Rank tests for association with right censored data

Abstract

SUMMARY Rank tests for association between a time variable and a continuous covariate, and between two time variables are given in the presence of censoring. In the first case, these tests are related to the semiparametric tests of Cox (1972) and Prentice (1978) but differ in that the covariate is replaced by a score computed from its rank. In the second case, the test statistic is again a simple inner product, which in the proportional hazards model reduces to the correlation between the two vectors of log rank scores. The loss of efficiency arising from incorrect score functions is also explored when there is no censoring.