We propose time-dependent association measures for application to bivariate survival analysis. Such association measures provide informative summaries for data on twins, ophthalmic and auditory studies, and for other matched-pair designs. We develop several desirable properties of time-dependent association measures and study three measures motivated by these properties. We examine the measures from a general bivariate survival perspective and for the proportional hazards frailty model. We use monozygotic (MZ) and dizygotic (DZ) twin data from the Danish Twin Registry to illustrate how these measures depend on the specification of the proportional hazards frailty model. This model consists of two components: A baseline hazard function and a frailty distribution. We produce gamma and nonparametric maximum likelihood estimates of the frailty distribution and estimate a Gompertz baseline hazard function. For two of the measures, a nonparametric estimate provides a comparison to the model-based estimates. As expected, the MZ twins display greater association at all ages, but the association measures give different insights into the association structure.
- Danish twins
- Local association
- Nonparametric maximum likelihood
- Proportional hazards frailty model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty