An asymptotic analysis of the logrank test.
Copyright policy )An asymptotic analysis of the logrank test.
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.
- University of Michigan–Flint United States
- University of Michigan United States
Quality Control, Biometry, Sample Size Calculation, Science, Safety and Risk, Social Sciences, Unbalanced Versus Randomized Trials, Cox Regression, Statistics for Life Sciences, Applications of statistics to biology and medical sciences; meta analysis, Asymptotic U -Statistic, asymptotic U-statistic, Edgeworth expansion, Asymptotic properties of nonparametric inference, Health Sciences, Humans, Clinical Trials, Life Tables, General, Nonparametric hypothesis testing, Proportional Hazards Models, Edgeworth Expansion, clinical trials, Clinical Trials as Topic, Asymptotic properties of parametric tests, martingale, Statistics, Bias-corrected Adjustment, unbalanced versus randomized trials, Reliability, LeCam's Third Lemma, bias-corrected adjustment, Statistics and Numeric Data, Martingale, LeCam's third lemma, Linear Models, Medicine, simulations, sample size calculations, Operation Research/Decision Theory, Mathematics, Statistics for Business/Economics/Mathematical Finance/Insurance, Cox regression
Quality Control, Biometry, Sample Size Calculation, Science, Safety and Risk, Social Sciences, Unbalanced Versus Randomized Trials, Cox Regression, Statistics for Life Sciences, Applications of statistics to biology and medical sciences; meta analysis, Asymptotic U -Statistic, asymptotic U-statistic, Edgeworth expansion, Asymptotic properties of nonparametric inference, Health Sciences, Humans, Clinical Trials, Life Tables, General, Nonparametric hypothesis testing, Proportional Hazards Models, Edgeworth Expansion, clinical trials, Clinical Trials as Topic, Asymptotic properties of parametric tests, martingale, Statistics, Bias-corrected Adjustment, unbalanced versus randomized trials, Reliability, LeCam's Third Lemma, bias-corrected adjustment, Statistics and Numeric Data, Martingale, LeCam's third lemma, Linear Models, Medicine, simulations, sample size calculations, Operation Research/Decision Theory, Mathematics, Statistics for Business/Economics/Mathematical Finance/Insurance, Cox regression
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