Indirect standardization

Definitions & Key takeaways

In statistics, standardization is a method used to adjust for differences in characteristics (e.g. mortality rates, incidence or prevalence rates, etc.) between two populations. When the number of events or the mortality rates in each age group is unknown, it is indirect standardization. On the other hand, when the number of events or the mortality rates in each age group is known, it is direct standardization.

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In epidemiology, we often want to compare the mortality rates, or the frequency of deaths, and the morbidity rates, or the frequency of a certain disease , in different populations.
Typically, we do this by calculating the crude mortality rate for each population, which is the number of deaths in that occur within a certain timespan, like a year, divided by the total number of people in the population.
For example, let’s say we want to compare the crude mortality rates in two cities - City 1, which has a population of 23,000 people, and City 2, which has a population of 26,000 people.
In one year, there were 68 deaths in City 1, and 105 deaths in City 2. So the crude mortality rate in City 1 is 68 deaths divided by 23,000 people, or 0.003.
This means that there were 3 deaths for every 1,000 people that year in City 1. The crude mortality rate for City 2 is 105 divided by 26,000, which equals 0.004, or 4 deaths per 1,000 people.
We can use a mortality ratio, or a ratio of two mortality rates, to compare the crude mortality rate of City 1 to the mortality rate of City 2, and we get a ratio of 3 to 4.
And if we divide both sides by the bigger number, 4, we get a mortality ratio of 0.75 to 1, which means that, in one year, City 1 had a mortality rate 25% lower than City 2.
That may convince some folks to pack their bags and move to City 1! Sometimes though, calculating the crude mortality ratio doesn’t provide an accurate picture of the two populations, and this is usually because the populations have different distributions of certain characteristics, like age, sex, or race.
For example, let’s say City 1 and City 2 have different age distributions, so City 1 has an older population with a large percentage of people over the age of 40, whereas City 2 has a younger population with only a small percentage of people over the age of 40.
Typically, mortality rates tend to be higher in older populations and lower in younger populations. So, we can speculate that if City 2 has a smaller percentage of older people, then the crude mortality rate for City 2 might be lower.
Perhaps it’s time to put down those bags and pick up a calculator instead. Standardization is a method that’s used to adjust for differences in characteristics between two populations, and when standardization is used to adjust for age, the result is called an age-adjusted rate.
Oftentimes, standardization is used to adjust mortality rates, but it can also be used to adjust incidence rates - the frequency of new diseases - or prevalence rates - the frequency of currently existing diseases.
There are two ways to calculate standardized rates, direct standardization and indirect standardization. Direct standardization is used when the number of events or the mortality rates in each age group within the population, is known, whereas indirect standardization is used when the number of events or the mortality rates in each age group within the population is not known.
So let’s say we know the age- specific mortality rates in City 1 but we don’t know the age- specific mortality rates in City 2.
In that situation, we have to use indirect standardization. In City 1, let’s say that within the total population of 23, 000 and 68 deaths, there are 18,000 people in the over 40 age group, and 5,000 people in the under 40 age group.
And let’s say that we know the age- specific mortality rate is 0.001 in the over 40 age group, and 0.01 in the under 40 age group.
Multiplying 0.001 by 18,000 people gives us 18 deaths in the over 40 group, and multiplying 0.01 by 5,000 gives us 50 deaths in the under 40 group, adding up to the total of 68 total deaths in City 1.
In City 2, let’s say there are 3,000 people in the over 40 age group and 23,000 people in the under 40 age group, for a total of 26,000 people.
Now, in City 2 we know that 105 total people died, but we don’t know the age- specific mortality rates, so we don’t know how many people died in each age group.
The first step in indirect standardization is to choose a reference or standard population, which is the population whose age- specific mortality rates will be used.
The reference population can be a completely separate population, like if you’re comparing two cities within the same country, you might use national- level information as the reference.
On the other hand, you can also use one of the two populations of interest as the reference, since you already have information on the age- distribution.
In our example, let’s say we use City 1 as the reference population. Next up is step 2.
Going back to our two tables, we can multiply the age- specific mortality rates from the reference population - City 1 - by the number of people in each age category in City 2 to get the expected number of deaths, or the number of deaths you would expect to see in City 2 if it had the same age- specific mortality rates as City 1.
So, for City 2, 3,000 people times 0.001 is 3 expected deaths in the over 40 group, and 23,000 people times 0.01 equals 230 expected deaths in the under 40 group, so 3 plus 230 is 233 expected deaths in City 2.
Next, for step 3 we can calculate the standardized mortality ratio, or SMR, which is a ratio of the number of observed deaths in City 2, to the number of expected deaths in City 2.
If the risk of mortality is the same in City 2 and in City 1, then standardized mortality ratio is equal to 1. If the standardized mortality ratio is greater than 1, then it means that City 2 had a greater risk of mortality than the reference population which was City 1.
And if the standardized mortality ratio is less than 1, then it means that City 2 had a lower risk of mortality than the reference population.
So to calculate it for City 2, the observed number of deaths is 105 and the expected number of deaths is 233, so the standardized mortality ratio is 0.45 to 1.
This means that, if both cities had the same age- specific mortality rates, then City 2 has around 65% lower risk of mortality compared to City 1.
This is different than what we saw when we just looked at the crude mortality rates. Time to pack our bags and head to City 2 instead!
Alright, as a quick recap, standardization is a method used to calculate adjusted mortality and morbidity rates, when populations have different distributions of characteristics like age, sex, or race.
Standardization can be direct, when the rates in each group is known, or indirect, when the rates in each group is unknown.
In indirect age standardization of mortality rates, the age- specific mortality rates from a reference population are multiplied by the number of people in each age group to get an expected number of deaths for each age group.
The total expected deaths is then divided by the total observed number of deaths to get a standardized mortality ratio.