Rates are a useful tool for comparing characteristics across different populations, different segments of a population, or the same population over time. One type of rate is a percentageFootnote 1. The number of Canadians who, for example, smoke or are obese is often expressed as a percentage of the population to facilitate comparison across provinces, sexes and age groups.
When rates are used to examine unusual events, such as certain crimes or the incidence of rare diseases, they are often expressed as the number of people or occurrences per 1,000 or 100,000 individuals in the population. These rates are often referred to as crude ratesFootnote 2. As with percentages, these rates take into account the underlying population size.
For example, the data in Table 1, from 2000, show that 62,672 Canadians died of cancer, while, in 2011, 72,476 died. Over this same time period, the Canadian population grew from 30,685,730 in 2000, to 34,342,780 in 2011. When we express this information as a crude rate, we see that the cancer mortality rate was 204.2 deaths per 100,000 persons in 2000, and 211.0 deaths per 100,000 persons in 2011. By using a rate, we are able to quickly and clearly see that over the 11-year period, the rate of death due to cancer has increased.
|0 to 39 years||Estimate of population||17,068,876||17,191,850|
|Number of deaths||1,345||1,004|
|40 years and over||Estimate of population||13,616,854||17,150,930|
|Number of deaths||61,325||71,472|
|Total all ages||Estimate of population||30,685,730||34,342,780|
|Number of deaths||62,672||72,476|
However, during the same period, the crude rate for each age group decreased. Is something wrong? The short answer is that the crude rate for the total population, while it accurately represents the incidence of death due to cancer each year, it is not the correct indicator to use to compare the incidence between years.
Comparing rates between two time periods or two different geographical areas is usually more representative when taking into account differences in the age structure of the two populations. This is particularly true if the characteristic being observed varies by age. This is the case in our example of mortality rates since cancer affects considerably more Canadians in their later years of life than those in their younger years.
Age-standardized rates are often used to make such comparisons, as they account for the differences in the age structure of the populations being compared. In the calculation of the age-standardized rate, either one population is mathematically adjusted to have the same age structure as the other; or both populations are mathematically adjusted to have the same age structure as a third population, called the standard populationFootnote 3. In this way, the two groups are given the same age distribution structure so that a more representative picture of the characteristic in question is provided.
In the cancer mortality example, the 2011 Canadian population has a higher proportion of those 40+ than the 2000 population does: almost half (49.9%) of the 2011 population was 40 years of age or older, compared to 44.4% in 2000. Due to the high mortality rate in the 40+ age group, considerably more cancer deaths are observed in 2011. But, it is only by removing the effect of the differing age distributions that we can make conclusions about the relative decreases or increases in mortality over time. The exact calculation of the age-standardized rate for this example is given at the end of the Fact Sheet.
In the interest of simplicity, the example here used only two age groups: often, the characteristic being studied varies considerably across ages and therefore, narrower age categories are required. The age-standardized rates appearing in many CANSIM tables use 20 different age groups, making age-specific comparisons more intricate particularly when many years or provinces are involved.
Calculation of the Age-standardized Rate
The detailed calculation of the age-standardized mortality rate is presented here using the example of deaths due to cancer, and the year 2000 data from Table 1. The rates are standardized to the 1991 population.
To calculate the age-standardized mortality rate (ASMR), we must first calculate the age-specific (mortality) rates for each age group by dividing the number of deaths by the respective population, and then multiplying the resulting number by 100,000:
- Age-specific rate, 0 to 39 years
- = 1,345 (number of deaths) ÷ 17,068,876 (total population) × 100,000
- = 7.9 cancer deaths per 100,000 population
- Age-specific rate, 40+ years
- = 61,325 (number of deaths) ÷ 13,616,854 (total population) × 100,000
- = 450.4 cancer deaths per 100,000 population
We then multiply each of the age-specific rates by the proportion of the 1991 population belonging to the particular age group (called the standard population weight). In 1991, 61.6% of Canadians were under 40 years of age and 38.4% were age 40 or older. The age-standardized rate is obtained by adding the resulting numbers:
- = (7.9 × 61.6%) + (450.4 × 38.4%)
- = 4.9 + 173.0
- = 177.9 cancer deaths per 100,000 standard population.
In a similar fashion, the 2011 age-specific rates and age-standardized rate are obtained, respectively, as 5.8 (0 to 39 years), 416.7 (40+ years) and 163.6 cancer deaths per 100,000 (standard) population.
Using the data from Table 1, we obtained the:
- 2000 age-standardized mortality rate of 177.9 deaths per 100,000 standard population, and
- 2011 age-standardized mortality rate of 163.6 deaths per 100,000 standard population.
Note that both age-specific rates are lower in 2011 than in 2000 and yet the crude mortality rate for 2011 is higher. This is because the 2011 population is older than the 2000 population: almost half (49.9%) of the 2011 population was 40 years of age or older, compared to 44.4% in 2000. Because of the much higher mortality rate in this age group, considerably more cancer deaths are observed in 2011 than in 2000, contributing to a higher crude mortality rate although both age-specific crude rates are lower. It is only by adjusting the two populations to have the same age distribution—in this case, that of the 1991 population—that we can make general and more accurate conclusions about relative decreases or increases in mortality.
- Footnote 1
the number of individuals exhibiting a characteristic or particular behaviour per 100 people
- Footnote 2
by dividing both numbers by their respective population size measures, and then multiplying them by 100,000, to express them as a rate
- Footnote 3
For many of the age-standardized rates appearing in CANSIM, the 1991 Canadian Census of Population is used as the standard population, although a transition to a more recent age structure is being considered.