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Proceedings Paper

Classification of microarray data with penalized logistic regression
Author(s): Paul H. C. Eilers; Judith M. Boer; Gert-Jan van Ommen; Hans C. van Houwelingen
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Paper Abstract

Classification of microarray data needs a firm statistical basis. In principle, logistic regression can provide it, modeling the probability of membership of a class with (transforms of) linear combinations of explanatory variables. However, classical logistic regression does not work for microarrays, because generally there will be far more variables than observations. One problem is multicollinearity: estimating equations become singular and have no unique and stable solution. A second problem is over-fitting: a model may fit well into a data set, but perform badly when used to classify new data. We propose penalized likelihood as a solution to both problems. The values of the regression coefficients are constrained in a similar way as in ridge regression. All variables play an equal role, there is no ad-hoc selection of most relevant or most expressed genes. The dimension of the resulting systems of equations is equal to the number of variables, and generally will be too large for most computers, but it can dramatically be reduced with the singular value decomposition of some matrices. The penalty is optimized with AIC (Akaike's Information Criterion), which essentially is a measure of prediction performance. We find that penalized logistic regression performs well on a public data set (the MIT ALL/AML data).

Paper Details

Date Published: 4 June 2001
PDF: 12 pages
Proc. SPIE 4266, Microarrays: Optical Technologies and Informatics, (4 June 2001); doi: 10.1117/12.427987
Show Author Affiliations
Paul H. C. Eilers, Leiden Univ. Medical Ctr. (Netherlands)
Judith M. Boer, Leiden Univ. Medical Ctr. (Netherlands)
Gert-Jan van Ommen, Leiden Univ. Medical Ctr. (Netherlands)
Hans C. van Houwelingen, Leiden Univ. Medical Ctr. (Netherlands)

Published in SPIE Proceedings Vol. 4266:
Microarrays: Optical Technologies and Informatics
Michael L. Bittner; Yidong Chen; Andreas N. Dorsel; Edward R. Dougherty, Editor(s)

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