# Calculating Rates for Health Events

- A specified time period.
- The numerator, the number of people in whom an event occurred during a given period of time, and
- 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."
- 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 |

# 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 Region | Average Annual Number of Deaths | Average Annual Population Estimate | Crude 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...

- The specified time period is 2003 through 2005.
- The numerator, or the number of events was averaged over the three years, for a value of 525.33 (before rounding).
- 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.
- The constant was 100,000.

The calculation for the Region 1 heart disease crude death rate for 2003 - 2005 looks like this:

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

# 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 greatestThe 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 Group | Male | Female | ||||
---|---|---|---|---|---|---|

Suicide Deaths | Population | Age- and Sex-Specific Rate per 100,000 Population | Suicide Deaths | Population | Age- 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 |

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.

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.

# Deciding Which Measure to Use

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 |