研究期間：10108~10207;Recent scientific interest has been shifted to analysis of data under complex sampling schemes, such as doubly-truncated data and multivariate competing risks data that appear in epidemiology, astronomy, biology and industrial reliability. In statistical analysis of doubly-truncated data (or multivariate competing risks data), one often needs to take into account the dependency among truncation variables (or dependency among multivariate competing risks variables). As demonstrated in this NSC proposal, both double truncation and multivariate competing risks are frequently seen in real-world applications; the latter appears in a experimental design for analyzing the time-to-metamorphosis of multiple larvae of a frog grown in a cage. Due to its wide applications, inference methods for doubly-truncated data and multivariate competing risks data have received increasing attentions in recent years. There are many open problems with doubly truncated data and multivariate competing risks data that had been ignored in the literature. My previous work considered dependently-truncated data and bivariate censored data, which would provide the basis for studying doubly-truncated data and bivariate competing risks data, respectively. The two-year research plan will be divided into three stages: (a) Developing multivariate parametric models and Archimedean copula (AC) models that provide mathematically tractable and practically important parameters (e.g., cross-odds ratio, Kendall’s tau) to describe the dependence in doubly truncated data and in multivariate competing risks data. (b) Derive a powerful independence test for doubly-truncated data under the multivariate Archimedean copula models developed in (a). (c) Develop a semi-parametric inference method for multivariate competing risks data, utilizing the recent advancement in multivariate Archimedean copula models (e.g., Genest et al.) and the results of (a). We focus on the case that multivariate competing risk failures have exchangeable structure for which the Archimedean copula structure fits naturally.
