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A class of rank test procedures for censored survival data. (English) Zbl 0532.62026
A class of linear rank statistics for the k-sample problem with right censored survival data is introduced. The class contains as special cases the well-known log rank test and a Wilcoxon’ type test due to R. Peto and J. Peto, Asymptotically efficient rank invariant test procedures. J. R. Stat. Soc., Ser. A 135, 185-206 (1972). Asymptotic normality of test statistics is established under the null hypothesis and asymptotic efficiencies of the tests involved for contiguous alternatives are established.
The proofs are based on martingale theory and employ recent results of R. D. Gill [Censoring and stochastic integrals. Mathematical Centre Tracts 124 (1980; Zbl 0456.62003)]. A class of distributions is found for which the proposed class of linear rank statistics has some optimality properties for detecting differences in location.
Reviewer: R.Helmers

MSC:
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62E20 Asymptotic distribution theory in statistics
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