Open Journal of Statistics > Vol.4 No.7, August 2014

Behrouz Madahian, Lih Y. Deng, Ramin Homayouni

Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA.
Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA.
Bioinformatics Program, University of Memphis, Memphis, TN, USA; Department of Biology, University of Memphis, Memphis, TN, USA.

A major limitation of expression profiling is caused by the large number of variables assessed compared to relatively small sample sizes. In this study, we developed a multinomial Probit Bayesian model which utilizes the double exponential prior to induce shrinkage and reduce the number of covariates in the model [1]. A hierarchical Sparse Bayesian Generalized Linear Model (SBGLM) was developed in order to facilitate Gibbs sampling which takes into account the progressive nature of the response variable. The method was evaluated using a published dataset (GSE6099) which contained 99 prostate cancer cell types in four different progressive stages [2]. Initially, 398 genes were selected using ordinal logistic regression with a cutoff value of 0.05 after Benjamini and Hochberg FDR correction. The dataset was randomly divided into training (N = 50) and test (N = 49) groups such that each group contained equal number of each cancer subtype. In order to obtain more robust results we performed 50 re-samplings of the training and test groups. Using the top ten genes obtained from SBGLM, we were able to achieve an average classification accuracy of 85% and 80% in training and test groups, respectively. To functionally evaluate the model performance, we used a literature mining approach called Geneset Cohesion Analysis Tool [3]. Examination of the top 100 genes produced an average functional cohesion p-value of 0.007 compared to 0.047 and 0.131 produced by classical multi-category logistic regression and Random Forest approaches, respectively. In addition, 96 percent of the SBGLM runs resulted in a GCAT literature cohesion p-value smaller than 0.047. Taken together, these results suggest that sparse Bayesian Multinomial Probit model applied to cancer progression data allows for better subclass prediction and produces more functionally relevant gene sets.

LASSO, Robustness, Sparsity, MCMC, Gibbs Sampling

Madahian, B. , Deng, L. and Homayouni, R. (2014) Application of Sparse Bayesian Generalized Linear Model to Gene Expression Data for Classification of Prostate Cancer Subtypes. Open Journal of Statistics, 4, 518-526. doi: 10.4236/ojs.2014.47049.