  We describe a unified framework within which we can build survival models.
The motivation for this work comes from a study on the prediction of relapse
among breast cancer patients treated at the Curie Institute in Paris, France.
Our focus is on how to best code, or characterize, the effects of the
variables, either alone or in combination with others. We consider simple
graphical techniques that not only provide an immediate indication as to the
goodness of fit but, in cases of departure from model assumptions, point in the
direction of a more involved alternative model. These techniques help support
our intuition. This intuition is backed up by formal theorems that underlie the
process of building richer models from simpler ones. Goodness-of-fit techniques
are used alongside measures of predictive strength and, again, formal theorems
show that these measures can be used to help identify models closest to the
unknown non-proportional hazards mechanism that we can suppose generates the
observations. We consider many examples and show how these tools can be of help
in guiding the practical problem of efficient model construction for survival
data.
