"... indirect standardization in epidemiology is defined as the ratio
between the observed number cases (O) over the expected number cases (E)
of any disease or death, which is denote as SIR (SMR)=O/E. Typically,
the E is computed based on the age-specific rates (incidence or
mortality of a standard population) times the age distribution of the
study group.?? The indirect standardized (incidence or mortality) rate is
computed as the following product: SIR*Crude rate. My question is how
the SIR can be best interpreted. I have used relative excess with
respect to the standard population. I appreciate any suggestion. "
The SIR or SMR is simply the proportionate incidence or mortality excess
(or if?? under 1, the deficit) observed in a target (study) group
relative to what would be expected based on its age distribution and the
age-specific rates from the reference (standard) population - see for
example Modern Epidemiology, 3rd ed. (2008) Ch. 4. Without further
assumptions it has no further interpretation. The traditional last step
of multiplying by the crude rate obscures the proportionate relationship
and is more often than not omitted in the literature I see.
Despite being pointed at least as far back as 1934 by Yates, sometimes
overlooked is that the ratio of SMRs or indirectly standardized rates
from two different targets will generally not equal the proportionate
excess of one target relative to the other after categorical age
adjustment; this is so even if the two SMRs are computed using the same
reference standard, unless the population and age effects on the rates
are multiplicative
- see Breslow et al. JASA 1983 for a classic and still useful article on
methods and pitfalls of comparing and modeling SIRs and SMRs:
Breslow NE, Lubin JH, Marek P, Langholz, B. Multiplicative models and
cohort analysis. J Am Stat Assoc 1983;78: 1???12.
More details of SMR extensions, analysis and modeling can be found in
Breslow NE, Day NE. Statistical methods in cancer research. Vol II: the
design and analysis of cohort studies. Lyon: IARC, 1987.
Original Message------
Dear All:
The indirect standardization in epidemiology is defined as the ratio between the observed number cases (O) over the expected number cases (E) of any disease or death, which is denote as SIR (SMR)=O/E. Typically, the E is computed based on the age-specific rates (incidence or mortality of a standard population) times the age distribution of the study group. The indirect standardized (incidence or mortality) rate is computed as the following product: SIR*Crude rate. My question is how the SIR can be best interpreted. I have used relative excess with respect to the standard population. I appreciate any suggestion.
Erick Suárez, PhD
Department of BIostatistics and Epidemiology
School of Public Health, University of Puerto Rico