An odds-ratio approach for handling proportional and bounded values in data envelopment analysis

The usual assumption in data envelopment analysis (DEA) that all input and output values are unconstrained positive values is not always satisfied, such as when analysing proportions, rates, and percentages bound between 0 and 1 (e.g., defect, graduation, satisfaction, or mortality rates). In such cases, solving standard constant returns-to-scale (CRS) DEA models can produce output target values that exceed their upper bounds (e.g., 130% survival or 210% market penetration). Data constrained on other intervals (e.g., patient satisfaction scores between 1 and 5) present a related problem, where a computed target theoretically can exceed its upper bound. We introduce an odds-ratio transformation for such cases that always produces targets within their given bounds and explore its impact on analysis results (efficiency scores, targets, weights), offering the modeller an alternative for evaluating relative efficiency and setting management goals when variable returns-to-scale (VRS) relationships are not appropriate.