  Background: The standardized mortality ratio (SMR) is often used to assess
and compare hospital performance. While it has been recognized that hospitals
may differ in their SMRs due to differences in patient composition, there is a
lack of rigorous analysis of this and other - largely unrecognized - properties
of the SMR. Methods: This paper proposes five axiomatic requirements for
adequate standardized mortality measures: strict monotonicity, case-mix
insensitivity, scale insensitivity, equivalence principle, and dominance
principle. Given these axiomatic requirements, effects of variations in patient
composition, hospital size, and actual and expected mortality rates on the SMR
were examined using basic algebra and calculus. In this regard, we
distinguished between standardization using expected mortality rates derived
from a different dataset (external standardization) and standardization based
on a dataset including the considered hospitals (internal standardization).
Results: Under external standardization, the SMR fulfills the axiomatic
requirements of strict monotonicity and scale insensitivity but violates the
requirement of case-mix insensitivity, the equivalence principle, and the
dominance principle. All axiomatic requirements not fulfilled under external
standardization are also not fulfilled under internal standardization. In
addition, the SMR under internal standardization is scale sensitive and
violates the axiomatic requirement of strict monotonicity. Conclusions: The SMR
fulfills only two (none) out of the five proposed axiomatic requirements under
external (internal) standardization. Generally, the SMRs of hospitals are
differently affected by variations in case mix and actual and expected
mortality rates unless the hospitals are identical in these characteristics.
These properties hamper valid assessment and comparison of hospital performance
based on the SMR.
