Logistic regression for disease classification using microarray data: model selection in a large p and small n case.
BACKGROUND
Logistic regression is a standard method for building prediction models for a binary outcome and has been extended for disease classification with microarray data by many authors. A feature (gene) selection step, however, must be added to penalized logistic modeling due to a large number of genes and a small number of subjects. Model selection for this two-step approach requires new statistical tools because prediction error estimation ignoring the feature selection step can be severely downward biased. Generic methods such as cross-validation and non-parametric bootstrap can be very ineffective due to the big variability in the prediction error estimate.


RESULTS
We propose a parametric bootstrap model for more accurate estimation of the prediction error that is tailored to the microarray data by borrowing from the extensive research in identifying differentially expressed genes, especially the local false discovery rate. The proposed method provides guidance on the two critical issues in model selection: the number of genes to include in the model and the optimal shrinkage for the penalized logistic regression. We show that selecting more than 20 genes usually helps little in further reducing the prediction error. Application to Golub's leukemia data and our own cervical cancer data leads to highly accurate prediction models.


BACKGROUND
R library GeneLogit at http://geocities.com/jg_liao
Liao
J G
JG
Drexel University School of Public Health, Philadelphia, PA 19102, USA. jl544@drexel.edu
Chin
Khew-Voon
KV
D000465:Algorithms; D014408:Biomarkers, Tumor / Q000032:analysis*; D003627:Data Interpretation, Statistical; D003936:Diagnosis, Computer-Assisted / Q000379:methods*; D006801:Humans; D016015:Logistic Models; D008954:Models, Biological; D009363:Neoplasm Proteins / Q000032:analysis*; D009369:Neoplasms / Q000145:classification / Q000175:diagnosis* / Q000378:metabolism*; D020411:Oligonucleotide Array Sequence Analysis / Q000379:methods*; D012044:Regression Analysis; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity
D014408:Biomarkers, Tumor; D009363:Neoplasm Proteins