Screening interventions can produce very different treatment outcomes, depending on the reasons why patients had been unscreened in the first place. Economists have paid scant attention to these complexities and their implications for evaluating screening programs. In this paper, we propose a simple economic framework to guide policy-makers and analysts in designing and evaluating the impact of screening on treatment uptake. We apply these insights to several salient empirical examples that illustrate the different kinds of effects screening programs might produce. Our empirical examples focus on contexts relevant to the top cause of death in the United States, heart disease. We find that currently undiagnosed patients differ from currently diagnosed patients in important ways, leading to lower predicted uptake of recommended treatment if these patients were diagnosed. Additionally, changes in the composition of diagnosed patients can produce misleading conclusions during policy analysis, such as spurious reductions in measured health system performance as screening expands.