Survival model construction guided by fit and predictive strength

Survival model construction can be guided by goodness-of-fit techniques as well as measures of predictive strength. Here, we aim to bring together these distinct techniques within the context of a single framework. The goal is how to best characterize and code the effects of the variables, in particular time dependencies, when taken either singly or in combination with other related covariates. Simple graphical techniques can provide an immediate visual indication as to the goodness-of-fit but, in cases of departure from model assumptions, will point in the direction of a more involved and richer alternative model. These techniques appear to be intuitive. This intuition is backed up by formal theorems that underlie the process of building richer models from simpler ones. Measures of predictive strength are used in conjunction with these goodness-of-fit techniques 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. Illustrations from studies in breast cancer show how these tools can be of help in guiding the practical problem of efficient model construction for survival data.