(1) Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;(2) Department of Mathematics and Science, Stavanger University College, P.O.Box 2557 Ullandhaug, N-4091 Stavanger, Norway
Abstract:
A new approach for constructing tests for association between a random right censored life time variable and a covariate is proposed. The basic idea is to first arrange the observations in increasing order of the covariate and then base the test on a certain point process defined by the observation times. Tests constructed by this approach are robust against outliers in the covariate values or misspecification of the covariate scale since they only use the ordering of the covariate. Of particular interest is a test based on the Anderson-Darling statistic. This test has good power properties both against monotonic and nonmonotonic dependencies between the covariate and the life time variable.