Abstract
In animal carcinogenesis experiments or comparative clinical trials where the r groups correspond to increasing dosages of an agent or an increasing number of additional modalities and the primary outcome is time to a certain event (e.g., tumor occurrence, death) T, ordered alternatives of the form H1 : S1 ≤ S2 ≤ · · · ≤ Sr , where Si(t) = Pr (Ti > t) is the survival function for group are of special interest. Using the counting process formulation of the problem and generalizing earlier results, we show that the class of all two-sample weighted logrank statistics can be extended to test specifically for ordered alternatives. Ordered versions of the Gehan-Wilcoxon, unweighted logrank, and Peto–Prentice–Wilcoxon tests are investigated in detail. Asymptotic relative efficiencies under Lehmann and scale alternatives are evaluated analytically and numerically among these three tests and against Tarone's trend test (1975) for Weibull, gamma, and lognormal survival distributions. Effects of censoring and unequa...
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