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Efficiency improvement in a class of survival models through model-free covariate incorporation. (English) Zbl 1279.62204
Summary: In randomized clinical trials, we are often concerned with comparing two-sample survival data. Although the log-rank test is usually suitable for this purpose, it may result in substantial power loss when the two groups have nonproportional hazards. In a more general class of survival models of S. Yang and R. Prentice [Biometrika 92, No. 1, 1–17 (2005; Zbl 1068.62102)], which includes the log-rank test as a special case, we improve model efficiency by incorporating auxiliary covariates that are correlated with the survival times. In a model-free form, we augment the estimating equation with auxiliary covariates, and establish the efficiency improvement using the semiparametric theories in [M. Zhang et al., Biometrics 64, No. 3, 707–715 (2008; Zbl 1170.62082)] and X. Lu and A. A. Tsiatis [Biometrika 95, No. 3, 679–694 (2008; Zbl 1437.62548)]. Under minimal assumptions, our approach produces an unbiased, asymptotically normal estimator with additional efficiency gain. Simulation studies and an application to a leukemia study show the satisfactory performance of the proposed method.

62N01 Censored data models
62G10 Nonparametric hypothesis testing
62P10 Applications of statistics to biology and medical sciences; meta analysis
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