Approximation by Cubic Splines Leads to Highly Specific Discovery by Microarrays

Bona, Jerry L.; ,

Approximation by Cubic Splines Leads to Highly Specific Discovery by Microarrays

Jerry L. Bona¹, Hassan M. Fathallah-Shaykh^{*, 1, 2}*12

¹ Department of Mathematics, Statistics, & Computer Science, The University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607, USA

² Department of Neurological Sciences, Section of Neuro-Oncology, Rush University Medical Center, 1725 West Harrison Street, Chicago, IL, 60612, USA

Article Information

Identifiers and Pagination:

Year: 2008
Volume: 2
First Page: 54
Last Page: 59
Publisher ID: TOBIOIJ-2-54
DOI: 10.2174/1875036200802010054

Article History:

Received Date: 10/07/2008
Revision Received Date: 12/08/2008
Acceptance Date: 17/08/2008
Electronic publication date: 12/09/2008
Collection year: 2008

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© 2008 Bona and Fathallah-Shaykh et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

^* Address correspondence to this author at the University of Alabama at Birmingham, Department of Neurology, Faculty Office Towers 1020, 510 20th Street South, Birmingham, AL 35294-3410, USA; Tel: 205-934-1432; Fax: 205-975-7546; E-mail: hfathallah@msn.com

Genome-scale microarray datasets are noisy. We have previously reported an algorithm that yields highly specific genome-scale discovery of states of genetic expression. In its original implementation, the algorithm computes parameters by globally fitting data to a function containing a linear combination of elements that are similar to the Hill equation and the Michaelis-Menten differential equation. In this essay, we show that approximation by cubic splines yields curves that are closer to the datasets, but, in general, the first derivatives of the cubic splines are not as smooth as the derivatives obtained by global fitting. Nonetheless, little variation of the first derivative is seen in the area of the curve where the Cutoff Rank is computed. The results demonstrate that piece-wise approximation by cubic splines yields sensitivity and specificity equal to those obtained by global fitting.

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RESEARCH ARTICLE

Approximation by Cubic Splines Leads to Highly Specific Discovery by Microarrays

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