The distribution of unobserved heterogeneity in competing risks models

We show that in a large class of proportional hazard competing risks models, the distribution of the bivariate frailty among survivors converges to a limiting distribution. This generalizes the result of Abbring and van den Berg (Biometrika 94(1):87-99, 2007), who show that in a single spell duration model, the frailty distribution converges to the gamma distribution. The resulting limiting distribution has an interpretation in terms of partition of a gamma distribution, and allows for both positive and negative correlation between the survival variables. This result provides a natural and flexible specification for the frailty in competing risks models.