We conduct the first large-scale analysis of the accessibility of mobile apps, examining what unique insights this can provide into the state of mobile app accessibility. We analyzed 5,753 free Android apps for label-based accessibility barriers in three classes of image-based buttons: Clickable Images, Image Buttons, and Floating Action Buttons. An epidemiology-inspired framework was used to structure the investigation. The population of free Android apps was assessed for label-based inaccessible button diseases. Three determinants of the disease were considered: missing labels, duplicate labels, and uninformative labels. The prevalence, or frequency of occurrences of barriers, was examined in apps and in classes of image-based buttons. In the app analysis, 35.9% of analyzed apps had 90% or more of their assessed image-based buttons labeled, 45.9% had less than 10% of assessed image-based buttons labeled, and the remaining apps were relatively uniformly distributed along the proportion of elements that were labeled. In the class analysis, 92.0% of Floating Action Buttons were found to have missing labels, compared to 54.7% of Image Buttons and 86.3% of Clickable Images. We discuss how these accessibility barriers are addressed in existing treatments, including accessibility development guidelines.