Daniels's association measures under right censoring

This paper considers extensions of the Daniels generalized measures of association (Daniels 1944) to censored data. A number of existing tests for the detection of association in the presence of right‐censoring (Gehan 1965; Efron 1967; Brown, Hollander and Korwar 1974; Weier and Basu 1980) are seen to be special cases of the Daniels coefficient under particular scoring schemes. The Daniels coefficient provides a very general framework for the construction of tests and a number of other scoring schemes, simplifying to give well known tests in the non‐censored case, are considered. In this paper we focus attention on tests which are, in some sense, non‐parametric with respect to both variables, i.e. the explanatory variable as well as the failure time variable, such a property, though, not necessarily implying rank invariance. Parametric tests can be seen to fit in with the same formulation although no exploration of this approach is given here. Moving away from the null hypothesis of no association, it is also possible to obtain population measures of association applicable to right censored data. These will not in general converge to their non‐censored equivalents although, for a large family of cases studied, they do come very close. We illustrate these findings by some simulations.