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Tests for comparing estimated survival functions. (English) Zbl 1334.62164

Summary: We describe a class of statistical tests for the comparison of two or more survival curves, typically estimated using the Kaplan-Meier method. The class is based on the construction of the second author [ibid. 90, No. 3, 577–584 (2003; Zbl 1436.62473)], and some special cases are of particular interest. Underlying the inferential development are the arguments of B. Efron and D. V. Hinkley [ibid. 65, 457–487 (1978; Zbl 0401.62002)], leading to a theoretical sampling model that is in some sense closer to the observed data. The log-rank and weighted log-rank tests arise as special members of the class. In practice the log-rank test will often be a suboptimal, even poor, test due to the presence of non-proportional hazards. The proposed test maintains good power and, in all the cases considered, has greater power than the log-rank test under non-proportional hazards. The power will depend on the alternatives being considered, and under reasonable assumptions on the alternatives, we conclude that the proposed test is more powerful than the log-rank test. Simulations support these conclusions. An example is given as an illustration.

MSC:

62N03 Testing in survival analysis and censored data
62G05 Nonparametric estimation
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
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