In the linear regression model with normal errors the squared product-moment correlation provides the standard measure of dependence between the explanatory variable and the response variable. Using the concept of information gain, a measure of dependence can also be defined for more general regression models used in survival analysis, such as the Weibull regression model or Cox's proportional hazards model. Further, this measure of dependence can be conveniently estimated even when the response variable is subject to censoring, and a simple approximation is available.
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Kent et al. (1988) studied this question.
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