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Radiomics involves the study of tumor images to identify quantitative markersexplaining cancer heterogeneity. The predominant approach is to extracthundreds to thousands of image features, including histogram features comprisedof summaries of the marginal distribution of pixel intensities, which leads tomultiple testing problems and can miss out on insights not contained in theselected features. In this paper, we present methods to model the entiremarginal distribution of pixel intensities via the quantile function asfunctional data, regressed on a set of demographic, clinical, and geneticpredictors. We call this approach quantile functional regression, regressingsubject-specific marginal distributions across repeated measurements on a setof covariates, allowing us to assess which covariates are associated with thedistribution in a global sense, as well as to identify distributional featurescharacterizing these differences, including mean, variance, skewness, andvarious upper and lower quantiles. To account for smoothness in the quantilefunctions, we introduce custom basis functions we call quantlets that aresparse, regularized, near-lossless, and empirically defined, adapting to thefeatures of a given data set. We fit this model using a Bayesian framework thatuses nonlinear shrinkage of quantlet coefficients to regularize the functionalregression coefficients and provides fully Bayesian inference after fitting aMarkov chain Monte Carlo. We demonstrate the benefit of the basis spacemodeling through simulation studies, and apply the method to Magnetic resonanceimaging (MRI) based radiomic dataset from Glioblastoma Multiforme to relateimaging-based quantile functions to demographic, clinical, and geneticpredictors, finding specific differences in tumor pixel intensity distributionbetween males and females and between tumors with and without DDIT3 mutations.

Regression Analyses of Distributions using Quantile Functional Regression