A rate describes the number of cases observed in a defined population during a defined time period.
A rate is a proportion with the added element of time. In other words, it is the "velocity" of a disease. Time can be measured in a simple manner, such as a calendar year. This is useful for describing a cancer rate for a county. Given the number of cases observed from January 1 to December 31, and the population of the county, a simple rate can be calculated.
Gastric cancer in San Francisco County in 1990
Time: 1 year
Rate = 83 / 723,959 / 1 = 0.000114 cases per person per year
When describing rare outcomes such as cancer, rates can be small. Rates such as this are standardly written using a denominator of 10,000 or 100,000 population:
Rate = 11.4 cases per 100,000 per year.
Suppose a smaller county of 200,000 has 36 cases over 1 year = 0.00018 cases per person per year. By standardizing to 18 cases per 100,000 per year, the comparison with the first city is much easier (11.4 against 18 versus 0.000114 against 0.00018).
Time is sometimes described in "person-years". In this case, the denominator is the number of people studied times the amount of time each person was followed up to the date an outcome might have occurred. Person-years allows for calculation of rates in a population where not everyone is contributing the same amount of time.
Quantifying disease in populations