基於Copula 之貝氏方法的比較兩診斷測試之整合性分析

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：61

、訪客IP：18.220.160.216

姓名

黃子恒(Tz-Heng Huang) 查詢紙本館藏

畢業系所

統計研究所

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)

相關論文

★ Credit Risk Illustrated under Coupled diffusions	★ The analysis of log returns using copula-based Markov models
★ Systemic risk with relative behavior	★ 在厚尾分配下的均值收斂交易策略
★ Comparison of Credit Risk in Coupled Diffusion Model and Merton′s Model	★ Estimation in copula-based Markov mixture normal model
★ 金融系統性風險的回顧分析	★ New insights on ′′A semi-parametric model for wearable sensor-based physical activity monitoring data with informative device wear"
★ A parametric model for wearable sensor-based physical activity monitoring data with informative device wear	★ Optimal Asset Allocation using Black-Litterman with Smooth Transition Model
★ VIX Index Analysis using Copula-Based Markov Chain Models	★ 使用雙重指數平滑預測模型及無母數容忍限的配對交易策略
★ Intraday Pairs Trading on Taiwan Semiconductor Companies through Mean Reverting Processes	★ Target index tracing through portfolio optimization
★ Estimation in Copula-Based Markov Models under Weibull Distributions	★ Optimal Strategies for Index Tracking with Risky Constrains

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 (2024-9-21以後開放)

摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 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

關鍵字(英)

★ Meta-analysis
★ Bayesian approach
★ copula
★ beta-binomial distributions
★ DIC
★ credible interval
★ diagnostic test
★ MCMC

論文目次

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

參考文獻

[1] Aas, K., Czado, C., Frigessi, A. and Bakken, H. (2009). Pair-copula constructions
of multiple dependence, Insurance: Mathematics and Economics, 44, 182-198.
[2] Andrieu, C. and Thoms, J. (2008). A tutorial on adaptive MCMC, Statistics and
Computing, 18(4):343–73.
[3] Bennett, C. M., Guo M. and Dharmage S. C. (2007). HbA(1c) as a screening tool
for detection of Type 2 diabetes: a systematic review, Diabet Med, 24, 333–343.
[4] Biller, B. and Corlu, C. G. (2012). Copula-based multivariate input modeling,
Surveys in Operations Research and Management Science, 17,69-84
[5] Brooks, S. P. and Gelman, A. (1998). General Methods for Monitoring Convergence
of Iterative Simulations, Journal of Computational and Graphical Statistics, 7, 434-
455.
[6] Carlin, B. P. and Louis, T. A. (2008). Bayesian Methods for Data Analysis, London:
Chapman and Hall.
[7] Chu, H. and Cole, S. R. (2006). Bivariate meta-analysis of sensitivity and specificity
with sparse data: a generalized linear mixed model approach, Journal of Clinical
Epidemiology, 59, 1331–2.
[8] Czado, C. and Nagler, T. (2021). Vine copula based modeling, Annual Review of
Statistics and Its Application, 9, 453-477
[9] dos Santos Silva, R. and Freitas Lopez, H. (2008) Copula, marginal distributions
and model selection: A Bayesian note, Statistics and Computing, 18, 313–320
56
[10] Elfadaly, F. G. and Garthwaite, P. H. (2017). Eliciting Dirichlet and Gaussian
copula prior distributions for multinomial models, Statistics and Computing, 27,
449–467.
[11] Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D.
B. (2004).Bayesian Data Analysis, London: Chapman and Hall.
[12] Gelman, A., Roberts, G. O. and Gilks, W. R. (1996). Examples of Adaptive MCMC,
Bayesian Statistics, 5, 599-608.
[13] Gelman, A. and Rubin, D. B. (1992). A Single Series from the Gibbs Sampler
Provides a False Sense of Security, Bayesian Statistics, 4, 625-631
[14] Guo, J., Riebler, A. and Ruem H. (2017) Bayesian bivariate meta-analysis of diagnostic
test studies with interpretable priors, Statistics in Medicine, 36(19):3039-
3058.
[15] Haario, H., Saksman, E. and Tamminen, J. (2005). Componentwise adaptation for
high dimensional MCMC, Computational Statistics, 20, 265–273.
[16] Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and
their applications, Biometrika, 57, 97–109.
[17] Hoyer, A. (2016). Statistical methods for meta-analysis to compare two diagnostic
tests to a common gold standard, Biostatistics and Medical Biometry, Medical School
OWL, Bielefeld University.
[18] Hoyer, A. and Kuss, O. (2015). Statistical methods formeta-analysis of diagnostic
tests accounting for prevalence—a new model using trivariate copulas, Statistics in
Medicine, 27(5):1410-1421.
[19] Hoyer, A. and Kuss, O. (2016). Meta-analysis for the comparison of two diagnostic
tests to a common gold standard: A generalized linear mixed model approach,
Statistics in Medicine, 27(5):1410-1421.
[20] Hoyer, A. and Kuss, O. (2017). Meta-analysis for the comparison of two diagnostic
tests—A new approach based on copulas, Statistics in Medicine, 37(5):739-748.
57
[21] Hurtado Rúa, S. M., Mazumdar, M. and Strawderman, R. L. (2015). The choice of
prior distribution for a covariance matrix in multivariate meta-analysis: a simulation
study, Statistics in Medicine, 34(30):4083-104.
[22] Johny, P. C., Sergio B. O., Ana N. L., Ana S.G. and Puri G. V. (2021). Hierarchical
Modeling for Diagnostic Test Accuracy Using Multivariate Probability Distribution
Functions, Mathematics, 9(11), 1310
[23] Kodama, S., Horikawa C. and Fujihara K., et al. (2013). Use of high-normal levels
of haemoglobin A(1C) and fasting plasma glucose for diabetes screening and for
prediction: a meta-analysis, Diabet/Metab Res Rev, 29, 680–692.
[24] Kuss, O., Hoyer, A. and Solms, A. (2014). Meta-analysis for diagnostic accuracy
studies: a new statistical model using beta-binomial distributions and bivariate
copulas, Statistics in Medicine, 33(1):17-30.
[25] Lemoine, N. P. (2019). Moving beyond noninformative priors: why and how to
choose weakly informative priors in Bayesian analyses, Oikos, 128, 912-928.
[26] Li, Z., Zhao, Y. and Fu, J. (2020). SYNC: A Copula based Framework for Generating
Synthetic Data from Aggregated Sources, IEEE International Conference on
Data Mining Workshops, arXiv:2009.09471.
[27] Liu, H., Zhang, Z. and Grimm, K. J. (2019). Comparison of Inverse Wishart and
Separation-Strategy Priors for Bayesian Estimation of Covariance Parameter Matrix
in Growth Curve Analysis, Structural Equation Modeling, 23, 354-367.
[28] Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E.
(1953). Equations of state calculations by fast computing machines, J. Chemical
Physics, 21, 1087-1091.
[29] Min, A. and Czado, C. (2010). Bayesian inference for multivariate copulas using
pair-copula constructions, Journal of Financial Econometrics, 8, 511–546.
[30] Nelsen, R. B. (2006). An Introduction to Copulas, New York: Springer.
[31] Nikoloulopoulos, A. K. (2015). A mixed effect model for bivariate meta-analysis of
diagnostic test accuracy studies using a copula representation of the random effects
distribution, Statistics in Medicine, 34, 3842-3865.
58
[32] Parikh, R. , Mathai, A., Parikh, S., Sekhar, G C. and Thomas, R. (2008). Understanding
and using sensitivity, specificity and predictive values, Indian J Ophthalmol,
56(1): 45–50.
[33] Picano, E., Bedetti, G., Varga, A. and Cseh, E. (2000). The comparable diagnostic
accuracies of dobutamine-stress and dipyridamole-stress echocardiographies: a
meta-analysis, Coronary Artery Dis, 11(2):151-159.
[34] Reitsma, J. B., Glas, A. S., Rutjes, Anne W.S., Scholten, Rob J.P.M., Bossuyt, P.
M. and Zwinderman, A. H. (2005). Bivariate analysis of sensitivity and specificity
produces informative summary measures in diagnostic reviews, Journal of Clinical
Epidemiology, 58(10):982-990.
[35] Roberts, G. O. and Rosenthal, J. S. (2006). Examples of Adaptive MCMC, Journal
of Computational and Graphical Statistics, 18(2):349–67
[36] Rott, K. W., Lin L., Hodges, J. S., Siegel, L., Shi, A., Chen, Y. and Chu, H.
(2021). Bayesian meta-analysis using SAS PROC BGLIMM, Res Synth Methods,
12(6):692-700.
[37] Röver, C., Bender, R., Dias, S., Schmid, C. H. ,Schmidli, H., Sturtz, S., Weber,
S. and Friede, T. (2021). On weakly informative prior distributions for the heterogeneity
parameter in Bayesian random-effects metaanalysis, Res Synth Methods.,
12, 448-474
[38] Sklar A. (1959). Fonctions de repartition a n dimensions et leurs marges, Publications
de l’Institut de Statistique de L’Université de Paris, 8, 229-231.
[39] Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and Van Der Linde, A. (2002).
Bayesian measures of model complexity and fit, Journal of the Royal Statistical
Society: Series B (Statistical Methodology), 64, 583–639.
[40] Vats, D. and Knudson, C. (2018). Revisiting the Gelman–Rubin Diagnostic, Statistical
Science, 36(4):518-529.
[41] Vernieuwe, H., Vandenberghe, S., Baets, B. D. and Verhoest, N. E. C. (2015). A
Continuous Rainfall Model based on Vine Copulas, Hydrology and Earth System
Sciences, 19(6):2685-2699.
59
[42] Zapf, A., Hoyer, A., Kramer, K. and Kuss, O. (2015). Nonparametric meta-analysis
for diagnostic accuracy studies, Statistics in Medicine, 34(29):3831-3841.
[43] Zhu, L. and Carlin, B. P. (2000). Comparing hierarchical models for spatio-temporally
misaligned data using the deviance information criterion, Statistics in Medicine,
34(29):3831-3841.

指導教授

孫立憲(Li-Hsien Sun)

審核日期

2022-9-21

推文