Explained variation in shared frailty models

Explained variation measures the relative gain in predictive accuracy when prediction based on prognostic factors replaces unconditional prediction. The factors may be measured on different scales or may be of different types (dichotomous, qualitative, or continuous). Thus, explained variation permits to establish a ranking of the importance of factors, even if predictive accuracy is too low to be helpful in clinical practice. In this contribution, the explained variation measure by Schemper and Henderson (2000) is extended to accommodate random factors, such as center effects in multicenter studies. This permits a direct comparison of the importance of centers and of other prognostic factors. We develop this extension for a shared frailty Cox model and provide an SAS macro and an R function to facilitate its application. Interesting empirical properties of the variation explained by a random factor are explored by a Monte Carlo study. Advantages of the approach are exemplified by an Austrian multicenter study of colon cancer.