# Standardized Rates of Disease

This method, sometimes referred to as direct standardization, provides a useful way to compare health outcomes among populations that may have different age distributions. This is done by applying a standard age distribution to the populations being compared in order to compute hypothetical summary rates indicating how the overall rates would have compared if the populations had had the same age distibution. This method is used when age-specific rates of disease are known for the populations being compared.

## Death Rates in Florida and Alaska

This table summarizes the data used to calculate crude (unadjusted) rates for Florida and Alaska. Note that the crude rate for Florida is substantially greater than Alaska's, raising the possibility that it is riskier to live in Florida. Are there social, behavioral, or environmental factors that account for the higher mortality rates? Is the risk of death really greater in Florida?

Florida

Number of deaths

131,902

2,116

Total population

12,340,000

530,000

Crude mortality rate (per 100,000)

1,069

399

Note also that the crude mortality rate ratio is 1,069/399 = 2.68. However, as you probably know, many older people move to Florida when they retire, so the population of Florida contains a higher percentage of older people, and they have an inherently greater risk of dying compared to young people. As a result, comparing the crude rates is likely to be misleading about whether the risk of death is truly greater in Florida. This is illustrated in detail in the table below.

Table - Age-specific Mortality Rates in Florida

Age Group

Number of People

% of Total Pop.

Death Rate per 100,000

<5

850,000

7%

284

5-19

2,280,000

18%

57

20-44

4,410,000

36%

198

45-64

2,600,000

21%

815

>64

2,200,000

18%

4,425

Totals

12,340,000

100%

1,069 (crude rate)

Table - Age-specific Mortality Rates in Alaska

Age Group

Number of People

% of Total Pop.

Death Rate per 100,000

<5

60,000

11%

274

5-19

130,000

25%

65

20-44

240,000

45%

188

45-64

80,000

15%

629

>64

20,000

4%

4,350

Totals

530,000

100%

399 (crude rate)

When we look at the age-specific mortality rates, we see that there is little difference within each age group, certainly nothing like the approximately 2.7 (1069/399) times higher crude death rate in Florida than in Alaska . In theory, we could simply report the age-specific rates and let people compare different states by looking at the rates within each age group separately, but that is less than ideal for two reasons.   First, if we wanted to look at all of the 50 states side-by-side, it would be extremely difficult to compare by looking at all the age-specific rates in each state.   More importantly, looking at the age-specific rates doesn't necessarily tell us whether one state is higher than another and certainly not the size of any difference. What we would like is a single summary rate like we have with the crude rate, but with the distortion caused by age removed. This is what standardization accomplishes.

In order to understand how this works, it is helpful to take another look at the crude rate.

Method #1: The simple, logical way to calculate the crude death rates is to divide the total events by the total population.

(total # deaths / total population)   =  (131,902 / 12,340,000 = 0 .01069 = 1,069 / 100,000 population

Method #2: The Long Way to Calculate the Crude Rate (Just to make a teaching point)*

If asked to compute a crude rate, the sensible thing would be to use method #1. However, it is also possible to calculate the crude rate by multiplying the age-specific rates by the fraction of the population that they represent and then summing this up. The "weight" of each age category is given by the fraction of the total population that it represents. For example, the "weight" of the youngest age group in Florida is 0.07 or 7%, while the weight of the oldest age group in Florida is 0.18, or 18%.

So, in the example above, we could calculate the crude rate for Florida as:

(.07) x  (284/100,000) =     19.88/100,000

+ (.18) x      (57/100,000) =     10.26/100,000

+ (.36) x    (198/100,000) =     71.28/100,000

+ (.21) x    (815/100,000) =   171.15/100,000

+ (.18) x (4,425/100,000) =   796.25/100,000

Total =  1,069 /100,000 population

NOTE: This is a laborious way to calculate the crude rate; it makes much more sense to just divide the total number of deaths by the total population size. However, we are doing this the long way just to illustrate that if you weight the category-specific rates according to the proportion of the population in each group and then add them, you end up with the crude rate. Because of this, even if two populations have identical category-specific rates, the crude rates will vary if the distributions of the populations are different.