Jin, Jin2019-09-172019-09-172019-06https://hdl.handle.net/11299/206655University of Minnesota Ph.D. dissertation. June 2019. Major: Biostatistics. Advisors: Joseph Koopmeiners, Lin Zhang. 1 computer file (PDF); xiv, 134 pages.As a continuously developing tool for the diagnosis and prognosis of prostate cancer, multi-parametric magnetic resonance imaging (mpMRI) has been widely used in a variety of prostate cancer-related topics. While current research has shown the great potential of mpMRI in detecting prostate cancer, further investigation is needed for modeling some specific features of mpMRI, including the anatomic difference between different regions of a prostate, the spatial correlation between voxels within each prostate image, and the difference in the distribution of the observed mpMRI parameters between patients. This dissertation focuses on novel statistical methods for the voxel-wise classification of prostate cancer using mpMRI data. Systematic modeling frameworks will be proposed to improve cancer classification by incorporating the aforementioned features of mpMRI. Three topics are discussed in depth: (1) development of a general Bayesian modeling framework that can incorporate the various mpMRI features; (2) how to model the mpMRI features in the proposed Bayesian framework, preferably in a computationally efficient manner; (3) development of an alternative approach to accounting for the mpMRI features, which uses a multi-resolution modeling technique to account for the regional heterogeneity, and is flexible to be extended to more complex classification problems for prostate cancer. The solutions are presented in the following order. In Chapter 2, we propose a Bayesian hierarchical modeling framework that allows complex distributional assumptions for the various data components. Based on the modeling framework, two approaches will be proposed for modeling the heterogeneity between regions of the prostate, which can be combined with a spatial Gaussian kernel smoother to account for residual spatial correlation and reduce random noise in the data. In Chapter 3, we add additional layers in the hierarchical model to model the spatial correlation structure and between-patient heterogeneity. Modeling the spatial correlation structure is computationally challenging and even infeasible for our mpMRI data set, due to the large number of voxels within each image. Three scalable spatial modeling approaches are then proposed for the correlation between voxels. In Chapter 4, we develop an alternative, machine learning-based method to account for the mpMRI features: a super learner with an ensemble learning technique is utilized to combine base learners trained in multi-resolution sub-regions. Specific algorithms will be introduced for both the classification of binary cancer status, and a more complex problem: classification of an ordinal outcome that indicates the clinical significance of prostate cancer. Method performance will be illustrated by simulation studies and applications to in vivo data that motivated the method's development.enBayesian hierarchical modelsMulti-image spatial modelingMulti-parametric magnetic resonance imagingProstate CancerSuper LearnerVoxel-wise ClassificationThesis or Dissertation