Angle-closure glaucoma is a major cause of irreversible visual impairment and can be identified by measuring the anterior chamber angle (ACA) of the eye. The ACA can be viewed clearly through anterior segment optical coherence tomography (AS-OCT), but the imaging characteristics and the shapes and locations of major ocular structures can vary significantly among different AS-OCT modalities, thus complicating image analysis. To address this problem, we propose a data-driven approach for automatic AS-OCT structure segmentation, measurement, and screening. Our technique first estimates initial markers in the eye through label transfer from a hand-labeled exemplar data set, whose images are collected over different patients and AS-OCT modalities. These initial markers are then refined by using a graph-based smoothing method that is guided by AS-OCT structural information. These markers facilitate segmentation of major clinical structures, which are used to recover standard clinical parameters. These parameters can be used not only to support clinicians in making anatomical assessments, but also to serve as features for detecting anterior angle closure in automatic glaucoma screening algorithms. Experiments on Visante AS-OCT and Cirrus high-definition-OCT data sets demonstrate the effectiveness of our approach.