Spatial patterns of radiotracer binding in positron emission tomography (PET) images may convey information related to the disease topology. However, this information is not captured by the standard PET image analysis that quantifies the mean radiotracer uptake within a region of interest (ROI). On the other hand, spatial analyses that use more advanced radiomic features may be difficult to interpret. Here we propose an alternative data-driven, voxel-based approach to spatial pattern analysis in brain PET, which can be easily interpreted. We apply principal component analysis (PCA) to identify voxel covariance patterns, and optimally combine several patterns using the least absolute shrinkage and selection operator (LASSO). The resulting models predict clinical disease metrics from raw voxel values, allowing for inclusion of clinical covariates. The analysis is performed on high-resolution PET images from healthy controls and subjects affected by Parkinson's disease (PD), acquired with a pre-synaptic and a post-synaptic dopaminergic PET tracer. We demonstrate that PCA identifies robust and tracer-specific binding patterns in sub-cortical brain structures; the patterns evolve as a function of disease progression. Principal component LASSO (PC-LASSO) models of clinical disease metrics achieve higher predictive accuracy compared to the mean tracer binding ratio (BR) alone: the cross-validated test mean squared error of adjusted disease duration (motor impairment score) was 16.3 ± 0.17 years2 (9.7 ± 0.15) with mean BR, versus 14.4 ± 0.18 years2 (8.9 ± 0.16) with PC-LASSO. We interpret the best-performing PC-LASSO models in the spatial sense and discuss them with reference to the PD pathology and somatotopic organization of the striatum. PC-LASSO is thus shown to be a useful method to analyze clinically-relevant tracer binding patterns, and to construct interpretable, imaging-based predictive models of clinical metrics.