Background: While discontinuation of COPD maintenance medication is a known problem, the proportion of patients with discontinuation and its geographical and sociodemographic distribution are so far unknown in Sweden. Therefore, we analyse this question by applying an innovative approach called multilevel analysis of individual heterogeneity and discriminatory accuracy (MAIHDA). Patients and Methods: We analysed 49,019 patients categorized into 18 sociodemographic contexts and 21 counties of residence. All patients had a hospital COPD diagnosis and had been on inhaled maintenance medication during the 5 years before the study baseline in 2010. We defined "discontinuation" as the absolute lack of retrieval from a pharmacy of any inhaled maintenance medication during 2011. We performed a cross-classified MAIHDA and obtained the average proportion of discontinuation, as well as county and sociodemographic absolute risks, and compared them with a proposed benchmark value of 10%. We calculated the variance partition coefficient (VPC) and the area under the receiver operating characteristics curve (AUC) to quantify county and sociodemographic differences. To summarize the results, we used a framework with 15 scenarios defined by the size of the differences and the level of achievement in relation to the benchmark value. Results: Around 18% of COPD patients in Sweden discontinued maintenance medication, so the benchmark value was not achieved. There were very small county differences (VPC=0.35%, AUC=0.54). The sociodemographic differences were small (VPC=4.98%, AUC=0.57). Conclusion: Continuity of maintenance medication among COPD patients in Sweden could be improved by reducing the unjustifiably high prevalence of discontinuation. The very small county and small sociodemographic differences should motivate universal interventions across all counties and sociodemographic groups. Geographical analyses should be combined with sociodemographic analyses, and the cross-classified MAIHDA is an appropriate tool to assess health-care quality.