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    政大機構典藏 > 商學院 > 統計學系 > 學位論文 >  Item 140.119/57973

    请使用永久网址来引用或连结此文件: http://nccur.lib.nccu.edu.tw/handle/140.119/57973

    题名: 多標記接受者操作特徵曲線下部分面積最佳線性組合之研究
    The study on the optimal linear combination of markers based on the partial area under the ROC curve
    作者: 許嫚荏
    Hsu, Man Jen
    贡献者: 薛慧敏

    Hsueh, Huey Miin
    Chang, Yuan Chin Ivan

    Hsu, Man Jen
    关键词: 判別能力
    Discriminatory power
    Hypothesis testing
    Optimal linear combination
    Partial area under ROC curve
    Stepwise biomarker selection
    Receiver operating curve
    日期: 2012
    上传时间: 2013-05-01 11:52:23 (UTC+8)
    摘要: 本論文的研究目標是建構一個由多標記複合成的最佳疾病診斷工具,所考慮的評估準則為操作者特徵曲線在特定特異度範圍之線下面積(pAUC)。在常態分布假設下,我們推導多標記線性組合之pAUC以及最佳線性組合之必要條件。由於函數本身過於複雜使得計算困難。除此之外,我們也發現其最佳解可能不唯一,以及局部極值存在,這些情況使得現有演算法的運用受限,我們因此提出多重初始值演算法。當母體參數未知時,我們利用最大概似估計量以獲得樣本pAUC以及令其極大化之最佳線性組合,並證明樣本最佳線性組合將一致性地收斂到母體最佳線性組合。在進一步的研究中,我們針對單標記的邊際判別能力、多標記的複合判別能力以及個別標記的條件判別能力,分別提出相關統計檢定方法。這些統計檢定被運用至兩個標記選取的方法,分別是前進選擇法與後退淘汰法。我們運用這些方法以選取與疾病檢測有顯著相關的標記。本論文透過模擬研究來驗證所提出的演算法、統計檢定方法以及標記選取的方法。另外,也將這些方法運用在數組實際資料上。
    The aim of this work is to construct a composite diagnostic
    tool based on multiple biomarkers under the criterion of
    the partial area under a ROC curve (pAUC) for a predetermined specificity range. Recently several studies are interested in the optimal linear combination maximizing the whole area under a ROC curve (AUC). In this study, we focus on finding the optimal linear combination by a direct maximization of the pAUC under normal assumption. In order
    to find an analytic solution, the first derivative of the
    pAUC is derived. The form is so complicated, that a further validation on the Hessian matrix is difficult. In addition,
    we find that the pAUC maximizer may not be unique and sometimes, local maximizers exist. As a result, the existing algorithms, which depend on the initial-point, are inadequate to serve our needs. We propose a new algorithm by
    adopting several initial points at one time. In addition,
    when the population parameters are unknown and only a
    random sample data set is available, the maximizer of the sample version of the pAUC is shown to be a strong consistent estimator of its theoretical counterpart. We further focus on determining whether a biomarker set, or one specific biomarker has a significant contribution to the disease diagnosis. We propose three statistical tests for the identification of the discriminatory power. The proposed tests are applied to biomarker selection for reducing the variable number in advanced analysis. Numerical studies are performed to validate the proposed algorithm and the proposed statistical procedures.
    參考文獻: [1] Baker, S. G., Pinsky, P. F., 2001. A proposed design
    and analysis for comparing digital and analog
    mammography: special receiver operating characteristic
    methods for cancer screening. Journal of the American
    Statistical Association 96, 421–428.
    [2] Bamber, D., 1975. The area above the ordinal dominance
    graph and the area below the receiver operating
    characteristic graph. Journal of Mathematical
    Psychology 12, 387–415.
    [3] Bast Jr, R., 1993. Perspectives on the future of cancer
    markers. Clinical Chemistry 39, 2444–2451.
    [4] Beam, C. A., Conant, E. F., A.Sickles, E., Weinstein,S.
    P., 2003. Evaluation of proscriptive health care policy
    implementation in screening mammography. Radiology 229,
    [5] Blume, J. D., 2009. Bounding sample size projections
    for the area under a roc curve. Journal of Statistical
    Planning and Inference 139, 711–721.
    [6] DeLong, E. R., DeLong, D. M., Clarke-Pearson, D. L.,
    1988. Comparing the areas under two or more correlated
    receiver operating characteristic curves: A
    nonparametric approach. Biometrics 44, 837–845.
    [7] Friedman, J. H., Popescu, B. E., 2004. Gradient
    directed regularization for linear regression and
    classification [online].
    [8] Janes, H., Pepe, M., 2006. The optimal ratio of cases
    to controls for estimating the classification accuracy
    of a biomarker. Biostatistics 7, 456–468.
    [9] Komori, O., Eguchi, S., 2010. A boosting method for
    maximizing the partial area under the roc curve
    [online]. BMC Bioinformatics 11, 314.
    [10] Li, C., Liao, C., Liu, J., 2008. A non-inferiority
    test for diagnostic accuracy based on the paired
    partial areas under roc curves. Statistics in Medicine
    27, 1762–1776.
    [11] Liu, A., Schisterman, E., Zhu, Y., 2005. On linear
    combinations of biomarkers to improve diagnostic
    accuracy. Statistics in Medicine 24, 37–47.
    [12] Ma, S., Huang, J., 2005. Regularized roc method for
    disease classification and biomarker selection with
    microarray data. Bioinformatics 21, 4356–4362.
    [13] Marsaglia, G., 1972. Choosing a point from the surface
    of a sphere. The Annals of Mathematical Statistics 43,
    [14] Marshall, R., 1989. The predictive value of simple
    rules for combining two diagnostic tests. Biometrics
    45, 1213–1222.
    [15] McClish, D., 1989. Analyzing a portion of the ROC
    curve. Medical Decision Making 9, 190–195.
    [16] Muller, M., 1959. A note on a method for generating
    points uniformly on n-dimensional spheres.
    Communications of the ACM 2, 19–20.
    [17] Obuchowski, N., McClish, D. K., 1997. Sample size
    determination for diagnostic accuracy studies involving
    binormal roc curve indices. Statistics in Medicine 16,
    [18] Obuchowski, N. A., 2000. Sample size tables for
    receiver operating characteristic studies. American
    Journal of Roentgenology 175, 603–608.
    [19] Pepe, M., 2004. The Statistical Evaluation Of Medical
    Tests For Classification And Prediction. Oxford
    Statistical Science Series. Oxford University Press.
    [20] Pepe, M., Thompson, M., 2000. Combining diagnostic
    test results to increase accuracy. Biostatistics 1,
    [21] Schott, J., 2005. Matrix Analysis For Statistics.
    Wiley Series in Probability and Statistics. Wiley.
    [22] Shao, J., 1999. Mathematical Statistics. Springer-
    Verlag Inc.
    [23] Silva, J. E., Mqrques, J. P., Jossinet, J., 2000.
    Classification of breast tissue by electrical impedance
    spectroscopy. Medical and Biological Engineering and
    Computing 38, 26–30.
    [24] Su, H. M., Voon, W. C., Lin, T. H., Lee, K. T., Chu,
    C. S., Lee, M. Y., Sheu, S. H., Lai, W. T., 2004.
    Ankle-brachial pressure index measured using an
    automated oscillometric method as a predictor of the
    severity of coronary atherosclerosis in patients with
    coronary artery disease. The Kaohsiung Journal of
    Medical Sciences 20, 268–272.
    [25] Su, J., Liu, J., 1993. Linear combinations of multiple
    diagnostic markers. Journal of the American Statistical
    Association 88, 1350–1355.
    [26] Thompson, M., Zucchini, W., 1989. On the statistical
    analysis of ROC curves. Statistics in Medicine 8,
    [27] Tian, L., 2010. Confidence interval estimation of
    partial area under curve based on combined biomarkers.
    Computational Statistics & Data Analysis 54, 466–472.
    [28] Wang, Z., Chang, Y.-C. I., 2010. Marker selection via
    maximizing the partial area under the roc curve of
    linear risk scores. Biostatistics 12, 369–385.
    [29] Woolas, R., Conaway, M., Xu, F., Jacobs, I., Yu, Y.,
    Daly, L., Davies, A., O’Briant, K., Berchuck, A.,
    Soper, J., et al., 1995. Combinations of multiple
    serum markers are superior to individual assays for
    discriminating malignant from benign pelvic masses.
    Gynecologic Oncology 59, 111–116.
    描述: 博士
    資料來源: http://thesis.lib.nccu.edu.tw/record/#G0095354503
    数据类型: thesis
    显示于类别:[統計學系] 學位論文


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