Estimation of dependence measures and hazards from bivariate censored data.

摘要

Bivariate failure time data frequently arise in biomedical research when each study subject experiences two types of events or there exists natural or artificial pairing. Such data are often subject to either univariate or bivariate censoring.;While nonparametric estimation of bivariate survival function (Dabrowska, 1988; Prentice-Cai, 1992; Pruitt, 1991) is a useful analytical tool, bivariate hazard and density functions offer the prospect of more powerful inferences about the strength of association between survival outcomes. We discuss kernel estimation of the bivariate hazard function, density function, as well as some related time-dependent association measures, especially Oakes' odds ratio function (Oakes, 1989). To achieve better hazard estimation based on the mean integrated squared error (MISE), integrated squared error (ISE), and mean squared error (MSE) criteria, we develop three data-adaptive bandwidth selection procedures respectively; biased cross-validation, least-square cross-validation, and local bandwidth selector. Further, to adjust for the "edge effect" of bounded data, we discuss two approaches, the reflection and boundary kernel methods. These procedures are evaluated in a series of simulation studies.;An analytic tool perhaps more revealing and easier to understand in bivariate survival analysis is the use of time-dependent association measures. These functions marked by age or time provide a powerful means of detecting possible changes of survivorship across time. Frequently, estimation of such time-dependent measures is based on the density estimates. Therefore applying smoothing techniques to obtain nonparametric estimation of time dependent association measures, particularly the Oakes' odds ratio function, is the other focus of this dissertation.;The Classic Twin Method (Galton, 1887), i.e. studying both monozygotic (MZ) and dizygotic (DZ) twins is the underlying principle of our methods applied in population genetic research. By comparing the strength of association of MZ and DZ twins, we intend to draw inferences about possible genetic contributions to disease correlations among human beings. The Australian Twin Registry's appendectomy data are used for illustration.