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| Title: | 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 |
| Authors: | 許嫚荏
Hsu, Man Jen |
| Contributors: | 薛慧敏
張源俊
Hsueh, Huey Miin
Chang, Yuan Chin Ivan
許嫚荏
Hsu, Man Jen |
| Keywords: | 判別能力
疾病偵測
操作者特徵曲線下的部份面積
標記選取
最佳線性組合
操作者特徵曲線
特異度
敏感度
Discriminatory power
Hypothesis testing
Optimal linear combination
Partial area under ROC curve
Stepwise biomarker selection
Receiver operating curve
Specificity
Sensitivity |
| Date: | 2012 |
| Issue Date: | 2013-05-01 11:52:23 (UTC+8) |
| Abstract: | 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. |
| Reference: | [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,
534–540.
[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,
645–646.
[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,
1529–1542.
[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,
123–140.
[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,
1277–1290.
[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. |
| Description: | 博士
國立政治大學
統計研究所
95354503
101 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0095354503 |
| Data Type: | thesis |
| Appears in Collections: | [統計學系] 學位論文
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