Survival model construction guided by fit and predictive strength

TL;DR

This paper introduces a unified framework for constructing survival models that combines goodness-of-fit assessments with measures of predictive strength, supported by formal theorems and illustrated through practical examples.

Contribution

It presents novel graphical and formal techniques for building survival models that effectively balance fit and predictive power, guiding model selection and complexity.

Findings

Graphical techniques indicate model fit and suggest alternatives.

Formal theorems support model building from simple to complex.

Tools help identify models close to the true non-proportional hazards mechanism.

Abstract

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.