Disease can be measured in one population or compared between populations. Within one population, it is common to summarize disease burden with the *number* of cases. Another measure is the *crude rate* (i.e., *x* cases / *y* population at-risk), which you will also recognize as the cumulative incidence rate. If the distribution of a modifier of disease frequency (such as age) is different between two populations, however, a comparison of the crude rates in the two populations can mask the rate. If the goal is to compare rates between populations, it is helpful standardize the rates, which removes the effect of a potential confounder, such as the age distribution, that differs between the populations. Standardization is also helpful when comparing rates of one population over time, such as monitoring a disease in a population over many years. A *standardized rate* is a measure of disease frequency that facilitates comparisons of populations with a different distribution of one or more potential confounding variables. (e.g., *x* cases / *y* population at-risk, adjusted to remove the effect of potential confounder [e.g., age]).

There are two different approaches to standardizing a rate. **Direct standardization, **more commonly used, creates a summary disease rate for a population that would be expected if the study population had a *population distribution* identical to that of an arbitrarily chosen standard population. A reference population is used as the standard population. The standardized rate is the sum of weighted group-specific rates, with weights derived from the standard population. The weights sum to 1.0. A standardized rate is essentially a weighted average of the age-specific rates.

\[I_{W}=\frac{\sum W_{i}I_{i}}{\sum W_{i}}\]

where \(I_{i}\) is a group-specific rate and \(\sum W_{i}=1\).

The necessary data for direct standardization are the group-specific disease rates for the study population and the population distribution from the standard population.

Review the SEER Stat Tutorials: Calculating Age-adjusted Rates. for producing an adjusted rate by the direct method. Do you understand how direct adjustment is a weighted average of age-specific rates?

**Indirect standardization** also produces a weighted average, through the production of a summary disease rate for the study population which would be expected if the *disease experience of the study population* were identical to that of a standard population. The standard population is arbitrarily chosen, but should be as similar as possible to the study population Indirect adjustment is used when accurate group-specific rates for the study population are not available. (If these rates are available, direct adjustment is preferred because it uses more information from the study population.) Indirect adjustment produces an expected rate. Observed and expected rates are typically compared as a standardized ratio. Indirect adjustment is often used in occupational health to calculate standardized mortality ratios, which is dividing the observed death rate by the expected death rate.

The data required for indirect standardization is the crude rate for the study population; the population distribution for the study population and group-specific rates for the standard population.

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Example 4-1:
Section* *

Consider the above data for which the researcher could not obtain the gender-specific rates. From a standard population it is known that the crude rate is 1.5/1000, male rate is 2.2/1000, and female rate is 0.9/1000.

The expected crude rate for group 1 then is (2.2 × 0.6) + (0.9 × 0.4) = 1.68 / 1000. The observed crude rate is 1.6.

*Come up with an answer to this question by yourself and then click on the button below to reveal the solution.*

What is the expected crude rate for group 2?

In Group 2, the expected crude rate is (2.2 * 0.8) + (0.9 * 0.2) = 1.94.

The observed rate is 1.8.

The standardized ratio will be less than 1.

**Age-specific rates*** *(i.e.., *x* cases in a specific age group/(population at-risk in same age group) are also useful in summarizing health status of a population.

In what situations would indirect adjustment be preferred over direct adjustment? Read this comparison of direct and indirect adjustment from New Mexico Department of Health.

Can you answer the true/false questions below based on your reading?

Direct standardized rates are only comparable if the same standard population is used. For example, the US standard population of 1940 was considerably younger than the US standard population based on the 2000 census. This will affect the adjusted rates. Always pay attention to the reference population when comparing standardized rates.

The age-adjusted rates and confidence intervals or a relative risk (rate ratio) adjusted for age.