Bayesian penalized cumulative logit model for high-dimensional data with an ordinal response

Many previous studies have identified associations between gene expression, measured using high-throughput genomic platforms, and quantitative or dichotomous traits. However, we note that health outcome and disease status measurements frequently appear on an ordinal scale, that is, the outcome is categorical but has inherent ordering. Identification of important genes may be useful for developing novel diagnostic and prognostic tools to predict or classify stage of disease. Gene expression data are usually high-dimensional, meaning that the number of genes is much larger than the sample size or number of patients. Herein we describe some existing frequentist methods for modeling an ordinal response in a high-dimensional predictor space. Following Tibshirani (1996), who described the LASSO estimate as the Bayesian posterior mode when the regression coefficients have independent Laplace priors, we propose a new approach for high-dimensional data with an ordinal response that is rooted in the Bayesian paradigm. We show that our proposed Bayesian approach outperforms existing frequentist methods through simulation studies. We then compare the performance of frequentist and Bayesian approaches using a study evaluating progression to hepatocellular carcinoma in hepatitis C infected patients.