臺灣博碩士論文加值系統

在基因組分析中經常會遇到高維度的問題，因此許多學者紛紛提出不同的解決方法。在我們的文章中，主要探討不同的檢定統計量所呈現出的型一錯誤率及檢定力的差異。其中，我們是使用了ridge regression 的技巧來估計Hotelling’s T2 檢定統計量。也運用了重新排列的方法來計算其型一錯誤率和檢定力。與其他檢定方法比較之下，發現其檢定力有明顯的增加。我們也把此方法運用在一組有關糖尿病的資料中，進而挑選出幾個較有顯著性的基因組。

In gene sets analyses, there are a lot of methods dealing with the problem of highdimensional dataset. In our article, we use the ridge regression technique to estimate Hotelling’s T2 statistic. The permutation is used to obtain the Type I error rates and powers. The simulation results show that our method has higher power comparing to other test statistics. We apply our testing procedure to a human diabetes data set to search the significant gene sets.

1. Introduction 1
1.1. One-Group Hotelling’s T2 test 1
1.2. Two-Group Hotelling’s T2 test 2
2. Reviews 3
3. Methods 7
3.1. Algorithm for the RRHT 10
4. Simulations 11
4.1. Algorithm for finding the Type I error rates and powers of RRHT with permutation 28
5. Application 29
6. Summary 31

[1] Bai, Z., and Saranadasa, H. (1996): Effect of High Dimension: By an Example of a Two Sample Problem,
Statistica Sinica, 6, 311-329.
[2] Dempster, A. P. (1958): A High Dimensional Two Sample Significance Test,
The Annals of Mathematical Statistics, 29, 995-1010.
[3] Dudoit, S., Fridlyand, J. and Speed, T. P. (2002): Comparison of discrimination methods for the classification of Tumors using gene expression data, J. Amer. Statist. Assoc., 97, 77-87.
[4] Efron, B., Tibshirani, R., Storey, J. D. and Tusher, V. (2001): Empirical Bayes analysis of a microarray experiment, J. Amer. Statist. Assoc., 96, 1151-1160.
[5] Eisen, M. B., Spellman, P. T., Brown, P. O. and Botstein, D. (1998): Cluster analysis and display of genome-wide expression-patterns, Proceeding of the National Academy of Sciences, 95, 14863-14868.
[6] Ibrahim, J., Chen, M. and Gray, R. J. (2002): Bayesian models for gene expression with DNA microarray data,
J. Amer. Statist. Assoc., 97, 88-99.
[7] Kong SW, Pu WT, Park PJ (2006): A multivariate approach for integrating genome-wide expression data and biological knowledge. Bioinformatics, 22(19):2373-2380.
[8] Kim SY, Volsky DJ (2005): PAGE: parametric analysis of gene set enrichment.
BMC Bioinformatics , 6:144.40
[9] Ledoit, O., and Wolf, M. (2004): A Well-Conditioned Estimator for Large-Dimensional Covariance Matrices, Journal of Multivariate Analysis, 99, 365-411.
[10] Chen, Lin S., Paul, Debashis, Prentice, Ross L., Wang, Pei (2011): A Regularized Hotellings T2 Test for Pathway Analysis in Proteomic Studies. Journal of the American Statistical Association December , Vol. 106, No. 496,Applications and Case Studies.
[11] Lin, S., and Perlman, M. (1985): A Monte Carlo Comparison of Four Estimators of a Covariance Matrix, in Multivariate Analysis - VI: Proceedings of the Sixth International Symposium on Multivariate Analysis, ed. P. R.Krishnaiah, Amsterdam: North-Holland, pp. 411-429.
[12] Mootha V. K., Lindgren, C. M., Eriksson, K. F., Subramanian, A., Sihag, S. et al. (2003): PGC-1alpharesponsive genes involved in oxidative phosphorylation are coordinately downregulated in human diabetes. Nat Genet,
34(3):267-273.
[13] M. S. Srivastava (2007): MULTIVARIATE THEORY FOR ANALYZING HIGH DIMENSIONAL DATA.
J. Japan Statist. Soc., Vol. 37 No. 1 53-86.
[14] Yates P. D., and Reimers M. A. (2009): RCMAT: a regularized covariance matrix approach to testing gene sets.
BMC Bioinformatics 2009, 10:300.
[15] Schafer J, Strimmer K (2005): A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics. Statistical Applications in Genetics and Molecular Biology, 4(1):32.