A Flexible Copula Model for Bivariate Survival Data

Thesis (Ph.D.)--University of Rochester. School of Medicine & Dentistry. Dept. of Biostatistics and Computational Biology, 2012.Copulas are bevariate distributions with uniform marginals. They provide a general method for binding several univariate marginal distributions together to form a multivariate distribution. Following Clayton (1978), several families of single-parameter copula models have been proposed for analyzing survival data. This dissertation explores the use of a flexible two-parameter copula family for bivariate survival data. The two parameters reflect respectively lower and upper tail dependence, allowing these two important aspects of a bivariate distribution to be modeled separately. The basic properties of this family are described and investigated. Under parametric assumptions on the univariate marginals, besides the commonly used one-stage M.L.E., a two-stage parametric estimator is developed for the dependence parameters. In addition we study a semi-parametric generalization of the two-stage approach in which the two marginal distributions are estimated nonparametrically. The asymptotic properties of all proposed estimators are derived and finite sample properties under different censorship scenarios are assessed by simulation. We find that the one-stage and two-stage parametric estimators perform similarly, with somewhat lower variances than the two-stage semi-parametric estimator. Robustness of the parametric estimator to the specification of the marginals is explored. We also design and implement a goodness-of-fit test for model checking, and a model selection test for choosing the best model among commonly used copula families. The practical application of the proposed two-parameter model is illustrated through a data example