Please download our Microsoft Excel file to calculate Standardized Mortality Ratios (XLS).
The Standardized Mortality Ratio (SMR) uses the indirect method of adjustment to compare the mortality experience of a given area with a standard or to evaluate the mortality experience due to several causes of death within a given area against a common standard. The table below shows the computation of a standardized mortality ratio.
| Ages | 11 Year State Rate Per 100,000 |
| Population |
| Expected Deaths | Observed Deaths | Excess Deaths |
|---|---|---|---|---|---|---|---|
| 0 to 4 | 0.26 | x | 2531 | = | 0.01 | 0 | -0.01 |
| 5 to 9 | 0.00 | x | 2491 | = | 0.00 | 0 | 0.00 |
| 10 to 14 | 0.00 | x | 3067 | = | 0.00 | 0 | 0.00 |
| 15 to 9 | 0.73 | x | 3877 | = | 0.03 | 0 | -0.03 |
| 20 to 24 | 0.96 | x | 3918 | = | 0.04 | 0 | -0.04 |
| 25 to 29 | 3.63 | x | 3221 | = | 0.12 | 0 | -0.12 |
| 30 to 34 | 16.82 | x | 2518 | = | 0.42 | 1 | 0.58 |
| 35 to 39 | 61.06 | x | 1920 | = | 1.17 | 1 | -0.17 |
| 40 to 44 | 217.01 | x | 1718 | = | 3.73 | 4 | 0.27 |
| 45 to 49 | 541.73 | x | 1736 | = | 9.40 | 14 | 4.60 |
| 50 to 54 | 1019.55 | x | 2353 | = | 23.99 | 31 | 7.01 |
| 55 to 59 | 1764.28 | x | 2511 | = | 44.30 | 53 | 8.70 |
| 60 to 64 | 2847.98 | x | 2583 | = | 73.56 | 76 | 2.44 |
| 65 to 69 | 3860.44 | x | 2277 | = | 87.90 | 93 | 5.10 |
| 70 to 74 | 4960.76 | x | 1739 | = | 86.27 | 95 | 8.73 |
| 75 to 79 | 5547.40 | x | 1026 | = | 56.92 | 64 | 7.08 |
| 80 to 84 | 5231.93 | x | 552 | = | 28.88 | 32 | 3.12 |
| 85+ | 4139.12 | x | 344 | = | 14.24 | 17 | 2.76 |
| Total | | | | 430.98 | 481 | 50.02 |
Standardized Mortality Ratio
= Observed deaths / Expected deaths
= 481 / 430.98
= 1.12
Excess Deaths
= Observed deaths - Expected deaths
= 481 - 430.98
= 50.02 or 4.5 deaths per year (50.02 deaths / 11 years)
Age by sex (and sometimes race) specific rates for the comparison population are multiplied by the local population counts or estimates, cell by cell, and summed to yield expected deaths. Actual (observed) deaths are then divided by the expected deaths to give the ratio. This ratio expresses the difference between the mortality experience of the population under study and the experience of that population as it would be if it experienced the age specific rates of the comparison population. A ratio greater than 1.0 indicates that more mortality has occurred than would have been expected, while a ratio less than 1.0 indicates that less mortality has occurred. The decimal fraction shows the percentage comparison. The SMR of 1.12 for lung cancer among males in Scranton in the example means that 12% more deaths occurred than would have been expected.
The computation of the statistic also allows easy calculation of the excess mortality which is due to variables other than age, sex, or race. This information may be obtained for both the whole population, or, as the table shows, for each age group.
SMRs for several causes of death may be compared within the same geographic area. The table below shows that cancers other than lung are also of major importance for program action in Scranton. Prevention and education activities directed against tobacco use are needed to fight mouth and lung cancers, of course. But dietary education and screening activities are needed to prevent colon cancer, and to detect it in its early, treatable stages.
| Cause of Death Grouping (ICD-9 Codes 140 to 204) | Expected Deaths | Observed Deaths | SMR |
|---|---|---|---|
| All Cancer Deaths | 1,325.37 | 1516 | 1.14 |
| Lip, Oral Cavity and Pharynx | 33.81 | 47 | 1.39 |
| Esophagus | 36.84 | 45 | 1.22 |
| Stomach | 54.58 | 72 | 1.32 |
| Colon, Rectum, Rectosigmoid | 180.48 | 238 | 1.32 |
| Pancreas | 62.51 | 72 | 1.15 |
| Trachea, Bronchus & Lung | 430.98 | 481 | 1.12 |
| Genitourinary | 168.90 | 162 | 0.96 |
| Bladder | 45.02 | 50 | 1.11 |
| Lymphomas | 44.57 | 47 | 1.05 |
As with many other statistics, the SMR has to be interpreted with full consciousness of the possible effects of random variation due to low numbers. If a very few deaths would make a difference to the interpretation, caution is indicated. Use of an appropriate measure of statistical significance can be helpful for this purpose.
Another important limitation to the use of the SMR is that it cannot be used to compare different areas, because each area's population profile weights the age specific death rates differently. Comparison of differrent areas should be done with the direct method of standardization described in Age-Adjusted Rates.
Analysts should also bear in mind the quality of the data which are used to compute the SMR. To the extent that change in population or death rates are not linear, as would be the case, for example, if there had been sharp increases in population or deaths after 1980, the accuracy of the SMR suffers. The SMR assumes that geocoding of death certificates is accurate, but analysts of the data know that too many deaths are, in fact, often allocated to cities and boroughs, at the expense of surrounding townships, because people think that their post office address corresponds to their place of residence. Finally, the cause of death codes are subject to errors of unknown magnitude, and those errors can produce misleading results. The SMR can be very useful as an indicator of what may be taking place in a community, if it is used with an awareness of its limitations.