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 (δ₁, δ₂), 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.

Key Words:

• Bivariate symmetry
• Censored data
• Paired-rank tests