Non-adherence in health care results when a patient does not initiate or continue care that a provider has recommended. Previous research identifies non-adherence as a major source of waste in US health care, totaling approximately 2.3% of GDP, and has proposed a plethora of interventions to raise adherence. However, health economics provides little explicit analyses of the important dynamic demand behavior that drives non-adherence, and it is often casually attributed to uninformed patients. We argue that whereas providers may be more informed about the population-wide effects of treatments, patients are more informed about the individual-specific value of treatment. We interpret a patient’s decision to adhere to a treatment regime as an optimal stopping problem in which patients learn the value of a treatment through treatment experience. We derive strong positive and normative implications resulting from interpreting non-adherence as an optimal stopping problem. Our positive analysis derives an “adherence survival function,” depicting the share of patients still on treatment as a function of time, and predicts how various observable factors alter adherence. Our normative analysis derives the efficiency effects of non-adherence and the conditions under which adherence is too high or low. We consider the efficiency implications of this analysis for common adherence interventions. We argue that personalized medicine is intimately linked to adherence issues. It replaces the learning through treatment experience with a diagnostic test, and thereby speeds up the learning process and cuts over-adherence and raises under-adherence. We assess the quantitative implications of our analysis by calibrating the degree of over- and under-adherence for one of the largest US drug categories: cholesterol-reducing drugs. Contrary to frequent normative claims of under-adherence, our estimates suggest the efficiency loss from over-adherence is over 80% larger than from under-adherence, even though only 43% of patients fully adhere.