In the early part of any epidemiology course, few things throw students as much as computing age-adjusted mortality. It seems really counter-intuitive that two populations could have the exact same mortality rate and yet one is significantly less healthy than the other.
Thinking about it for a moment, though, before diving into computation, makes it pretty clear.
Say you have a class of 30 members of a senior citizens center in Florida and 30 second-graders in Santa Monica. In each group, 4 members died this year. Is the mortality rate the same?
This is where age-adjusted mortality comes in. It just so happens that in fact the CRUDE MORTALITY RATE is the same.
Crude mortality rate is simply (# of people who died)/(population at midyear)
We take midyear population because the denominator is the population at risk and if you have already died you cannot die again. Poets talk about dying a thousand deaths but statisticians don’t believe in that crap.
Since, we will assume, no one is joining your community center or class, mid-year population = 28.
How did I get 28? I assumed that people died randomly throughout the year so 1/2 of the year, 2 of your 4 people have died.
So, your crude mortality rate is 143 per 1,000.
Does it bother you that more of the second-graders died? Does that not seem right? That’s because you have some intuitive understanding of age-adjusted mortality.
Age-adjusted mortality is what you get when you apply ACTUAL age specific rates to a HYPOTHETICAL STANDARD POPULATION.
Let’s say we want to compare the mortality rates of two relatively small cities, each with the same size population and in each city, 74 people died in the last year. We are arguing that pollution is causing increased mortality but the main polluter in town points to the fact that City B has no more deaths than City A, on the other side of the state.
To compute the age-adjusted population, we would take the actual mortality rate for each age group for each city, as in the example below. Applying that to a standard population, let’s say each city had 10,000 children born that year, 20,000 ages 1-5 and so on.
Age Group |
Standard Population |
CITY A Mortality Rates per 100,000 |
Expected Deaths A |
CITY B Mortality Rates per 100,000 |
Expected Deaths B |
< 1 | 10,000 | 160 | 16 | 70 | 7 |
1-5 | 20,000 | 20 | 4 | 12 | 2.4 |
6-40 | 50,000 | 30 | 15 | 14 | 7 |
41-65 | 10,000 | 50 | 5 | 45 | 4.5 |
Over 65 | 10,000 | 350 | 35 | 300 | 30 |
TOTAL | — | 75 | 50.9 |
The cities may have different age distributions, so city A, which is a college town, has a lot more young people than City B. Given the City A mortality rates for each age group, one would expect 75 deaths in a standard population – that is, with the age distribution given above.
However, given the mortality rates by age in City B, one would expect only 50.9 deaths in a year. So, yes, City A has the same number of people and the same number of deaths, but if the people in City A are much younger, they should have FEWER deaths.
The standardized mortality ratio is the observed number of deaths per year divided by the expected number of deaths.
Let’s say we use the rate for City B, without the polluter, as our expected number
SMR = 75/ 50.9 = 1.47
Usually, we multiply it by 100. So, this says the deaths in City A are 147% of what would be expected for this distribution of ages based on the mortality rate in a city with no polluting plant.
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