相依截切資料的統計推論

Abstract

In this dissertation, we investigate the dependent relationship between two failure time variables which have a truncation relationship. Chaieb et al. (2006) considered semi-parametric framework under a “semi-survival” Archimedean-copula assumption and proposed estimating functions to estimate the association parameter, the truncation probability and the marginal functions. In the first project, we adopt the same model assumption but propose different estimating methods. In particular we extend Clayton’s conditional likelihood approach (1978) to dependent truncation data for estimation of the association parameter. For marginal estimation, we propose a recursive algorithm and derive explicit formula to obtain the solution. The functional delta method is applied to establish large sample properties which can handle more general estimating functions than the U-statistic approach. Simulations are performed and the proposed methods are applied to the transfusion-related AIDS data for illustrative purposes. Quasi-independence has been assumed by many inference methods for analyzing truncation data. By forming a series of tables, we also propose a weighted log-rank statisitcs for testing this assumption, which is our second project. Power improvement is possible by choosing an appropriate weight function. Here, we derive score tests when the dependence structure under the alternative hypothesis is specified semiparametrically. Asymptotic analysis and simulations are used to justify our proposed methods.

In this dissertation, we investigate the dependent relationship between two failure time variables which have a truncation relationship. Chaieb et al. (2006) considered semi-parametric framework under a “semi-survival” Archimedean-copula assumption and proposed estimating functions to estimate the association parameter, the truncation probability and the marginal functions. In the first project, we adopt the same model assumption but propose different estimating methods. In particular we extend Clayton’s conditional likelihood approach (1978) to dependent truncation data for estimation of the association parameter. For marginal estimation, we propose a recursive algorithm and derive explicit formula to obtain the solution. The functional delta method is applied to establish large sample properties which can handle more general estimating functions than the U-statistic approach. Simulations are performed and the proposed methods are applied to the transfusion-related AIDS data for illustrative purposes. Quasi-independence has been assumed by many inference methods for analyzing truncation data. By forming a series of tables, we also propose a weighted log-rank statisitcs for testing this assumption, which is our second project. Power improvement is possible by choosing an appropriate weight function. Here, we derive score tests when the dependence structure under the alternative hypothesis is specified semiparametrically. Asymptotic analysis and simulations are used to justify our proposed methods.