Adarabioyo Mumini Idowu
Ogunboyo Ojo Femi
Fadugba Sunday Emmanuel
Egbon Osafu Augustine
Akinyemi Oluwadare
Ogunwale Olukunle Daniel
Faweya Olanrewaju
Kawiso Martin


This paper considered the comparison of some tests for assessing the overall homogeneity of Kaplan-Meier survival curves under low and high censoring rates when the curves are disjointed towards the end. The performances of these tests were measured by their statistical powers. Monte Carlo simulation study was conducted to evaluate and numerically compare the relative performances of Log-rank,Wilcoxon, Tarone-Ware, Peto-Peto, Modified Peto-Peto, the Fleming-Harrington (1,1), and the Babalola-Adeleke tests. The result obtained shows that the Babalola-Adeleke and Fleming-Harrington (1,1) tests have more robust performances than the other five popular tests with relatively high power in detecting differences when the censoring rates in the groups are both low and high. The highest overall average powers under low and high censoring rates were produced by Babalola-Adeleke and Fleming-Harrington (1,1) tests respectively. Hence, these two tests are the most suitable tests for diagnosing homogeneity of survival curves under these conditions.

Article Details


  1. B.T. Babalola, R.E. Ogunsakin, O.A. Egbon, et al. A Simulation Based Comparative Study of Some Tests for Checking Homogeneity of Non-Crossing Survival Curves Under High Censoring Rates, J. Appl. Probab. Stat. 17 (2022), 87-99.
  2. J.C. Goldsack, A. Coravos, J.P. Bakker, et al. Verification, Analytical Validation, and Clinical Validation (V3): The Foundation of Determining Fit-For-Purpose for Biometric Monitoring Technologies (BioMeTs), Npj Digit. Med. 3 (2020), 55.
  3. J. Lepš, P. Šmilauer, Biostatistics with R: An Introductory Guide for Field Biologists, Cambridge University Press, Cambridge, (2020).
  4. K. Sumathi, D. Balakrishnan, V. Naveen, et al. Talent Flow Employee Analysis Based Turnover Prediction on Survival Analysis, Ann. Roman. Soc. Cell Biol. 25 (2021), 3844-3857.
  5. T. Saegusa, Z. Zhao, H. Ke, et al. Detecting Survival-Associated Biomarkers From Heterogeneous Populations, Sci Rep. 11 (2021), 3203.
  6. Z. Cai, Y. Wang, H. Cao, et al. Life Prediction of Self-Locking Nut for Aeroengine Based on Survival Analysis and Bayesian Network, in: 2020 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), IEEE, Singapore, Singapore, 2020: pp. 414–418.
  7. S. Nematolahi, S. Nazari, Z. Shayan, et al. Improved Kaplan-Meier Estimator in Survival Analysis Based on Partially Rank-Ordered Set Samples, Comput. Math. Methods Med. 2020 (2020), 7827434.
  8. B.T. Babalola, W.B. Yahya, Effects of Collinearity on Cox Proportional Hazard Model With Time Dependent Coefficients: A Simulation Study, J. Biostat. Epidemiol. 5(2020), 172-182.
  9. E. Ilker, A. Sulaiman, A. Rukayya, The Kaplan Meier Estimate in Survival Analysis, Biometrics Biostat. Int. J. 5 (2017), 00128.
  10. D.G. Kleinbaum, M. Klein, Survival Analysis a Self-Learning Text, Springer, New York, 44-66, (2005).
  11. C.J. Pelz, J.P. Klein, Analysis of Survival Data: A Comparison of Three Major Statistical Packages (SAS, SPSS and BMDP). Working paper (Medical College of Wisconsin, Milwaukee). Rep.17: 1-6. (1996).
  12. E.L. Kaplan, P. Meier, Nonparametric Estimation From Incomplete Observations, J. Amer. Stat. Assoc. 53 (1958), 457-481.
  13. J. Klein, J. Rizzo, M.-J. Zhang, N. Keiding, Statistical Methods for The Analysis and Presentation of the Results of Bone Marrow Transplants. Part I: Unadjusted analysis, Bone Marrow Transplant. 28 (2001), 909–915.
  14. E.T. Lee, J.W. Wang, Statistical Methods for Survival Data Analysis, John Wiley & Sons Inc. New Jersey, (2003).
  15. T.R. Fleming, D.P. Harrington, M. O’sullivan, Supremum Versions of the Log-Rank and Generalized Wilcoxon Statistics, J. Amer. Stat. Assoc. 82 (1987), 312–320.
  16. J.W. Lee, Some Versatile Tests Based on the Simultaneous Use of Weighted Log-Rank Statistics, Biometrics. 52 (1996), 721-725.
  17. S. Buyske, R. Fagerstrom, Z. Ying, A Class of Weighted Log-Rank Tests for Survival Data When the Event Is Rare, J. Amer. Stat. Assoc. 95 (2000), 249–258.
  18. R.E. Tarone, J. Ware, On Distribution-Free Tests for Equality of Survival Distributions, Biometrika. 64 (1977), 156–160.
  19. M.S. Pepe, T.R. Fleming, Weighted Kaplan-Meier Statistics: A Class of Distance Tests for Censored Survival Data, Biometrics. 45 (1989), 497-507.
  20. R.B. Latta, A Monte Carlo Study of Some Two-Sample Rank Tests With Censored Data, J. Amer. Stat. Assoc. 76 (1981), 713–719.
  21. M.S. Beltangady, R.F. Frankowski, Effect of Unequal Censoring on the Size and Power of the Logrank and Wilcoxon Types of Tests for Survival Data, Stat. Med. 8 (1989), 937–945.
  22. E. Letón, P. Zuluaga, Equivalence Between Score and Weighted Tests for Survival Curves, Commun. Stat. – Theory Methods. 30 (2001), 591–608.
  23. E. Letón, P. Zuluaga, Relationships Among Tests for Censored Data, Biom. J. 47 (2005), 377–387.
  24. A. Akbar, G.R. Pasha, Properties of Kaplan-Meier Estimator: Group Comparison of Survival Curves, Eur. J. Sci. Res. 32 (2009), 391–397.
  25. T. Jurkiewicz, E. Wycinka, Significance Tests of Differences Between Two Crossing Survival Curves for Small Samples. Acta Univ. Lodziensis Folia Oecon. 255 (2011), 114-119.
  26. P.C. Austin, Generating Survival Times to Simulate Cox Proportional Hazards Models With Time-Varying Covariates, Stat. Med. 31 (2012), 3946–3958.
  27. J. Wu, A New One-Sample Log-Rank Test, J. Biometrics Biostat. 05 (2014), 1000210.
  28. T.G. Karrison, Versatile Tests for Comparing Survival Curves Based on Weighted Log-Rank Statistics, Stata J. 16 (2016), 678–690.
  29. Z. Chen, G. Zhang, Comparing Survival Curves Based on Medians, BMC Med. Res. Methodol. 16 (2016), 33.
  30. P.G. Karadeniz, I. Ercan, Examining Tests for Comparing Survival Curves With Right Censored Data, Stat. Transition. New Ser. 18 (2017), 311–328.
  31. B.T. Babalola, R.A. Adeleke, O.Y. Halid, et al. Statistical Powers of an Alternative Test for Comparison of Survival Distributions With Crossed Survival Curves in the Presence of Censoring: A Simulation Study, Int. J. Civil Eng. Technol. 10 (2019), 366-379.
  32. M. Stevenson, An Introduction to Survival Analysis, EpiCentre, IVABS. Massey Massey University, (2009).
  33. X. Wang, F. Bai, H. Pang, et al. Bias-adjusted Kaplan–Meier Survival Curves for Marginal Treatment Effect in Observational Studies, J. Biopharmaceutical Stat. 29 (2019), 592–605.
  34. R.L.M.C. Martinez, J.D. Naranjo, A Pretest for Choosing Between Logrank And Wilcoxon Tests in the Two-Sample Problem, METRON. 68 (2010), 111–125.
  35. J. Xie, C. Liu, Adjusted Kaplan–Meier Estimator and Log-Rank Test With Inverse Probability of Treatment Weighting for Survival Data, Stat. Med. 24 (2005), 3089–3110.
  36. A. Winnett, P. Sasieni, Adjusted Nelson–Aalen Estimates With Retrospective Matching, J. Amer. Stat. Assoc. 97 (2002), 245–256.
  37. S. Galimberti, P. Sasieni, M.G. Valsecchi, A Weighted Kaplan-Meier Estimator for Matched Data With Application to the Comparison of Chemotherapy And Bone-Marrow Transplant in Leukaemia, Stat. Med. 21 (2002), 3847–3864.
  38. B.T. Babalola, R.A. Adeleke, O.Y. Halid, et al. An Alternative Test for Comparison of Survival Distributions With Proportional Hazard Functions in the Presence of Low Censoring Rates, J. Appl. Stat. Probab. 15 (2020), 61-75.
  39. X. Lin, Q. Xu, A New Method for the Comparison of Survival Distributions, Pharmaceut. Stat. 9 (2010), 67–76.
  40. J. Shanahan, A New Method for the Comparison of Survival Distributions, Master's Thesis, University of South Carolina, (2013).
  41. C. Dardis, Package "survMisc". (2018).
  42. H. Uno, L. Tian, B. Claggett, L.J. Wei, A Versatile Test for Equality of Two Survival Functions Based on Weighted Differences of Kaplan-Meier Curves, Stat. Med. 34 (2015), 3680–3695.
  43. R.G. Miller, Survival Analysis, John Wiley & Sons, Hoboken, 1981.
  44. S.H. Embury, L. Elias, P.H. Heller, et al. Remission Maintenance Therapy in Acute Myelogenous Leukaemia, Western J. Med. 126 (1977), 267-272.