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Background: The standardized mortality ratio (SMR) is often used to assessand compare hospital performance. While it has been recognized that hospitalsmay differ in their SMRs due to differences in patient composition, there is alack of rigorous analysis of this and other - largely unrecognized - propertiesof the SMR. Methods: This paper proposes five axiomatic requirements foradequate standardized mortality measures: strict monotonicity, case-mixinsensitivity, scale insensitivity, equivalence principle, and dominanceprinciple. Given these axiomatic requirements, effects of variations in patientcomposition, hospital size, and actual and expected mortality rates on the SMRwere examined using basic algebra and calculus. In this regard, wedistinguished between standardization using expected mortality rates derivedfrom a different dataset (external standardization) and standardization basedon a dataset including the considered hospitals (internal standardization).Results: Under external standardization, the SMR fulfills the axiomaticrequirements of strict monotonicity and scale insensitivity but violates therequirement of case-mix insensitivity, the equivalence principle, and thedominance principle. All axiomatic requirements not fulfilled under externalstandardization are also not fulfilled under internal standardization. Inaddition, the SMR under internal standardization is scale sensitive andviolates the axiomatic requirement of strict monotonicity. Conclusions: The SMRfulfills only two (none) out of the five proposed axiomatic requirements underexternal (internal) standardization. Generally, the SMRs of hospitals aredifferently affected by variations in case mix and actual and expectedmortality rates unless the hospitals are identical in these characteristics.These properties hamper valid assessment and comparison of hospital performancebased on the SMR.

Can we trust the standardized mortality ratio? A formal analysis and evaluation based on axiomatic requirements