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研究生: 黃子恒
Tz-Heng Huang
論文名稱: 基於Copula 之貝氏方法的比較兩診斷測試之整合性分析
A Bayesian-copula-based approach for meta-analysis of studies comparing two diagnostic tests
指導教授: 孫立憲
Li-Hsien Sun
口試委員:
學位類別: 碩士
Master
系所名稱: 理學院 - 統計研究所
Graduate Institute of Statistics
論文出版年: 2022
畢業學年度: 110
語文別: 英文
論文頁數: 102
中文關鍵詞: 整合性分析貝氏方法耦合貝它二項式分布DIC可信區間診斷測試馬可夫鏈蒙地卡羅
外文關鍵詞: Meta-analysis, Bayesian approach, copula, beta-binomial distributions, DIC, credible interval, diagnostic test, MCMC
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  • 診斷研究的整合性分析已被廣泛用在生物醫學領域上,而基於Copula 之貝氏方法是被所提倡在比較兩診斷測試的整合性分析中,在控制異質性跟相關性下,我們使用四維度之Copula 模型來彙整診斷測試中的靈敏度跟特異度,特別地說,針對兩診斷測試中真陽性跟真陰性的人數,假設他們的邊際分布為貝它二項式的結構,以及藉由Copula方法來獲得聯合分布。其中,對於有興趣的參數,我們使用貝氏馬可夫鏈蒙地卡羅來做估計,最後,我們透過兩筆不同的診斷測試跟模擬研究來呈現所提出的方法。


    Meta-analysis of diagnostic studies is widely used in biomedical research. A Bayesiancopula-
    based approach is proposed for meta-analysis of studies comparing two diagnostic
    tests. We use a quadrivariate copula model to pool the sensitivities and specificities of the two diagnostic tests across studies while controlling heterogeneity and correlations. Specifically, the marginal distribution of the numbers of true positive and true negative for the two diagnostic tests of each study is assumed to be beta binomial and the joint distribution is then obtained via copula methods. The parameters of interest are
    estimated using the Bayesian MCMC approaches. We assess the performance of the proposed method by simulations and two different mata-analysis data.

    摘要 i Abstract ii 誌謝iii Contents iv List of Figures vi List of Tables ix 1 Introduction 1 2 Method and model 3 2.1 | Model description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 | Copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 | Gaussian copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 | Vine copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Bayesian inference 8 3.1 | Bayesian Gaussian copula . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 | Bayesian vine copula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 | Single component adaptive Metropolis (SCAM) algorithm . . . . . . . . . 10 3.4 | Bayesian diagnostic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4.1 | DIC principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4.2 | Gelman–Rubin diagnostic . . . . . . . . . . . . . . . . . . . . . . 14 4 Simulation study 16 4.1 | Hyperparameters setting . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 | Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Applications 30 5.1 | Type 2 diabetes data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2 | Echocardiography data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6 Conclusion and future work 54 Reference 56 Appendix 61 A.1 Codes of the Bayesian Gaussian copula model . . . . . . . . . . . . . . . . 61

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