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Spatial process decomposition for quantitative imaging biomarkers using multiple images of varying shapes. Statistics in Medicine. 2021; 40: 1243– 1261. https://doi.org/10.1002/sim.8838, , , , .
Biomarkers are diagnostic and prognostic tools, objectively measured and evaluated as an indicator of biological processes or response to therapy. Medical images, such as computed tomography (CT) or positron emission tomography (PET) are not just pictures but potential biomarkers, too. Features of images can be evaluated qualitatively (e.g., shape description and stages of disease) or quantitatively (e.g., tumor volume). Recently, significant effort has been aimed towards transition from qualitative to quantitative imaging which allows development of objective and quantifiable quantitative imaging biomarkers (QIBs). QIBs are therefore promising tools to overcome the subjective visual interpretation and inter-observer variability that often occur in medical image assessment.
For developing QIBs, a new field of “radiomics” has emerged, where high-throughput features are extracted from medical images, with ultimate goal of associating these features with clinical endpoints, such as duration of treatment benefit or patient survival. However, the number of available high-throughput features is easily much larger than the sample size of patients, in which case many classical statistical tools cannot work well. Too many features also leads to strong correlations, i.e., heavy redundancy among them, indicating little additional information is extracted by increasing the number of features. Moreover, most existing radiomics features focus on local spatial behaviors or ignore spatial structures, which were developed largely for rectangular images and require binning the intensity values into ad-hoc distinct categories.
Our study develops a novel statistical method to extract QIBs accounting for broader scale spatial characteristics of imaging, with features less correlated than other approaches, free of intensity binning, and directly applicable to non-rectangular regions of interest (ROIs) having varying shapes among patients. Our key strategy is model-based spatial process decomposition that can deal with 1D time point, 2D pixel, or 3D voxel data within a same general framework of spatial random-effects models. We formulate the observed image intensities within ROIs as linear combinations of common spatial processes. With these common processes as important building blocks, individual patients carry unique weights on the processes, where weights are estimated via the random effects in the model. Finally, an orthogonalization of these random effects produces nearly uncorrelated biomarkers. As a whole, model fitting and selection are based on maximum likelihood, and biomarker generation is via optimal prediction of the underlying true signals. If there exists evident large-scale spatial structure, our method is expected to extract much fewer, but at the same time much more unique QIBs. This data-driven methodology leads to a better understanding of the spatial patterns it captures.