Validation of prognostic indices using the frailty model

A major issue when proposing a new prognostic index is its generalisibility to daily clinical practice. Validation is therefore required. Most validation techniques assess whether "on average" the results obtained by the prognostic index in classifying patients in a new sample of patients are similar to the results obtained in the construction set. We introduce a new important aspect of the generalisibility of a prognostic index: the heterogeneity of the prognostic index risk group hazard ratios over different centers. If substantial variability between centers exists, the prognostic index may have no discriminatory capability in some of the centers. To model such heterogeneity, we use a frailty model including a random center effect and a random prognostic index by center interaction. Statistical inference is based on a Bayesian approach using a Laplacian approximation for the marginal posterior distribution of the variances of the random effects. We investigate different ways to summarize the information available from this marginal posterior distribution. Our approach is applied to a real bladder cancer database for which we demonstrate how to investigate and interpret heterogeneity in prognostic index effect over centers.