Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines

Annals of Applied Statistics

Volumn 7, Issue 2, 2013, Pages 823-845

  Leday, Gwenaël G R ^a   van der Vaart, Aad W ^b   van Wieringen, Wessel N ^c   van de Wiel, Mark A ^c  

^a VU UNIVERSITY AMSTERDAM   (Netherlands)

^b LEIDEN UNIVERSITY   (Netherlands)

^c VU UNIVERSITY MEDICAL CENTER   (Netherlands)

Author keywords

Confidence bands; Constrained inference; DNA copy number; Model selection; mRNA expression; Regression splines

Indexed keywords

EID: 84876210989     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/12-AOAS605     Document Type: Article

References (45)

1. AKAIKE, H. (1973). Information theory and an extension of the maximum likelihood principle. In Second International Symposium on Information Theory (Tsahkadsor, 1971) (B. N. Petrov and F. Csaki, eds.) 267-281. Akadémiai Kiadó, Budapest. MR0483125
2. ANDREWS, D. W. K. (2000). Inconsistency of the bootstrap when a parameter is on the boundary of the parameter space. Econometrica 68 399-405. MR1748009
3. ARNOLD, B. C. and SHAVELLE, R. M. (1998). Joint confidence sets for the mean and variance of a normal distribution. Amer. Statist. 52 133-140. MR1628439
4. ASIMIT, J. L., ANDRULIS, I. L. and BULL, S. B. (2011). Regression models, scan statistics and reappearance probabilities to detect regions of association between gene expression and copy number. Stat. Med. 30 1157-1178. MR2767848
5. BENJAMINI, Y. and HOCHBERG, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B 57 289-300. MR1325392
6. BICCIATO, S., SPINELLI, R., ZAMPIERI, M., MANGANO, E., FERRARI, F., BELTRAME, L., CIFOLA, I., PEANO, C., SOLARI, A. and BATTAGLIA, C. (2009). A computational procedure to identify significant overlap of differentially expressed and genomic imbalanced regions in cancer datasets. Nucleic Acids Res. 37 5057-5070.
7. BOYD, S. and VANDENBERGHE, L. (2004). Convex Optimization. Cambridge Univ. Press, Cambridge. MR2061575
8. BOZDOGAN, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika 52 345-370. MR0914460
9. BROWN, L. D., CAI, T. T. and DASGUPTA, A. (2003). Interval estimation in exponential families. Statist. Sinica 13 19-49. MR1963918
10. BUCKLAND, S. T., BURNHAM, K. P. and AUGUSTIN, N. H. (1997). Model selection: An integral part of inference. Biometrics 53 603-618.
11. BURNHAM, K. P. and ANDERSON, D. R. (2002). Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach, 2nd ed. Springer, New York. MR1919620
12. CARVALHO, B., POSTMA, C., MONGERA, S., HOPMANS, E., DISKIN, S., VAN DE WIEL, M. A., VAN CRIEKINGE, W., THAS, O., MATTHÄI, A., CUESTA, M. A., DROSTE, J. S. T. S., CRAANEN, M., SCHRÖCK, E., YLSTRA, B. andMEIJER, G. A. (2009). Multiple putative oncogenes at the chromosome 20q amplicon contribute to colorectal adenoma to carcinoma progression. Gut 58 79-89.
13. CHERNOFF, H. (1954). On the distribution of the likelihood ratio. Ann. Math. Statistics 25 573-578. MR0065087
14. GOURIÉROUX, C., HOLLY, A. and MONFORT, A. (1982). Likelihood ratio test, Wald test, and Kuhn-Tucker test in linear models with inequality constraints on the regression parameters. Econometrica 50 63-80. MR0640166
15. GRÖMPING, U. (2010). Inference with linear equality and inequality constraints using R: The package ic. infer. J. Stat. Softw. 33 1-31.
16. GU, W., CHOI, H. and GHOSH, D. (2008). Global associations between copy number and transcript mRNA microarray data: An empirical study. Cancer Inform. 6 17-23.
17. HUGHES, A. W. and KING, M. L. (2003). Model selection using AIC in the presence of one-sided information. J. Statist. Plann. Inference 115 397-411. MR1985874
18. JÖRNSTEN, R., ABENIUS, T., KLING, T., SCHMIDT, L., JOHANSSON, E., NORDLING, T. E. M., NORDLANDER, B., SANDER, C., GENNEMARK, P., FUNA, K., NILSSON, B., LINDAHL, L. and NELANDER, S. (2011). Network modeling of the transcriptional effects of copy number aberrations in glioblastoma. Mol. Syst. Biol. 7 486.
19. KODDE, D. A. and PALM, F. C. (1986). Wald criteria for jointly testing equality and inequality restrictions. Econometrica 54 1243-1248. MR0859464
20. KUDÔ, A. (1963). A multivariate analogue of the one-sided test. Biometrika 50 403-418. MR0163386
21. LEDAY, G. G. R., VAN DER VAART, A. W., VAN WIERINGEN, W. N. and VAN DE WIEL, M. A. (2013). Supplement to "Modeling association between DNA copy number and gene expression with constrained piecewise linear regression splines. " DOI:10.1214/12-AOAS605SUPP.
22. LEE, H., KONG, S. W. and PARK, P. J. (2008). Integrative analysis reveals the direct and indirect interactions between DNA copy number aberrations and gene expression changes. Bioinformatics 24 889-896.
23. LIPSON, D., BEN-DOR, A., DEHAN, E. and YAKHINI, Z. (2004). Joint analysis of DNA copy numbers and gene expression levels. In Algorithms in Bioinformatics. Lecture Notes in Computer Science 3240 135-146. Springer, Berlin. MR2155600
24. MEEKER, W. Q. and ESCOBAR, L. A. (1995). Teaching about approximate confidence regions based on maximum likelihood estimation. Amer. Statist. 49 48-53.
25. MENEZES, R., BOETZER, M., SIESWERDA, M., VAN OMMEN, G. J. and BOER, J. (2009). Integrated analysis of DNA copy number and gene expression microarray data using gene sets. BMC Bioinformatics 10 203.
26. NEVE, R. M., CHIN, K., FRIDLYAND, J., YEH, J., BAEHNER, F. L., FEVR, T., CLARK, L., BAYANI, N., COPPE, J.-P. P., TONG, F., SPEED, T., SPELLMAN, P. T., DEVRIES, S., LAPUK, A., WANG, N. J., KUO, W.-L. L., STILWELL, J. L., PINKEL, D., ALBERTSON, D. G., WALDMAN, F. M., MCCORMICK, F., DICKSON, R. B., JOHNSON, M. D., LIPPMAN, M., ETHIER, S., GAZDAR, A. and GRAY, J. W. (2006). A collection of breast cancer cell lines for the study of functionally distinct cancer subtypes. Cancer Cell. 10 515-527.
27. OLSHEN, A. B., VENKATRAMAN, E. S., LUCITO, R. and WIGLER, M. (2004). Circular binary segmentation for the analysis of array-based DNA copy number data. Biostatistics 5 557-572.
28. PENG, J., ZHU, J., BERGAMASCHI, A., HAN, W., NOH, D.-Y., POLLACK, J. R. and WANG, P. (2010). Regularized multivariate regression for identifying master predictors with application to integrative genomics study of breast cancer. Ann. Appl. Stat. 4 53-77. MR2758084
29. PINKEL, D. and ALBERTSON, D. G. (2005). Array comparative genomic hybridization and its applications in cancer. Nat. Genet. 37 Suppl. S11-S17.
30. QUACKENBUSH, J. (2002). Microarray data normalization and transformation. Nat. Genet. 32 Suppl. 496-501.
31. ROBERTSON, T., WRIGHT, F. T. and DYKSTRA, R. L. (1988). Order Restricted Statistical Inference. Wiley, Chichester. MR0961262
32. SALARI, K., TIBSHIRANI, R. and POLLACK, J. R. (2010). DR-Integrator: A new analytic tool for integrating DNA copy number and gene expression data. Bioinformatics 26 414-416.
33. SCHÄFER, M., SCHWENDER, H., MERK, S., HAFERLACH, C., ICKSTADT, K. and DUGAS, M. (2009). Integrated analysis of copy number alterations and gene expression: A bivariate assessment of equally directed abnormalities. Bioinformatics 25 3228-3235.
34. SHAPIRO, A. (1988). Towards a unified theory of inequality constrained testing in multivariate analysis. Internat. Statist. Rev. 56 49-62. MR0963140
35. SILVAPULLE, M. J. and SEN, P. K. (2005). Constrained Statistical Inference: Inequality, Order, and Shape Restrictions. Wiley, Hoboken, NJ. MR2099529
36. SOLVANG, H. K., LINGJÆRDE, O. C., FRIGESSI, A., BØRRESEN-DALE, A.-L. and KRISTENSEN, V. N. (2011). Linear and non-linear dependencies between copy number aberrations and mRNA expression reveal distinct molecular pathways in breast cancer. BMC Bioinformatics 12 197.
37. SONESON, C., LILLJEBJÖRN, H., FIORETOS, T. and FONTES, M. (2010). Integrative analysis of gene expression and copy number alterations using canonical correlation analysis. BMC Bioinformatics 11 191.
38. VAN DE WIEL, M. A., KIM, K. I., VOSSE, S. J., VAN WIERINGEN, W. N., WILTING, S. M. and YLSTRA, B. (2007). CGHcall: Calling aberrations for array CGH tumor profiles. Bioinformatics 23 892-894.
39. VAN DE WIEL, M. A., PICARD, F., VAN WIERINGEN, W. N. and YLSTRA, B. (2011). Preprocessing and downstream analysis of microarray DNA copy number profiles. Brief. Bioinformatics 12 10-21.
40. VAN DER VAART, A. W. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics 3. Cambridge Univ. Press, Cambridge. MR1652247
41. VAN WIERINGEN, W. N., BERKHOF, J. and VAN DE WIEL, M. A. (2010). A random coefficients model for regional co-expression associated with DNA copy number. Stat. Appl. Genet. Mol. Biol. 9 30. MR2721705
42. VAN WIERINGEN, W. N., VAN DE WIEL, M. A. and YLSTRA, B. (2007). Normalized, segmented or called aCGH data? Cancer Inform. 3 321-327.
43. VAN WIERINGEN, W. N. and VAN DE WIEL, M. A. (2009). Nonparametric testing for DNA copy number induced differential mRNA gene expression. Biometrics 65 19-29. MR2665842
44. VANANTWERP, J. (2000). A tutorial on linear and bilinear matrix inequalities. J. Process Contr. 10 363-385.
45. VANDENBERGHE, L. and BOYD, S. (1996). Semidefinite programming. SIAM Rev. 38 49-95. MR1379041