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Rates, Small Numbers, Percents, Etc.
Rates help equalize populations of varying sizes, and allow comparisons among different years, races, sexes and geographic areas. The numerator is the top number, the denominator is the bottom number.
Calculating a Rate
It is customary to use rates per 100,000 population for deaths and rates per 1,000 population for live births.
To calculate the rate for deaths from injuries and poisoning for Allen County in 2000, do the following calculation:
There may or may not be 100,000 residents in the county under review, but multiplying the result by 100,000 makes that rate comparable with counties with more than 100,000 or less than 100,000 (such as Bartholomew County).
Make sure you use the same population base when calculating rates for comparison. For comparing Allen County with Bartholomew County, use the 2000 population estimates for each population base. Population data can come from the Census Bureau (www.census.gov) or the Indiana Business Research Center ( www.stats.indiana.edu/ ).
Another example is the number of deaths from communicable diseases is 18 per 100,000. A rate of 18 per 100,000 is not 18 percent, but .018 percent. To make a rate into a percent, for the example of 18 deaths per 100,000 population, divide by 1,000:
Be careful about the decimal point. This formula cannot be used with ageadjusted rates. Be very clear about the denominator.
Age/RaceSpecific Rates
For particular age, race or sex groups, you can calculate a rate for that specific group. For example, to calculate the 2000 birth rate for white females age 2024 for Marion County, do the following calculation:
The same calculation can be used for the black birth rate (number of live births to black females divided by the population of black females age 1544 multiplied by 1,000). The calculation can also be used for the sexspecific rate of heart disease to males age 6574 (number of deaths from heart disease to males age 6574 divided by the population of males age 6574  remember to use the same years for deaths and population  multiplied by 100,000.
AgeAdjusted Rates
The ageadjusted death rate is a good way to compare death rates between counties, states and the U.S. The Epidemiology Resource Center at the Indiana State Department of Health uses the direct method to ageadjust. In this method, the agespecific rates are first calculated for the various age groups (e.g. <1, 14, 514, 1524, etc.). An example of an agespecific death rate would be the total number of deaths for residents age 1524 divided by the population for that age group then multiplied by 100,000 (use the same year for the number of deaths and population). The agespecific rates are then weighted according to the standard million. The standard million is the proportion of the total U.S. population for the same age groups used to determine the agespecific death rates. The year 2000 standard million is used in ERC mortality reports for 1999 forward. Prior to 1990, the 1940 standard million was used. After each agespecific rate is multiplied (weighted) according to the standard million, the agespecific rates are added together, and the sum of each of those weighted rates equals the ageadjusted death rate. Deaths of unknown age are not included. An example is below:
Age Group 
2000 standard million 
2000 Indiana population 
CAUSE OF DEATH (all causes used) 
Agespecific death rate 
agespecific death rate x standard million 
01 
0.013818 
81,378 
676 
830.6913 
11.47849296 
14 
0.055317 
327,764 
142 
43.3239 
2.396545685 
514 
0.145565 
867,821 
163 
18.7827 
2.73410012 
1524 
0.138646 
866,188 
735 
84.8546 
11.76474507 
2534 
0.135573 
821,920 
848 
103.1731 
13.98748102 
3544 
0.162613 
952,889 
1,824 
191.4179 
31.12703704 
4554 
0.134834 
811,110 
3,495 
430.8910 
58.09875726 
5564 
0.087247 
526,580 
5,632 
1069.5431 
93.31442592 
6574 
0.066037 
393,375 
10,601 
2694.8840 
177.9620558 
7584 
0.044842 
264,661 
16,345 
6175.8249 
276.9363412 
85+ 
0.015508 
91,127 
14,748 
16184.0069 
250.9815796 
Total 
1.000000 
6,004,813 
55,209 

930.78 
*The number in red is the ageadjusted death rate.
Two counties may each have an identical number of deaths; however, the ageadjusted death rates would not be the same unless the deceased were the same age and the population data were the same..
An ageadjusted death rate can be calculated for all causes of death (total) or individual causes, as is done in Tables 1 and 5 in the Mortality Report.
When comparing ageadjusted death rates between different reports and years, be sure that the same standard million is used (remember that the 1940 standard million was used prior to 1999 in mortality reports). Ageadjusted death rates using different standard millions are NOT comparable. Also remember that the ICD code changed from ICD9 to ICD10 in 1999. Even if you are using the same standard million, unless you are looking at the ageadjusted death rate for deaths from all causes (total), make sure the ICD codes are comparable.
Incidence Rate
The incidence rate, usually referred to as incidence, is the number of new cases in a given time frame. For example, to calculate the incidence rate for the number of HIV cases diagnosed in Indiana during 2000, the following formula would be used:
As with the other rates discussed above, incidence rates can be calculated by race, sex, age, etc.
Prevalence Rate
The prevalence rate, often referred to as prevalence, is the total number of cases (both new and preexisting) in a specific period of time. A case is counted in prevalence until death or recovery. For example, to calculate the prevalence rate of HIV cases diagnosed in Indiana through 2000, the following formula would be used:
Small Numbers
The Epidemiology Resource Center (ERC) at the Indiana State Department of Health follows the "Rule of Twenty" when examining rates. There should be at least twenty events in the numerator in order to produce a stable rate. While the ERC uses the rule for vital statistics events, it is also recommended for calculating rates for other areas of interest, such as traffic accidents or playground injuries.
When the numerator is less than 20, the rate is unstable, meaning that a small change in the numerator can lead to a large change in the rate from one year to the next. Unstable rates do not lend themselves to being used to make decisions.
An example of small numbers is found in infant mortality. As illustrated below, a small change in the numerator results in a large change in the rate.
An option when dealing with small numerators is to combine years of data. Using the infant death information from the example above, a threeyear rate is calculated:
The numerator is now 30 and the rate is more stable.
Percentage Change
To figure the percentage change, for example, Indiana's population from 1990 to 2000, use the following calculation:
The percentage change calculation will also work if there is a decrease from one year to the next. For example, to figure the percentage decrease in infant deaths for Indiana from 1996 to 2000:
Percent changes aren't always useful. For example, a county newspaper reports that drowning deaths to children age 514 has increased 300% in the past year. This increase appears to be appalling, but is it? The information is below:
Again, the numerator is less than 20. Changes in small numbers can lead to large, but meaningless, increases or decreases to the percent change.
Keep in mind that sometimes the most current information is "provisional," which means the data are not final and are incomplete. Provisional means that some numbers and rates may change when the data are final. Therefore, caution should be used in interpreting the data, and you may want to wait until the final data are released. Provisional data are released in order to help organizations that use vital statistics data begin looking at the most current year available.