Abstract
Modern biological experiments often involve high-dimensional data with thousands or more variables. A challenging problem is to identify the key variables that are related to a specific disease. Confounding this task is the vast number of statistical methods available for variable selection. For this reason, we set out to develop a framework to investigate the variable selection capability of statistical methods that are commonly applied to analyze high-dimensional biological datasets. Specifically, we designed six simulated cancers (based on benchmark colon and prostate cancer data) where we know precisely which genes cause a dataset to be classified as cancerous or normal – we call these causative genes. We found that not one statistical method tested could identify all the causative genes for all of the simulated cancers, even though increasing the sample size does improve the variable selection capabilities in most cases. Furthermore, certain statistical tools can classify our simulated data with a low error rate, yet the variables being used for classification are not necessarily the causative genes.
Acknowledgments:
The authors are grateful to the reviewers, as their comments led to substantial improvements in the final manuscript. In addition, the authors are very appreciative of Welling Howell from Wheatstone Analytics for his extensive works on R penalized-SVM, Random Forest, and for his critical review of the manuscript. In addition, we owe special thanks to Charlene Wang of Health First Incorporated on SAS computation. We also appreciate the comments and help from the following colleagues and friends: Chaur-Chin Chen of National Tsing-Hua University, Leonardo Auslender of Cisco Systems, Inc., and Sudhir Nayak of The College of New Jersey. Finally, we would like to thank the following students at The College of New Jersey for the cross-check of the computer experiments in this paper: Edward Lee, Roger Shan, Alana Huszar, Sahnaz Saleem, Cassidy Wilson, Joseph Ruffo, and Roger Shan.
Appendix
The histograms and scatterplots of simulated genes X1, X2, X3 are presented below:
The means and standard deviations of these variables are slightly different:
| Variable | N | Mean | Std dev |
|---|---|---|---|
| X1 | 102 | 4.6881029 | 3.1055643 |
| X2 | 102 | 8.3062417 | 3.7449357 |
| X3 | 102 | 13.6261146 | 5.0801841 |
The 3 variables are generated by the following formulas in a do-loop:
X1, X2, X3 are 10*Uniform(0,1)
Z2=2X2
Z3=3X3
X2(new)=X1+0.35Z2
X3(new)=X2(new)+0.35Z3
Consequently X2 and X3 have higher probability in the middle. The choice of these distributions were partly motivated by the prostate cancer data (Efron, 2008). See, e.g. the histograms of Gene-1 to Gene-4 below:
After examining the 6033 histograms of the prostate cancer data, along with other disease datasets, we believe the above distributions are reasonable compromises in the simulation study to test statistical methods in gene search.
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