Signed-Rank Tests for Censored Matched Pairs

Abstract

I consider the problem of testing bivariate symmetry in matched-pair experiments where the observations are subject to univariate censoring. Thus the observable random variables are given by ( Y 1 , Y 2 ) and (δ 1 , δ 2 ), where Y j = min( X j , C ) and δ j = I ( X j ≤ C ) ( j = 1, 2). Here ( X 1 , X 2 ) is a random pair of partially observable lifetimes and C is a fixed or random censoring variable. The hypothesis to be tested is that ( X 1 , X 2 ) and ( X 2 , X 1 ) have the same distribution. Following Woolson and Lachenbruch (1980), I consider censored data generalizations of signed-rank tests such as the sign, signed Wilcoxon, and signed-normal scores tests. I derive the asymptotic distribution of these test statistics under fixed and contiguous alternatives. The efficiencies of the signed-rank tests are considered in a log-linear model and compared with efficiencies of the paired Prentice-Wilcoxon and log-rank tests.