Esophageal cancer is a common malignant tumor of the digestive tract with a high incidence rate in China. Early detection, early diagnosis, and early treatment can greatly improve the survival rate of patients.To address the uncertainty and fuzziness existing in the selection of early esophageal cancer screening schemes, this paper establishes an extended REGIME decision-making framework under the q-rung orthopair fuzzy environment. First, a novel order relation of q-rung orthopair fuzzy numbers is proposed, which is strictly proved to be a q-rung orthopair fuzzy admissible order. Second, a new q-rung orthopair fuzzy distance operator is constructed to measure the differences between q-rung orthopair fuzzy sets, and the proposed order relation and distance operator are integrated into the construction process of the preference matrix of the REGIME method. Simulation results show that compared with existing methods, the proposed q-rung orthopair fuzzy order relation can obtain more reliable and convincing ranking results of fuzzy numbers, and the newly constructed distance operator can accurately identify subtle differences among q-rung orthopair fuzzy sets with better stability than state-of-the-art distance operators. Furthermore, the extended q-rung orthopair fuzzy REGIME method is applied to select optimal early esophageal cancer screening schemes. Practical application results reveal that when the parameter q ranges from 3 to 20, the proposed method achieves the optimal stability, and the relative ranking order of all alternatives remains unchanged.