SIMPLE-TREE WEIGHTED LOGRANK TESTS FOR RIGHT-CENSORED DATA

YUH-ING CHEN

Graduate Institute of Statistics, National Central University, Chung-Li, Taiwan 320, R.O.C.

(Received May 27, 1996; revised April 15, 1997)

Abstract. In this paper we are concerned with the problem of testing against the simple-tree alternative that there is at least one treatment more effective than the control when data are subject to random right-censorship. A class of tests based on linear combinations of two-sample weighted logrank statistics each comparing an individual treatment with the control is proposed. Asymptotic relative efficiencies of the simple-tree versions of Gehan-Wilcoxon, logrank and Peto-Prentice-Wilcoxon under Lehmann and scale alternatives are evaluated for various combinations of survival distributions and censoring probabilities. The results of a Monte Carlo level and power study are presented. An illustrated numerical example is also reported.

Key words and phrases: Asymptotic relative efficiency, right-censored data, simple-tree alternative.