Summary
Two commonly used tests for comparison of survival curves are the generalized Wilcoxon procedure of Gehan (1965) and Breslow (1970) and the logrank test proposed by Mantel (1966) and Cox (1972). In applications, the logrank test is often used after checking for validity of the proportional hazards (PH) assumption, with Wilcoxon being the fallback method when the PH assumption fails.
However, the relative performance of the two procedures depend not just on the PH assumption but also on the pattern of differences between the two survival curves. We show that the crucial factor is whether the differences tend to occur early or late in time. We propose diagnostics to measure early-or-late differences between two survival curves. We propose a pretest that will help the user choose the more efficient test under various patterns of treatment differences.
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References
Andersen, P. K., Borgan, O., Gill, R. D. and Keiding, N. (1993) Statistical Models Based on Counting Processes, Springer-Verlag, New York.
Bagdonavicius, V. B., Levuliene, R. J., Nikulin, M. S. and Zdorova-Cheminade, O. (2004) Tests for equality of survival distributions against non-location alternatives, Lifetime Data Analysis, 10(4), 445–460.
Bagdonavicius, V. B. and Nikulin, M. (2006) On goodness-of-fit tests for homogeneity and proportional hazards, Applied Stochastic Models in Business and Industry, 22, 607–619.
Bagdonavicius, V. B., Levuliene, R. J. and Nikulin, M. (2009) Testing absence of hazard rates crossing, Comptes Rendus de l’Academie des Sciences de Paris, 346(7—8), 445–450.
Beltangady, M. S. and Frankowski, R. F. (1989) Effect of unequal censoring on the size and power of the logrank and Wilcoxon types of tests for survival data, Statistics in Medicine, 8(8), 937–945.
Breslow, N. (1970) A generalized Kruskal-Wallis test for comparing K samples subject to unequal patterns of censorship, Biometrika, 57(3), 579–594.
Cox, D. R. (1972) Regression Models and Life-tables (with discussion), Journal of the Royal Statistical Society, 34(2), 187–220.
Gehan, E. A. (1965) A Generalized Wilcoxon Test for Comparing Arbitrarily Singly-Censored Samples, Biometrika, 52(1/2), 203–223.
Hess, K. (1995) Graphical Methods for Assessing Violations of the Proportional Hazards Assumption in Cox Regression, Statistics in Medicine, 14, 1707–1723.
Hogg, R. V., Fisher, D. M. and Randles, R. H. (1975) A Two-Sample Adaptive Distribution-Free Test, Journal of the American Statistical Association, 70(351), 656–661.
Kalbfleisch, J. D. and Prentice, R. L. (1980) The Statistical Analysis of Failure Time Data, John Wiley and Sons Inc., New York.
Klein, J. P. and Moeschberger, M. L. (1997) Survival Analysis, Springer, New York.
Lee, E. T., Desu, M. M. and Gehan, E. A. (1975) A Monte Carlo Study of the Power of Some Two-Sample Tests, Biometrika, 62(2), 425–432.
Lehmann, E. L. (1953) The power of rank tests, Ann. Math. Statist., 24, 23–43.
Leton, E. and Zuluaga P. (2001) Equivalence between score and weighted tests for survival curves, Communications in Statistics: Theory and Methods, 30, 591–608.
Leton, E. and Zuluaga P. (2005) Relationships among tests for censored data, Biometrical Journal, 47, 377–387.
Mantel, N. (1967) Evaluation of survival data and two new rank order statistics arising in its consideration, Cancer Chemotherapy Rep., 50, 163–170.
Peto, R. (1972) Rank tests of maximum power against Lehmann type alternatives, Biometrika, 59, 472–474.
Peto, R. and Peto, J. (1972) Asymptotically efficient rank invariant test procedures, Journal of the Royal Statistical Society, Series A (General) 135(2), 185–207.
Prentice, R. L. and Marek, P. (1979) A qualitative discrepancy between censored data rank tests, Biometrics, 35, 861–867.
Shen, W. and Le, C. T. (2000) Linear rank tests for censored survival data, Communication in Statistics-Simulation and Computation, 29(1), 21–36.
Stablein, D. M. and Koutrouvelis, I. A. (1985) A two sample test sensitive to crossing hazards in uncensored and singly censored survival data, Biometrics, 41, 643–652.
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Martinez, R.L.M.C., Naranjo, J.D. A pretest for choosing between logrank and wilcoxon tests in the two-sample problem. METRON 68, 111–125 (2010). https://doi.org/10.1007/BF03263529
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DOI: https://doi.org/10.1007/BF03263529