Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 641-650 |
| Number of pages | 10 |
| Journal | Journal of the American Statistical Association |
| Volume | 87 |
| Issue number | 419 |
| DOIs | |
| State | Published - Sep 1992 |
| Externally published | Yes |
Bibliographical note
Funding Information:* Jon E. Anderson is Assistant Professor, Department of Statistics, University of Georgia, Athens, GA 30602. Thomas A. Louis is Professor and Head, Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455. Niels V. Holm is Associate Professor of Medical Genetics, University ofOdense, Denmark Dk-5000. Bent Harvald is Professor, Department of Medicine, Odense University Hospital, Odense, Denmark Dk-5000. This work was supported in part by NSF Grant DMS8702402, Sloan Foundation Grant 88-6-12, and National Institute on Aging Grant POIAG08761. The authors are indebted to deceased professor Mogens Hauge for his great and skillful management of the Danish Twin Registry, which has been a prerequisite of the twin materials validity. This work has been made possible by a grant from the Boel Foundation, Olga & Esper Boels Fond, Nr. Alsev, Denmark, to the Danish Twin Registry and by further research grants from KreeftensBekeempelse (The Danish Cancer Society) to N. V. Holm, including a research fellowship from the society. We thank Anatoli Yashin, an associate editor, and the referees for helpful suggestions.
Keywords
- Danish twins
- Local association
- Nonparametric maximum likelihood
- Proportional hazards frailty model