In this thesis, we propose functional and spatial statistical methods for the purpose of improving radiation therapy treatments and optimizing patient outcomes. Medical imaging is crucial for the diagnosis and treatment of a wide range of diseases, and deep learning models have increasingly been used for contouring medical images. However, ensuring the accuracy and safety of computer-generated contours is essential, particularly for radiation treatment planning. This thesis addresses the need to quantify the quality of these contours and to account for uncertainty in the delivered dose when predicting radiotherapy toxicities. In the first project, we introduce an innovative method for the quality assurance of autocontours, computer-generated contours, in medical imaging using shape statistics. This approach is distinct from the prevalent use of models that rely on image-specific features and leverages the geometric properties of the contour itself, offering broad applicability across various imaging technologies and medical institutions. By focusing on shape features that are invariant to the imaging modality, we present a solution that significantly advances medical imaging quality assurance, enabling more accurate and safe radiation treatment plans. Building on this, in the second project, we present a novel Bayesian additive regression trees model specifically designed for functional data that addresses the challenge of location-specific errors within treatment plans. This model, a novel approach in the field, not only identifies clinically unacceptable contours but also pinpoints the precise location of errors, providing clinicians with actionable insights for plan correction. This capability represents a substantial improvement over existing methods, which either lack specificity in error localization or depend heavily on imaging features that may vary across imaging modalities and medical institutions. In the third project, we expand the scope of treatment planning quality assurance to include spatial and measurement error models for lung radiation treatment planning, specifically focusing on the voxel-wise prediction of pneumonitis, a severe inflammation of lung tissue, as a negative consequence of radiation treatment. By incorporating spatial random effects and addressing measurement errors in radiation dose delivery, we offer a novel methodology for radiation treatment planning that provides deeper insights into the factors influencing treatment success and patient safety. This approach addresses the limitations of current methods of voxel-wise disease prediction that overlook spatial information and measurement inaccuracies, providing a more accurate assessment of negative outcomes such as the development of pneumonitis. All together, these projects bridge significant gaps in radiation therapy research, from enhancing the interpretability and effectiveness of autocontour quality assurance to incor- porating spatial and measurement error considerations in treatment planning. This work not only contributes valuable tools and insights to the field of radiation therapy but also sets the stage for ongoing advancements in medical imaging and treatment optimization.