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Calculating Rates for Health Events

Counts of health events are useful, but have limitations for those who need to compare populations of unequal size, for instance, a subpopulation with an overall state population. Knowing the population sizes can help to interpret counts, but computing a rate will allow direct comparison between populations of unequal size that are otherwise similar (e.g., similar age composition, similar culturally). According to the dictionary, a rate is, "a quantity, amount, or degree of something [numerator], measured per unit of something else [denominator]." In public health, the numerator is the number of people among whom an event occurred during a certain period of time, and the denominator is the total number of people in the population at risk for the same period of time. A rate has four components:
  1. A specified time period.
  2. The numerator, the number of people in whom an event occurred during a given period of time, and
  3. The denominator, the total number of people in the population at risk for the same period of time. This is also referred to as the "person-years at risk."
  4. A constant. The result of the fraction is usually multiplied by some factor of 10 (such as 100,000), so that the rate may be expressed as a whole number.

Contents
1 Crude Rates
2 Age- and Sex-Specific Rates
3 Deciding Which Measure to Use

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Crude Rates

In general, a rate is called a "crude rate" if it has not been adjusted for the age and sex composition of a population.

Table 1 shows an example of crude rate calculations for heart disease by New Mexico health regions. The example, which is a three year time period, averages the number of deaths occurring per year and the population estimates to produce average annual crude death rates for the 3-year period.

Table 1: Crude Death Rate for Heart Disease by Health Region, New Mexico, 2003-2005


NM Health RegionAverage Annual Number of DeathsAverage Annual Population EstimateCrude Death Rate (Deaths per 100,000 Population)
Region 1, Northwest

525

402,242

130.60

Region 2, Northeast

426

292,729

145.64

Region 3, Bernalillo

952

601,700

158.16

Region 4, Southeast

617

247,678

249.11

Region 5, Southwest

707

388,285

182.08



Using the values, above, for Region 1 as an example...
  1. The specified time period is 2003 through 2005.
  2. The numerator, or the number of events was averaged over the three years, for a value of 525.33 (before rounding).
  3. The denominator, or the estimated population at risk, was also averaged over the three years. The average of the three July 1 population estimates was 402,242.33.
  4. The constant was 100,000.

The calculation for the Region 1 heart disease crude death rate for 2003 - 2005 looks like this:
info icon
info icon Many measures used in public health assessment specify a time period of one or more calendar years. This is because many public health numerator datasets have calendar year production periods. But other time periods are also commonly used; for example calendar weeks in the instance of notifiable diseases. To calculate the "person-years at risk" for a time period that is less than one year, you need to multiply the population estimate by the portion of the year represented in the numerator. For instance, to calculate a crude rate for the number of cases of disease over a 10-week period, your denominator would be the July 1 population estimate multiplied by 0.1923 (10 weeks/52 weeks).


FAQs for Crude Rates:


Combining Years

Q: I am looking at death rates for a five-year period. What should I use for a population denominator?
A: If you are combining numerator values over the five years by summing them, then use the sum of the population counts over the same period. If you are combining numerator values by taking an average, then take an average of the population counts for the same time period and geographic area. Alternatively, you could also use an average over the five years in the numerator, and a "mid-point" population estimate, that is, a population estimate for the mid-point, or middle, year in the denominator.


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Age- and Sex-specific Rates

An age-specific rate is calculated by dividing the total number of health events for the specific age-group of interest by the total population in that age group. In Table 2, the age- and sex-specific rates for suicide are shown. The example demonstrates that the greatest number of suicides occur among adolescents and young adults, whereas the highest rate occurs among elderly men.

The calculation for an age-specific rate is the same as for a crude rate.

Table 2: Suicide Mortality Rates by Age and Sex, New Mexico, 2003-2005


Age GroupMaleFemale
Suicide DeathsPopulationAge- and Sex-Specific Rate per 100,000 PopulationSuicide DeathsPopulationAge- and Sex-Specific Rate per 100,000 Population
<15

20

628,660

3.18

4

610,463

0.66

15-44

455

1,219,065

37.32

95

1,203,860

7.89

45-64

238

694,671

34.26

75

742,045

10.11

65+

140

307,886

45.47

15

391,255

3.83



info icon Looking at rates within groups is also called "stratification." In Table 2, the population has been stratified by age and sex. The data in Table 2 also show how useful stratification can be. Not only are the suicide death rates much higher among men, the rate of suicide increases with age for men, but not for women.


info icon The crude mortality rate for a population depends on the mortality rate in each age group as well as on the proportion of people in each age group. For instance, the age-specifc rate for most causes of death will be higher for older age groups. As a result, crude death rates tend to be higher in populations with a larger proportion of older persons, and lower in populations with a larger proportion of younger persons.



Age-specific rates are valuable for comparing rates across age groups, and crude rates provide a useful summary measure to compare similar populations of different sizes. But the word, "similar" is a key concept. It can be misleading to compare crude rates across populations that have relevant differences, such as different cultural traditions, or age, sex, or race composition.

One difference that is commonly controlled for statistically is age composition of the population. The crude mortality rate for a population depends on the mortality rate in each age group as well as on the proportion of people in each age group. For instance, the age-specifc rate for most causes of death will be higher for older age groups. As a result, crude death rates tend to be higher in populations with a larger proportion of older persons, and lower in populations with a larger proportion of younger persons.

An age-adjusted rate is a summary measure that may be used to compare mortality or disease risk in two populations with with different age compositions.

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Deciding Which Measure to Use



So, how do I know which one to use !? You will want to use the measure that best informs the question you are trying to answer. This is a guideline, not a hard and fast rule, but generally:

If your question is:Then use:
MAGNITUDE: How big is the problem? Number of events (count)
PROBABILITY: What is the underlying risk in my population? Crude rate and confidence interval
DISPARITY: Is there a difference in risk after controlling for age?Age-adjusted rate and confidence interval


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Go to the page on age-adjusted rates for health events.



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