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When comparing groups, it is important to make sure we are making a fair comparison. Thus, it is helpful to standardize the rates, in order to remove the effect of a potential confounder (often age), which might differ between populations and could distort the results. Standardization is also helpful when comparing rates of one population over time, such as monitoring disease in a population over many years.
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.
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 age-specific rates.
\(I_=\dfrac I_>>\)
where Ii is a group-specific rate and \(\sum W_=1\)
The necessary data for direct standardization is 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 and Pennsylvania Dept of Health’s tutorial on Age-Adjusted Rates (pa.gov) 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.
Consider the below 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, the male rate is 2.2/1000, and the female rate is 0.9/1000.
If we also know that:
What is the expected crude rate for group 1?
It is (2.2 × 0.6) + (0.9 × 0.4) = 1.68 / 1000. The observed crude rate is 1.68.
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?
Answer: the expected crude rate is (2.2 * 0.8) + (0.9 * 0.2) = 1.94.