  Quantitative imaging biomarkers (QIB) are extracted from medical images in
radiomics for a variety of purposes including noninvasive disease detection,
cancer monitoring, and precision medicine. The existing methods for QIB
extraction tend to be ad-hoc and not reproducible. In this paper, a general and
flexible statistical approach is proposed for handling up to three-dimensional
medical images in an objective and principled way. In particular, a model-based
spatial process decomposition is developed where the random weights are unique
to individual patients for component functions common across patients. Model
fitting and selection are based on maximum likelihood, while feature
extractions are via optimal prediction of the underlying true image. A
simulation study evaluates the properties of the proposed methodology and for
illustration, a cancer image data set is analyzed and QIBs are extracted in
association with a clinical endpoint.
