# Standardized Incidence Ratios

To calculate age-adjusted standardized rates, as above, one must first have the age-specific rates of disease for each of the populations to be compared. One then uses a standard age distribution to compute a hypothetical summary rate that indicates what the overall rate of disease would be for each population, if they had had the same age distribution as the standard. In other words, one uses each population's real age-specific rates and applies these to a single standard age distribution. In some situations, however, the age distribution of the populations being compared is know, but it is difficult, if not impossible, to obtain reliable estimates of age-specific rates, particularly if one is interested in smaller populations in which age-specific rates would be subject to random error because of relatively small numbers of observations. Consider the problem of a cluster of cancer cases that come to our attention in a specific community. The obvious question is whether the occurrence of cancer in this community is higher than that of other communities in the same state. However, the number of cases of a particular type of cancer occurring in even a relatively large community is typically small enough to produce very unstable rates due to random error. On the other hand, age-specific rates for the entire state would be much more stable, because of the larger sample size. In this situation one can approach the problem by using the age-specific rates observed for the entire state population as an estimate of the expected rates for the component communities. One can then apply these rates to the age distribution of each community to compute the expected number of specific cancer cases for a given community and then compare the expected number of cases to the observed cases. This approach is typically used by state cancer registries. Since the frequencies of different cancers oftern differ by gender, separate computations are performed for men and women.

Consider the following example adapted from the Massachusetts Department of Public Health:

Age Group

A) Overall Age-specific State Rate

B) Town's Population Size

C) Expected Cases (A x B)

Observed # of Cases

0-19

0.0001

74,857

7.47

11

20-44

0.0002

134,957

26.99

25

45-64

0.0005

54,463

27.23

30

65-74

0.0015

25,136

37.70

40

75-84

0.0018

17,012

30.62

30

85+

0.0010

6,337

6.34

8

Totals

136.35

144

SIR = (Observed Cases/Expected Cases) x 100 = (144/136.35 4) x 100 =106

Consequently, these results suggest that, after adjusting for age differences, the incidence of this particular type of cancer in this town was 6% higher than expected based on average age-specific rates for the state. The Massachusetts Department of Public Health provide the following comments regarding the limitations of thise type of data:

"... apparent increases or decreases in cancer incidence over time may reflect changes in diagnostic methods or case reporting rather than true changes in cancer incidence. Three other limitations must be considered when interpreting cancer incidence data for Massachusetts cities and towns: under-reporting in areas close to neighboring states, under-reporting of cancers that may not be diagnosed in hospitals, and cases being assigned to incorrect cities/towns."

Another important consideration is the precision of these estimates. This is best evaluated by computing a 95% confidence interval for the SIR. The Epi_Tools.XLS spreadsheet has a worksheet that will help you compute the confidence interval. For this example, the 95% confidence interval is:

95% confidence interval = 88 to123

What is the null value for a standardized incidence ratio (SIR)?

## Cancer Registries

One of the important applications of standardized incidence ratios is to monitor the frequency of cancer and other diseases. SIRs are partcularly useful because the number of any particular type of cancer cases is likely to be small in an individual town, particularly if the community is small. In this situation standardized rates are less useful since the age-specific rates for a particular cancer would be subject to a huge amount of random error due to the small number of cases. SIRs get around this problem hy using the more stable rates for the entire state in order to compute the expected number of cases of a given cancer for a community, given the community's age distribution.

In the video below Professor Richard Clapp, the first director of the Massachusetts Cancer Registry discusses the need for registries of this type.

The link below will take you to the website for the Massachusetts Cancer Registry, where you can explore the SIRs and confidence intervals for specific types of cancers throughout Massachusetts.

http://www.mass.gov/eohhs/gov/departments/dph/programs/health-stats/cancer-registry/

## Standardized Mortality Ratios

When the outcome of interest is a mortality rate, a standardized incidence ratio is referred to as a standardized mortality rate.