Exploring the Clustering Effect of the Frailty Survival Model by Means of the Brier Score

In this article, the Brier score is used to investigate the importance of clustering for the frailty survival model. For this purpose, two versions of the Brier score are constructed, i.e., a “conditional Brier score” and a “marginal Brier score.” Both versions of the Brier score show how the clustering effects and the covariate effects affect the predictive ability of the frailty model separately. Using a Bayesian and a likelihood approach, point estimates and 95% credible/confidence intervals are computed. The estimation properties of both procedures are evaluated in an extensive simulation study for both versions of the Brier score. Further, a validation strategy is developed to calculate an internally validated point estimate and credible/confidence interval. The ensemble of the developments is applied to a dental dataset.