Adjustment by Standardization
As noted above, age-specific rates provide a fairer comparison, but in many situations it is useful to have any overall summary rate that is adjusted for a confounding factor like age, so you can easily compare multiple populations. This can be done be calculating an "adjusted" overall rate which provides for a fairer comparison. In essence, this is accomplished by asking the question "How would the rates have compared if the two populations had had the same age distribution?" I will illustrate how to do this when comparing two populations, but keep in mind that multiple populations can be "adjusted" this way.
The Question We Would Like to Answer:
"What would the comparable death rate be in each state if both populations had identical age distributions?"
We saw above that the crude rate is a weighted average, but the comparison is distorted if the populations have different age distributions. In order to see how the two population would have compared if they had had the same distribution, we can calculate a summary rate by pretending that the distributions are the same in the populations being compared. We will use the long method of calculating the summary rate, as show at the bottom of the previous page. We will use each population's actual age-specific rates, BUT we will apply the same set of weights (fraction of people in each age group) to all of the populations being compared. In essence, this will give us a summary rate that is adjusted in a way that answers the question posed in the table above.
Basically, an age-standardized rate is also a weighted average, but the weights for the age categories are artificially set to be equal for the populations being compared by applying the weights of some standard population to each of them. We are still using the actual age-specific rates of each of the populations, but we are weighting them using a uniform standard population distribution.
What age distribution should you use? It doesn't really matter, but you usually see one of the following used for a standard age-distribution:
- The distribution of one of the populations being compared.
- An independent standard, e.g. US population in an arbitrarily chosen year.
- A distribution constructed by combining the populations, e.g. by averaging.
Example #1: Calculating standardized Rates using Florida's age distribution as the standard
If I wanted to ask the question "What would Alaska's overall mortality rate have looked like if Alaska had its actual age-specific rates but also had the same age distribution in the population as Florida?" I can do this quite simply by applying Florida's population distribution to Alaska's age-specific rates.
First, we will calculate the standardized rate for Florida by multiplying each of Florida's age-specific rates by the fraction of the Florida's population in each age group.
For the age group <5 years old: 0.07 x 284 = 19.18
For the age group 5 to 19 years: 0.18 x 57 = 10.26
For the age group 20 to 44 years: 0.36 x 198 = 71.28
For the age group 45 to 64 years: 0.21 x 815 = 154.85
For the age group greater than 64 year: 0.18 x 4,425 = 796.50
SUM = 1069 per 100,000 population
As you would expect, the standardized rate in Florida is the same as its crude rate, because we used Florida's age distribution as the standard.
Now let's use Florida's age distribution as the standard to calculate Alaska's standardized rate by multiplying each of Alaska's age-specific rates by the fraction of the Florida's population in each age group.
For the age group <5 years old: 0.07 x 274 = 19.18
For the age group 5 to 19 years: 0.18 x 65 = 11.70
For the age group 20 to 44 years: 0.36 x 188 = 67.68
For the age group 45 to 64 years: 0.21 x 629 = 132.09
For the age group greater than 64 year: 0.18 x 4,350 = 783.00
SUM = 1014 per 100,000 population
We can compare Florida's standardized rate to Alaska's standardized rate by computing a standardized rate ratio (SRR) = 1069/1014 = 1.054, much less than the crude mortality rate ratio of 2.68, suggesting that much of the crude difference was due to confounding by age.
In this example we adjusted for age differences by using Florida's age distribution as a standard set of weights and applied those weights to the age-specific rates of each state. However, we could have achieved a fair comparison by using other standards as well, as long as we applied the same standard or weights to each of the populations being compared. For example, I could have arbitrarily chosen to use the age distribution of the US population in 1988 as the standard, as demonstrated on the next page.