Implementation of complex interactions in a Cox regression framework

The standard Cox proportional hazards model has been extended by
functionally describable interaction terms. The first of which are
related to neural networks by adopting the idea of transforming
sums of weighted covariables by means of a logistic function. A
class of reasonable weight combinations within the logistic
transformation is described. Apart from the standard covariable
product interaction, a product of logistically transformed
covariables has also been included in the analysis of performance
of the new terms. An algorithm combining likelihood ratio tests and
AIC criterion has been defined for model choice. The critical
values of the likelihood ratio test statistics had to be corrected
in order to guarantee a maximum type I error of 5% for each
interaction term. The new class of interaction terms allows
interpretation of functional relationships between covariables with
more flexibility and can easily be implemented in standard software
packages.