A. R.2type measure of dependence for proportional hazards models

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Abstract
A measure of dependence for survival data was presented by Kent and O'Quigley (1988). The purpose of this present work is to show that an alternative, although less immediate specification of the problem, leads to great simplification and generality. This alternative specification is in fact more natural in the context of the semi-parametric proportional hazards regression. One consequence of this is that the alternative specification can imme diately accommodate time dependent covariates, a natural feature of the proportional hazards model and one that the Kent and O'Quigley specification was unable to deal with. This measure is invariant to monotonically increasing transformations on the time scale, such invariance being considered fundamental in the case of the regression coefficient β. Computational aspects involve only those quantities routinely calculated in a proportional hazards analysis. In practice our impressions are that the two measures will generally be close. A disadvantage of the alternative specification over the original Kent and O'Quigley one occurs with discrete covariates having few levels where the upper bound of the measure can be less than one. Nonetheless, for the ranges of values con sidered in the Kent and O'Quigley work, the two measures show good agreement. The new measure can be adapted to general forms of relative risk for survival models.

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