A flexible Bayesian variable selection approach for modeling interval data

Interval datasets are not uncommon in many disciplines including medical experiments, econometric studies, environmental studies etc. For modeling interval data traditionally separate models are used for modeling the center and the radius of the response variable. In this article, we consider a Bayesian regression framework for jointly modeling the center and the radius of the intervals corresponding to the response, and then use appropriate priors for variable selection. Unlike the traditional setting, both the centres and the radii of all the predictors are used for modeling the center and the radius of response. We consider spike and slab priors for the regression coefficients corresponding to the centers (radii) of the predictors while modeling the center (radius) of the response, and global-local shrinkage prior for the coefficients corresponding to the radii (centers) of the predictors. Through extensive simulation studies, we illustrate the effectiveness of our proposed variable selection approach for the analysis and prediction of interval datasets. Finally, we analyze a real dataset from a clinical trial related to the Acute Lymphocytic Leukemia (ALL), and then select the important set of predictors for modeling the lymphocyte count which is an important biomarker for ALL. Our numerical studies show that the proposed approach is efficient, and it provides a powerful statistical inference for handling interval datasets.