# Indirect standardization

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A researcher is studying the annual mortality rates of two Midwestern towns, Town A and Town B. The age distribution of the two towns are shown below:

Table 1: Age distribution of Town A and B

 Age Range Number of individuals in Town A within each age range Number of individuals in Town B within each age range 0-20 2,000 5,000 21-40 3,000 8,000 41-60 3,000 8,000 80+ 2,000 4,000

The recorded number of deaths in Town B is 2,000/year. The mortality rates by age bracket are available for only Town A and shown below:

Table 2: Mortality rates of Town A by age group
 Age range Town A annual mortality rate 0-20 1% 21-40 5% 41-60 8% 80+ 15%

Indirect standardization is performed using the mortality rates of Town A as the reference. Which of the following conclusions can be drawn from the above data?

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#### Content Reviewers:

Rishi Desai, MD, MPH

#### Contributors:

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.

Summary

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.