A note on assessing agreement for frailty models

Assessing agreement is often of interest in biomedical sciences to evaluate the similarity of measurements produced by different raters or methods on the same subjects. We investigate the agreement structure for a class of frailty models that are commonly used for analyzing correlated survival outcomes. Conditional on the shared frailty, bivariate survival times are assumed to be independent with Weibull baseline hazard distribution. We present the analytic expressions for the concordance correlation coefficient (CCC) for several commonly used frailty distributions. Furthermore, we develop a time-dependent CCC for measuring agreement between survival times among subjects who survive beyond a specified time point. We characterize the temporal pattern in the time-dependent CCC for various frailty distributions. Our results provide a better understanding of the agreement structure implied by different frailty models.