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Guidelines for Using and Developing Rates for Public Health
Assessment
Revision Date: May 31, 2012 Primary Contact: Juliet VanEenwyk, Ph.D., State Epidemiologist for Non-Infectious Conditions
Rate Basics
Why are rates used in public health assessment?
What is the difference between crude, age-adjusted and age-specific rates?
Should I calculate a rate when the number of events is small?
Will the rate be compared to other rates?
How do I know whether two rates are different?
Guidelines for using and developing rates
Number of events (numerator) Population at risk (denominator) Crude rates Age-adjusted rates Age-specific rates Comparing rates Unstable rates due to small numbers
Methods for age adjustment
Direct adjustment U.S. Standard Populations for direct adjustment Indirect adjustment
Glossary
References and Resources
Rate Basics
A rate consists of a numerator and a denominator.
The numerator is the number of health events. This is often the same as the number of people who experience an event, but for some health conditions, one person may experience the event more than once. For example, one individual may have multiple hospitalizations for the same condition in a given year.
To measure incidence or prevalence of the condition, you usually want to count people. To measure the public health burden, you may want to count events. Actions based on the data may be different depending on whether the rate represents many individuals with only one event or a smaller number of individuals who have had many events.
It is customary to count only events that occur among the population at risk.
Guideline: Number of events (numerator)
The denominator is also known as the population at risk. Everyone in the population at risk must be eligible to be counted in the numerator if they have the event of interest. For example, in looking at female breast cancer, we cannot include men in the population at risk, because men with breast cancer would not be included in the numerator.
Guideline: Population at risk (denominator)
Once the numerator and denominator are established, how do we decide which rate is the most appropriate to use. The following questions are useful.
Why are rates used in public health assessment?
Much of public health assessment involves describing the health status of a defined community by looking at changes in the community over time or by comparing health events in that community to events occurring in other communities or the state as a whole. In making these comparisons, we need to account for the fact that the number of health events depends in part on the number of people in the community. To account for growth in a community or to compare communities of different sizes, we usually develop rates to provide the number of events per population unit.
Also, the frequency with which health events occur is almost always related to age. For example, acute respiratory infections are more common in children of school age because of their immunologic susceptibility and exposure to other children in schools. Chronic conditions, such as arthritis and atherosclerosis, occur more frequently in older adults because of a variety of physiologic consequences of aging. Mortality tends to increase rapidly after the age of 40. In fact, the relationship of age to risk often dwarfs other important risk factors. Because the relationship of age to risk is often resistant or impervious to interventions, analysts often remove the effects of differences in age structure when comparing rates across populations by calculating age-adjusted and age-specific rates.
What is the difference between crude, age-adjusted and age-specific rates?
Crude rates
Crude rates are recommended when a summary measure is needed and it is not necessary or desirable to adjust for other factors. For example, rates of infectious diseases, such as tuberculosis and hepatitis, are usually not age adjusted, because public health officials are interested in the overall burden of disease in the total population irrespective of age.
A crude rate is calculated by dividing the total number of events in a specified time period by the total number of individuals in the population who are at risk for these events and multiplying by a constant, such as 1,000 or 100,000 [e.g., (numerator/denominator) x constant]. For example, number of deaths in King County for 2010 (numerator) divided by the population of King County in 2010 (denominator) times 100,000 (constant) gives the 2010 crude death rate per 100,000 population for King County.
Guideline: Crude Rates
Age-adjusted rates
Adjusted rates are used when comparing rates of health events affected by confounding factors. They are used when comparing different populations or for comparing trends in a given population over time. Because the occurrence of many health conditions is related to age, the most common adjustment for public health data is age adjustment.
The process of age adjustment removes differences in the age composition of two or more populations to allow comparisons between these populations independent of their age structures. For example, a county’s age-adjusted death rate is the weighted average of the age-specific death rates observed in
Will the rate be compared to other rates?
When calculating rates, the numerator and denominator (i.e., events and population) must be defined consistently over time and place. Areas where public health professionals are most likely to find inconsistencies include:
- The definition of the health event: Because analysts may classify diseases differently, it is useful to compare technical definitions of the number of events before comparing rates. For example, Healthy People 2020 defines coronary heart disease as International Classification of Diseases, 10 th^ Revision (ICD-10) codes I11 and I20–I25; the National Center for Health Statistic’s definition of coronary heart disease does not include I11. Likewise, the National Center for Health Statistics and the National Cancer Institute include use different code groups for several types of cancer.
- The coding scheme : Coding schemes that may appear to collect the same information can contain subtle differences. For example, starting with 1999 deaths, state and federal agencies changed from coding causes of death following the International Classification of Diseases (ICD) 9th Revision (ICD-9) to the ICD 10th Revision (ICD-10). Differences in coding practices between ICD-9 and ICD-10 affect mortality rates and trends for some disease categories, but not others.
- Data collection and definitions : Data collection processes or definitions for the number of events or the population at risk may change over time.
- Geographies : Data collection may vary from one geographic area to another. This issue is generally more relevant to the number of events than the population at risk and more relevant to some types of events than others.
In addition to the previous issues, when comparing age-adjusted rates, the standard population must be the same for all rates to be compared. Although most national, state and local agencies in the United States use the U.S. 2000 Standard Population for age adjustment, international agencies and older data developed in the United States may use different standard populations.
When comparing age-specific rates, if the age categories are relatively large, there can still be confounding by age. For example, if the proportions of very old individuals in the group "65 years and over" are different in two populations being compared, differences in rates may be a reflection of differences in the age distributions of the populations.
Guideline: Comparing Rates
How do I know whether two rates are different?
See Guidelines for Using Confidence Intervals for Public Health Assessment.
Guidelines for Using and Developing Rates
Number of events (numerator)
- In developing a rate, only count events that occur among the population at risk.
- For conditions where one person may be counted more than once, note whether you are counting events or people. The count of events may be a better estimate of the public health burden experienced by the total population.
- When reporting rates, provide precise definitions of the number of events (e.g., specify ICD codes) so that readers can calculate comparable rates.
- When reporting rates, specify the data source for the number of events.
Population at risk (denominator)
- Everyone in the population at risk must be eligible to be counted in the numerator if they have the event of interest. For example, in looking at female breast cancer, we cannot include men in the population at risk, because men with breast cancer would not be included in the number of events.
- See population denominators for guidelines related to choice of populations at risk.
- When reporting rates, specify the data source for the population at risk.
Crude rates
- Crude rates are recommended when a summary measure is needed and it is not necessary or desirable to adjust for age.
- Choose a constant (e.g., rate per 1,000 or rate per 100,000) that is compatible with commonly published rates for the topic (e.g., birth information is generally expressed per 1,000 live births; death information is commonly expressed per 100,000 population.)
Age-adjusted rates
- Age-adjusted rates are recommended when comparing rates of age-related health events across different populations or within a given population over time, especially when comparing populations with different age distributions. These comparisons are only valid if the direct method for age adjustment has been used.
- Only use age-adjusted rates for the purpose of comparison. Because an age-adjusted rate is based on an external standard population, it does not reflect the absolute frequency of the event in a population.
- Present age-adjusted rates when a single, summary measure is needed. Choi 1999 recommends developing age-specific rates before developing age-adjusted rates as explained above. However, this approach is not always practical in public health practice. Whether the data analyst follows this recommendation might depend on the purpose of the publication. For example, the Washington State Cancer Registry (WSCR) produces summary statistics for about 25 types of cancer annually. The purpose of the report is to provide an overview of cancer in Washington. One portion of the report presents age-adjusted incidence and death rates for the state and its 39 counties. Examining age-specific rates for this portion of the report alone could require hundreds of separate analyses. Age-specific analyses are more practical and important when investigating, for example, what a specific county looks like in relation to the state for a limited number of health conditions. If patterns by age in two or more jurisdictions or over time are not similar, presenting age-specific rates, rather than age- adjusted rates, is recommended.
- Use the U.S. 2000 Standard Population in current analyses, unless there is a need to compare to data that have been adjusted to another standard. In the latter case, you must use the standard population used in the comparison data. See U.S. Standard Populations.
Age-specific rates
- Use age-specific rates to compare age-defined subgroups between or within populations when rates are strongly age-dependent.
Where m is the number of age groups, d (^) i is the number of cases (events or people) in age group i, Pi is the population in age group i , and s (^) i is the proportion of the standard population in age group i. This is a weighted sum of Poisson random variables, with the weights being ( s (^) i / Pi ).
U.S. Standard Populations for Direct Adjustment
In 1998, the federal Department of Health and Human Services (DHHS) directed all DHHS agencies to use the 2000 projected U.S. population as the standard for age adjustment. This standard is generally called the U.S. 2000 Standard Population. This directive improved consistency in age adjustment across DHHS agencies. Prior to the directive, some agencies used the U.S. 1940 and others used the U.S. 1970 Standard Populations. However, not all DHHS agencies use the U.S. 2000 Standard Population in the same manner. The inconsistency most likely to affect rates is the use of different age groupings. Less substantive are small differences in how proportions are calculated. The following table shows the age groupings and proportions used by the National Center for Health Statistics and the National Cancer Institute. These distributions are frequently used for public health statistics. Groupings and proportions for other age ranges and methods for creating proportions for unique groupings are available in National Center for Health Statistics Statistical Notes 20 January 2001.
U.S. 2000 Standard Population: Proportions and Age Groups Used by the National Center for Health Statistics (NCHS) and the National Cancer Institute (NCI) NCHS 11, “10-yr” age groups
NCI
19, “5-yr” age groups age group proportion age group proportion <1 0.013818 <1 0. 1 – 4 0.055317 1 – 4 0. 5 – 14 0.145565 5 – 9 0. 15 – 24 0.138646 10 – 14 0. 25 – 34 0.135573 15 – 19 0. 35 – 44 0.162613 20 – 24 0. 45 – 54 0.134834 25 – 29 0. 55 – 64 0.087247 30 – 34 0. 65 – 74 0.066037 35 – 39 0. 75 – 84 0.044842 40 – 44 0. 85+ 0.015508 45 – 49 0. 50 – 54 0. 55 – 59 0. 60 – 64 0. 65 – 69 0. 70 – 74 0. 75 – 79 0. 80 – 84 0. 85+ 0.
Indirect Adjustment
When the number of events in a community is small, or when developing statistics for use in communities concerned about the number of events, compare the observed number of events to the expected number, using indirect age adjustment or age and sex adjustment.
- To develop a count of expected events using indirect adjustment, apply the age-specific rates in a larger population (e.g., Washington State) to the number of people in the age-specific group in the population of interest, and total the results for all age groups. Ideally, the larger population should be large enough that the rates in that population are stable (i.e., exhibit little random variation).
- Compare the observed number of events (usually abbreviated "O") and the expected number obtained using indirect adjustment (usually abbreviated "E").
o Generally, if the confidence interval (CI) around O does not include E, the observed number of events is statistically significantly different from the expected. (Breslow and Day, 1987) The Poisson confidence limits around O can be obtained from standard tables or can be calculated using several software packages. This method assumes that E is developed from stable rates (i.e., the standard population is large enough that there is little random variation in the rates for that population).
o A more conservative estimate of statistical significance (and the estimate that should be used when the rates in the larger population are not as stable as one would like) is to develop CIs around both E and O. If the CIs do not overlap, the difference between O and E is statistically significant. If they do overlap and either CI contains the point estimate of the other rate, O and E are not statistically significantly different. If the CIs overlap, but neither contains the point estimate of the other rate, a statistical test is needed to determine statistical significance.
- A more precise method of determining whether the observed number of events is different from the expected is to develop a ratio of O to E (O/E) and conduct a statistical test to determine whether the ratio is statistically significantly different from 1. Most biostatistics textbooks provide methods for conducting the statistical test. Fisher and van Belle (1993) provide an approximation for large samples only. Rosner (1990) provides methods for small and large samples.
Glossary
Rate: A rate is a measure of the frequency of an event per population unit. The use of rates, rather than raw numbers, is important for comparison among populations, since the number of events depends, in part, on the size of the population.
Numerator: In calculating rates, the numerator is the number of events in a specified population.
Denominator: In calculating rates, the denominator is the number of people in a specified population. Everyone in the denominator must be eligible to be counted in the numerator. The denominator is often called the "population at risk."
Crude rate: A crude rate is calculated by dividing the total number of events in a specified time period by the total number of individuals in the population who are at risk for these events and multiplying by a constant, such as 1,000 or 100,000 [e.g., (numerator/denominator) x constant].
Age Adjustment: Age adjustment is the process by which differences in the age composition of two or more populations are removed, to allow comparisons between these populations in the frequency with which an age-related health event occurs.
Age-adjusted rate (direct adjustment): An age-adjusted rate adjusted by the direct method is "…the rate that would occur if the observed age-specific…rates were present in a population with an age distribution equal to that of a standard population." (Anderson, 1998)
