Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):543-551; doi:10.1093/biomet/asm060
Copyright © 2007 Biometrika Trust
Articles |
The weighted log-rank class of permutation tests: P-values and confidence intervals using saddlepoint methods
Ain Shams University, Cairo, Egypt
Department of Statistical Science Southern Methodist University, Dallas, Texas 75275, U.S.A.
ehab{at}ASUnet.shams.edu.eg
rbutler{at}smu.edu
Received for publication 1 September 2005. Revision received 1 December 2006.
Test statistics from the weighted log-rank class are commonly used to compare treatment with control when there is right censoring. This paper uses saddlepoint methods to determine mid-p-values from the null permutation distributions of tests from the weighted log-rank class. Analytical saddlepoint computations replace the permutation simulations and provide mid-p-values that are virtually exact for all practical purposes. The speed of these saddlepoint computations makes it practicable to invert the weighted log-rank tests to determine nominal 95% confidence intervals for the treatment effect with right-censored data. Such analytical inversions lead to permutation confidence intervals that are easily computed and virtually identical to the exact intervals that would normally require massive amounts of simulation.
Key Words: Linear rank test • Log-rank test • Mid-p-value • Permutation distribution • Saddlepoint approximation • Weighted log-rank class
References
-
Agresti A. A survey of exact inference for contingency tables. Statist. Sci. (1992) 7:131–53.
Booth J. G., Butler RW. Randomization distributions and saddlepoint approximations in generalized linear models. Biometrika (1990) 77:787–96.
Box G. E. P, Anderson S. L. Permutation theory in the derivation of robust criteria and the study of departures from assumption (with Discussion). J. R. Statist. Soc. (1955) B 17:1–34.
Butler R. W. Saddlepoint Approximations with Applications (2007) Cambridge: Cambridge University Press.
Cox D. R. The regression analysis of binary sequences (with Discussion). J. R. Statist. Soc. (1958) B 20:215–42.
Daniels H. E. Discussion of a paper by G.E.P. Box and S.L. Anderson. J. R. Statist. Soc. (1955) B 17:27–8.
Daniels H. E. Discussion of a paper by D.R. Cox. J. R. Statist. Soc. (1958) B 20:236–8.
Davison A. C., Hinkley D. V. Saddlepoint approximations in resampling methods. Biometrika (1988) 75:417–31.
Davison A. C., Wang S. Saddlepoint approximations as smoothers. Biometrika (2002) 89:933–8.
Fleming T., Harrington D. P. A class of hypothesis tests for one and two samples censored survival data. Commun. Statist. (1981) A 10:763–94.
Garthwaite P. H. Confidence intervals from randomization tests. Biometrics (1996) 52:1387–93.[CrossRef][ISI]
Gehan E. A. A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika (1965) 52:203–23.
Heller G., Venkatraman E. S. Resampling procedures to compare two survival distributions in the presence of right censored data. Biometrics (1996) 52:1204–13.[CrossRef][ISI]
Henrici P. Applied and Computational Complex Analysis. Vol. 2. Special Functions-Integral Transforms-Asymptotics-Continued Fractions (1977) New York: Wiley.
Kalbfleisch J. D., Prentice R. L. The Statistical Analysis of Failure Time Data (2002) 2nd ed. New York: Wiley.
Kim D., Agresti A. Improved exact inference about conditional association in three-way contingency tables. J. Am. Statist. Assoc. (1995) 90:632–9.[CrossRef][ISI]
Peto R., Peto J. Asymptotically efficient rank invariant test procedures. J. R. Statist. Soc. (1972) A 135:185–206.
Pierce D. A., Peters D. Practical use of higher order asymptotics for multiparameter exponential families (with Discussion). J. R. Statist. Soc. (1992) B 54:701–37.
Pike M. C. A method of analysis of a certain class of experiments in carcinogenesis. Biometrics (1966) 22:142–61.[CrossRef][ISI][Medline]
Prentice R. L. Linear rank tests with right censored data. Biometrika (1978) 65:167–79.
Robinson J. Saddlepoint approximations for permutation tests and confidence intervals. J. R. Statist. Soc. (1982) B 44:91–101.
Routledge R. D. Practicing safe statistics with the mid-p. Can. J. Statist. (1994) 22:103–10.[CrossRef]
Skovgaard I. M. Saddlepoint expansions for conditional distributions. J. Appl. Prob. (1987) 24:875–87.[CrossRef][ISI]
Tarone R., Ware J. On distribution-free tests for equality of survival distributions. Biometrika (1977) 64:156–60.
Tritchler D. On inverting permutation tests. J. Am. Statist. Assoc. (1984) 79:200–7.[CrossRef][ISI]
CiteULike 
Connotea 
Del.icio.us What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||||