Bayesian spatial models for voxel‐wise prostate cancer classification using multi‐parametric magnetic resonance imaging data

Multi‐parametric magnetic resonance imaging (mpMRI) has been playing an increasingly important role in the detection of prostate cancer (PCa). Various computer‐aided detection algorithms were proposed for automated PCa detection by combining information in multiple mpMRI parameters. However, there are specific features of mpMRI, including between‐voxel correlation within each prostate and heterogeneity across patients, that have not been fully explored but could potentially improve PCa detection if leveraged appropriately. This article proposes novel Bayesian approaches for voxel‐wise PCa classification that accounts for spatial correlation and between‐patient heterogeneity in the mpMRI data. Modeling the spatial correlation is challenging due to the extreme high dimensionality of the data, and we propose three scalable approaches based on Nearest Neighbor Gaussian Process (NNGP), reduced‐rank approximation, and a conditional autoregressive (CAR) model that approximates a Gaussian Process with the Matérn covariance, respectively. Our simulation study shows that properly modeling the spatial correlation and between‐patient heterogeneity can substantially improve PCa classification. Application to in vivo data illustrates that classification is improved by all three spatial modeling approaches considered, while modeling the between‐patient heterogeneity does not further improve our classifiers. Among the proposed models, the NNGP‐based model is recommended given its high classification accuracy and computational efficiency.