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Biometrika Advance Access originally published online on August 5, 2007
Biometrika 2007 94(3):543-551; doi:10.1093/biomet/asm060
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Copyright © 2007 Biometrika Trust

Articles

The weighted log-rank class of permutation tests: P-values and confidence intervals using saddlepoint methods

Ehab F. Abd-Elfattah

Ain Shams University, Cairo, Egypt

Ronald W. Butler

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.
  Abstract

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


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