A gap exists in understanding how medication non-adherence differs across subgroups of patients, and the role cost-exposure plays therein. We use 2013 claims data for a sample of patients suffering from four chronic conditions (diabetes, asthma, hypertension, and coronary heart disease), and use agglomerative hierarchical cluster analysis, based on patients' clinical and demographic features, to identify patient clusters. We study the heterogeneous association of cost-exposure - the amount that patients incur out-of-pocket for medications - with adherence across the clusters. We compare this approach with an alternative model-based recursive partitioning method for identifying clusters with distinctive cost and adherence relationships, and evaluate the most relevant partitioning features and their clinical implications. We validate and compare the two approaches by running them on 'test' patients from 2012 claims data. Our study aims to better identify potential reasons for non-adherence across distinct patient groups, and serves as a data-driven way for generating hypotheses to identify patient groups for targeting in experiments aimed at mitigating non-adherence in the future.