  Diagnostic imaging has gained prominence as potential biomarkers for early
detection and diagnosis in a diverse array of disorders including cancer.
However, existing methods routinely face challenges arising from various
factors such as image heterogeneity. We develop a novel imaging-based
distributional data analysis (DDA) approach that incorporates the probability
(quantile) distribution of the pixel-level features as covariates. The proposed
approach uses a smoothed quantile distribution (via a suitable basis
representation) as functional predictors in a scalar-on-functional quantile
regression model. Some distinctive features of the proposed approach include
the ability to: (i) account for heterogeneity within the image; (ii)
incorporate granular information spanning the entire distribution; and (iii)
tackle variability in image sizes for unregistered images in cancer
applications. Our primary goal is risk prediction in Hepatocellular carcinoma
that is achieved via predicting the change in tumor grades at post-diagnostic
visits using pre-diagnostic enhancement pattern mapping (EPM) images of the
liver. Along the way, the proposed DDA approach is also used for case versus
control diagnosis and risk stratification objectives. Our analysis reveals that
when coupled with global structural radiomics features derived from the
corresponding T1-MRI scans, the proposed smoothed quantile distributions
derived from EPM images showed considerable improvements in sensitivity and
comparable specificity in contrast to classification based on routinely used
summary measures that do not account for image heterogeneity. Given that there
are limited predictive modeling approaches based on heterogeneous images in
cancer, the proposed method is expected to provide considerable advantages in
image-based early detection and risk prediction.
