8.4 Model building

Some guidelines for building a Cox model:

• decide in advance which covariates are of primary interest (in a trial, treatment) and which are adjustments; do not select the variable of interest by significance tests;
• for other covariates, use subject-matter knowledge first, then likelihood ratio tests or AIC; automatic stepwise selection gives over-optimistic \(p\)-values and unstable models;
• keep about \(10\) to \(20\) events per estimated coefficient; the veteran model’s \(6\) coefficients with \(128\) deaths is comfortable;
• check the functional form of continuous covariates (is the effect of age linear in the log hazard?) with splines or categories, and check proportional hazards (the next section).

A model’s ability to separate high-risk from low-risk subjects is measured by the concordance index \(C\): among pairs of subjects whose order of events can be determined, the proportion in which the subject with the higher predicted risk has the event first. \(C = 0.5\) is no better than chance and \(C = 1\) is perfect ordering; the veteran model has \(C = 0.737\), good discrimination for a clinical model.

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