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Journal of Biomedicine and Biotechnology
Volume 2011 (2011), Article ID 875309, 8 pages
http://dx.doi.org/10.1155/2011/875309
Research Article

Sparse Logistic Regression for Diagnosis of Liver Fibrosis in Rat by Using SCAD-Penalized Likelihood

1Department of Mathematics, Southeast University, Nanjing 210096, China
2Department of Mathematics, China Pharmaceutical University, Nanjing 210009, China
3State Key Laboratory of Natural Medicines, China Pharmaceutical University, Nanjing 210009, China

Received 28 November 2010; Revised 3 February 2011; Accepted 24 March 2011

Academic Editor: Sanford I. Bernstein

Copyright © 2011 Fang-Rong Yan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The objective of the present study is to find out the quantitative relationship between progression of liver fibrosis and the levels of certain serum markers using mathematic model. We provide the sparse logistic regression by using smoothly clipped absolute deviation (SCAD) penalized function to diagnose the liver fibrosis in rats. Not only does it give a sparse solution with high accuracy, it also provides the users with the precise probabilities of classification with the class information. In the simulative case and the experiment case, the proposed method is comparable to the stepwise linear discriminant analysis (SLDA) and the sparse logistic regression with least absolute shrinkage and selection operator (LASSO) penalty, by using receiver operating characteristic (ROC) with bayesian bootstrap estimating area under the curve (AUC) diagnostic sensitivity for selected variable. Results show that the new approach provides a good correlation between the serum marker levels and the liver fibrosis induced by thioacetamide (TAA) in rats. Meanwhile, this approach might also be used in predicting the development of liver cirrhosis.