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    题名: 存活模式中當某些共變量不可控時最適設計之探討
    其它题名: Optimal Design for Survival Models When Some Covariates Are Not Subject to Control
    作者: 丁兆平;陳麗霞
    贡献者: 國立政治大學統計學系
    行政院國家科學委員會
    关键词: 近似設計;設限資料;D-最適;等質定理;邊際設限設計;最適條件設計;存活模型
    Approximate designs;censored data;D-optimality;equivalence theorem;marginally restricted design;optimal conditional design;survival model
    日期: 2010
    上传时间: 2012-08-30 09:58:25 (UTC+8)
    摘要: 在存活模型(survival model)架構下，探討最適設計(optimal design)方面的研究，文 獻中甚為罕見。本研究計畫之目的即在探討，如何將最適設計之理論運用到存活分析 中，以增進存活分析中參數估計之效率(efficiency)。 本研究計畫囊括之模型為指數失敗時間(exponential failure time)和Weibull 失敗時 間。失敗時間之分配和共變量(covariates)以及未知參數間之關係是以某一線性模型 (linear model)呈現。共變量均為可控變數(controllable variable)之最適設計之研究，已有 文獻參考，然在實際情況中，某些共變量無法由實驗者所掌控之情形亦經常發生，這 些無法掌控之共變量之值，在實驗開始前是可觀察或可測量的。本研究計畫旨在研究 當這些無法掌控之共變量之值得知後，如何建立D-最適”條件”設計。 雖然共變量無法由實驗者所掌控之情形在實境中經常發生，但相關之文獻和研究卻 非常稀少，主因除問題本身之複雜度高之外，推導訊息矩陣(information matrix)可能遭 遇的數學上的困難，亦令人怯步。本研究計畫之第一年，我們將探討在資料為受限資 料(censored data)，模型為指數失敗時間，且某些共變量為不可控但邊際分配(marginal distribution)已知之情形下，最適條件設計之情形以及其建立之方法；第二年將著重於 探討Weibull 失敗時間，資料為完整或為受限，某些共變量亦為不可控且邊際分配已知 之情形下，最適條件設計之情形以及其建立之方法。
    The problem of investigating optimal designs for survival models has rarely been explored in the literature. The aim of this research project is to show how optimal design theory is applied to survival analysis such that the efficiency in parameter estimation can be improved. The models considered in this project include exponential failure time and Weibull failure time. The failure time distributions depend on the covariates and the unknown parameters through a linear model. Some of the covariates are not subject to control by the experimenter. These uncontrolled covariates, however, have known values before the experiment is performed. The objective is to construct approximate D-optimal conditional designs based on the values of the covariates when the design space is a product space. Despite of the urge to find optimal designs for survival model in real life experiments, research into this problem has received little attention. This is mainly due to the complexity of the problem itself and the difficulties in deriving the information matrix for the unknown parameters. We plan to proceed by studying the exponential failure time with censored data and the uncontrolled covariates with known marginal distribution in the first year. Weibull failure time with or with no censored data and the uncontrolled covariates with known marginal distribution will be investigated in the second year of this project.
    關聯: 基礎研究
    學術補助
    研究期間:9908~ 10007
    研究經費:331仟元
    数据类型: report
    显示于类别:[統計學系] 國科會研究計畫

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    99-2118-M-004-003.pdf328KbAdobe PDF2440检视/开启


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