Study and applications of an informational measure of dependence in survival models

In survival models, when the factor of interest is a continuous variable or is expressed through a group of several variables, the classical measures of risk, i.e. relative risk and odds ratio, are not appropriate and there is no standard measure of dependence between survival and the considered factor. The Information Gain has been proposed by Linfoot (1957) and Kent (1983), giving any parametric model as a generalization of the squared product-moment correlation coefficient of the linear regression model with normal errors. By using simulation methods, we studied the statistical properties of the information gain as a measure of dependence, in the particular case of survival regression models. We suggest several efficient applications of this informational concept to some classical problems of regression analysis and prognostic analysis. Our ideas are illustrated through an example on the prognosis of idiopathic dilated cardiomyopathy.