A note on assessing agreement with 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 between bivariate survival times for a class of frailty models. Conditional on the frailty, bivariate survival times are assumed to be independent and follow a Weibull distribution. We present the analytic expressions for the concordance correlation coefficient (CCC) for various choices of frailty distributions. Furthermore, we develop a time-dependent CCC for measuring the agreement between survival times among subjects who survive beyond a specified time point. The temporal pattern in the time-dependent CCC is characterized for various frailty distributions to provide a better understanding of the agreement structure generated by different frailty models.