An Asymptotic Analysis of the Logrank Test |
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Authors: | Strawderman Robert L |
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Institution: | (1) Department of Biostatistics, University of Michigan, 1420 Washington Heights, Ann Arbor, MI, 48109-2029 |
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Abstract: | Asymptotic expansions for the null distribution of the logrank statistic and its distribution under local proportional hazards
alternatives are developed in the case of iid observations. The results, which are derived from the work of Gu (1992) and
Taniguchi (1992), are easy to interpret, and provide some theoretical justification for many behavioral characteristics of
the logrank test that have been previously observed in simulation studies. We focus primarily upon (i) the inadequacy of the
usual normal approximation under treatment group imbalance; and, (ii) the effects of treatment group imbalance on power and
sample size calculations. A simple transformation of the logrank statistic is also derived based on results in Konishi (1991)
and is found to substantially improve the standard normal approximation to its distribution under the null hypothesis of no
survival difference when there is treatment group imbalance.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | Asymptotic U-statistic bias-corrected adjustment clinical trials Cox regression Edgeworth expansion LeCam's Third Lemma martingale sample size calculation unbalanced versus randomized trials |
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