| This dissertation uses a linear model approach to a bivariate survival model with right-censoring in either or both components. When the marginal distributions of this model are specified up to Lehmann alternatives, various parametric, semi-parametric and non-parametric methods can be applied to estimate the parameter governing the association between the two survival times. I extend the model to include covariates. I show that when the postulated model has fewer covariates than the true model has, the estimation bias can be smaller with the bivariate model than with the univariate model. The bivariate model is more efficient than the univariate one since the parameters common to both components of the pair can be treated as nuisance parameters and excluded from the model. I establish a new bivariate model with time-dependent covariates and competing risks. Maximum likelihood optimization, special goodness-of-fit technique for censored data and Monte Carlo stimulation are used. Section VI is an application to the bivariate distribution with association of ages at the first marriages for pairs of sisters in the United States. The data are from the National Longitudinal Study of Youth Data from 1978 to 1988. Covariates such as presence of children, whether she was a student, whether she was employed, and the grade of education she completed when she was married are used. Several models are investigated. Results show that there is an association between sisters' ages at their first marriages. Women having children before marriage tend to delay their first marriages if their husbands are not the children's fathers, and women who are students or are employed tend to get married a little later. |
