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Biometrika 1981 68(3):699-702; doi:10.1093/biomet/68.3.699
© 1981 by Biometrika Trust
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Miscllanea

Asymptotic relative efficiency of survival tests with covariates

CATHERINE HILL

Département de Statistique Médicale, Institut Gustave-Roussy Villejuif, France

Comparison of survival for two groups of patients when adjusting for covariates is a standard problem in clinical trials. In this paper the general life table models developed by Cox (1972) and the stratified log rank test (Mantel & Haenszel, 1959; Peto & Peto, 1972) are compared. An analytical expression and numerical results for the asymptotic relative efficiency of the two tests are given when there is no censoring. Stratification on the covariates is asymptotically as efficient as the test arising from Cox's model provided (i) there is no treatment effect, (ii) the covariates are balanced across treatment groups and (iii) the hypotheses underlying Cox's model are satisfied. However, if the proportional hazard model does not hold for the covariates then Cox's model leads to a biased estimate of the difference between the two treatments.

Key Words: Asymptotic efficiency • Covariate model • Proportional hazards • Survival data


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