Lesson 3: Measures of Risk

Section 3: Mortality Frequency Measures

Mortality rate

A mortality rate is a measure of the frequency of occurrence of death in a defined population during a specified interval. Morbidity and mortality measures are often the same mathematically; it’s just a matter of what you choose to measure, illness or death. The formula for the mortality of a defined population, over a specified period of time, is:

Deaths occurring during a given time period Size of the population among which
the deaths occurred

× 10 ⁿ

When mortality rates are based on vital statistics (e.g., counts of death certificates), the denominator most commonly used is the size of the population at the middle of the time period. In the United States, values of 1,000 and 100,000 are both used for 10ⁿ for most types of mortality rates. Table 3.4 summarizes the formulas of frequently used mortality measures.

Table 3.4 Frequently Used Measures of Mortality

Crude mortality rate (crude death rate)

The crude mortality rate is the mortality rate from all causes of death for a population. In the United States in 2003, a total of 2,419,921 deaths occurred. The estimated population was 290,809,777. The crude mortality rate in 2003 was, therefore, (2,419,921 ⁄ 290,809,777) × 100,000, or 832.1 deaths per 100,000 population.(8)

Cause-specific mortality rate

The cause-specific mortality rate is the mortality rate from a specified cause for a population. The numerator is the number of deaths attributed to a specific cause. The denominator remains the size of the population at the midpoint of the time period. The fraction is usually expressed per 100,000 population. In the United States in 2003, a total of 108,256 deaths were attributed to accidents (unintentional injuries), yielding a cause-specific mortality rate of 37.2 per 100,000 population.(8)

Age-specific mortality rate

An age-specific mortality rate is a mortality rate limited to a particular age group. The numerator is the number of deaths in that age group; the denominator is the number of persons in that age group in the population. In the United States in 2003, a total of 130,761 deaths occurred among persons aged 25–44 years, or an age-specific mortality rate of 153.0 per 100,000 25–44 year olds.(8) Some specific types of age-specific mortality rates are neonatal, postneonatal, and infant mortality rates, as described in the following sections.

Infant mortality rate

The infant mortality rate is perhaps the most commonly used measure for comparing health status among nations. It is calculated as follows:

Number of deaths among children < 1 year of age reported during a given time period Number of live births reported during the
same time period

× 1,000

The infant mortality rate is generally calculated on an annual basis. It is a widely used measure of health status because it reflects the health of the mother and infant during pregnancy and the year thereafter. The health of the mother and infant, in turn, reflects a wide variety of factors, including access to prenatal care, prevalence of prenatal maternal health behaviors (such as alcohol or tobacco use and proper nutrition during pregnancy, etc.), postnatal care and behaviors (including childhood immunizations and proper nutrition), sanitation, and infection control.

Is the infant mortality rate a ratio? Yes. Is it a proportion? No, because some of the deaths in the numerator were among children born the previous year. Consider the infant mortality rate in 2003. That year, 28,025 infants died and 4,089,950 children were born, for an infant mortality rate of 6.951 per 1,000.8 Undoubtedly, some of the deaths in 2003 occurred among children born in 2002, but the denominator includes only children born in 2003.

Is the infant mortality rate truly a rate? No, because the denominator is not the size of the mid-year population of children < 1 year of age in 2003. In fact, the age-specific death rate for children < 1 year of age for 2003 was 694.7 per 100,000.(8) Obviously the infant mortality rate and the age-specific death rate for infants are very similar (695.1 versus 694.7 per 100,000) and close enough for most purposes. They are not exactly the same, however, because the estimated number of infants residing in the United States on July 1, 2003 was slightly larger than the number of children born in the United States in 2002, presumably because of immigration.

Neonatal mortality rate

The neonatal period covers birth up to but not including 28 days. The numerator of the neonatal mortality rate therefore is the number of deaths among children under 28 days of age during a given time period. The denominator of the neonatal mortality rate, like that of the infant mortality rate, is the number of live births reported during the same time period. The neonatal mortality rate is usually expressed per 1,000 live births. In 2003, the neonatal mortality rate in the United States was 4.7 per 1,000 live births.(8)

Postneonatal mortality rate

The postneonatal period is defined as the period from 28 days of age up to but not including 1 year of age. The numerator of the postneonatal mortality rate therefore is the number of deaths among children from 28 days up to but not including 1 year of age during a given time period. The denominator is the number of live births reported during the same time period. The postneonatal mortality rate is usually expressed per 1,000 live births. In 2003, the postneonatal mortality rate in the United States was 2.3 per 1,000 live births.(8)

Maternal mortality rate

The maternal mortality rate is really a ratio used to measure mortality associated with pregnancy. The numerator is the number of deaths during a given time period among women while pregnant or within 42 days of termination of pregnancy, irrespective of the duration and the site of the pregnancy, from any cause related to or aggravated by the pregnancy or its management, but not from accidental or incidental causes. The denominator is the number of live births reported during the same time period. Maternal mortality rate is usually expressed per 100,000 live births. In 2003, the U.S. maternal mortality rate was 8.9 per 100,000 live births.(8)

Sex-specific mortality rate

A sex-specific mortality rate is a mortality rate among either males or females. Both numerator and denominator are limited to the one sex.

Race-specific mortality rate

A race-specific mortality rate is a mortality rate related to a specified racial group. Both numerator and denominator are limited to the specified race.

Combinations of specific mortality rates

Mortality rates can be further stratified by combinations of cause, age, sex, and/or race. For example, in 2002, the death rate from diseases of the heart among women ages 45–54 years was 50.6 per 100,000.(9) The death rate from diseases of the heart among men in the same age group was 138.4 per 100,000, or more than 2.5 times as high as the comparable rate for women. These rates are a cause-, age-, and sex-specific rates, because they refer to one cause (diseases of the heart), one age group (45–54 years), and one sex (female or male).

Table 3.5 All-Cause and Unintentional Injury Mortality and Estimated Population by Age Group, For Both Sexes and For Males Alone — United States, 2002

Data Source: Web-based Injury Statistics Query and Reporting System (WISQARS) [online database] Atlanta; National Center for Injury Prevention and Control. Available from: https://www.cdc.gov/injury/wisqars.

Age-adjusted mortality rates

Mortality rates can be used to compare the rates in one area with the rates in another area, or to compare rates over time. However, because mortality rates obviously increase with age, a higher mortality rate among one population than among another might simply reflect the fact that the first population is older than the second.

Consider that the mortality rates in 2002 for the states of Alaska and Florida were 472.2 and 1,005.7 per 100,000, respectively (see Table 3.6). Should everyone from Florida move to Alaska to reduce their risk of death? No, the reason that Alaska’s mortality rate is so much lower than Florida’s is that Alaska’s population is considerably younger. Indeed, for seven age groups, the age-specific mortality rates in Alaska are actually higher than Florida’s.

To eliminate the distortion caused by different underlying age distributions in different populations, statistical techniques are used to adjust or standardize the rates among the populations to be compared. These techniques take a weighted average of the age-specific mortality rates, and eliminate the effect of different age distributions among the different populations. Mortality rates computed with these techniques are age-adjustedor age-standardized mortality rates. Alaska’s 2002 age-adjusted mortality rate (794.1 per 100,000) was higher than Florida’s (787.8 per 100,000), which is not surprising given that 7 of 13 age-specific mortality rates were higher in Alaska than Florida.

Death-to-case ratio

Definition of death-to-case ratio

The death-to-case ratio is the number of deaths attributed to a particular disease during a specified time period divided by the number of new cases of that disease identified during the same time period. The death-to-case ratio is a ratio but not necessarily a proportion, because some of the deaths that are counted in the numerator might have occurred among persons who developed disease in an earlier period, and are therefore not counted in the denominator.

Table 3.6 All-Cause Mortality by Age Group — Alaska and Florida, 2002

Data Source: Web-based Injury Statistics Query and Reporting System (WISQARS) [online database] Atlanta; National Center for Injury Prevention and Control. Available from: https://www.cdc.gov/injury/wisqars.

Method for calculating death-to-case ratio

Number of deaths attributed to a particular disease during specified period Number of new cases of the disease identified during the specified period

× 10 ⁿ

Case-fatality rate

The case-fatality rate is the proportion of persons with a particular condition (cases) who die from that condition. It is a measure of the severity of the condition. The formula is:

Number of cause-specific deaths among the incident cases Total number of incident cases

× 10 ⁿ

The case-fatality rate is a proportion, so the numerator is restricted to deaths among people included in the denominator. The time periods for the numerator and the denominator do not need to be the same; the denominator could be cases of HIV/AIDS diagnosed during the calendar year 1990, and the numerator, deaths among those diagnosed with HIV in 1990, could be from 1990 to the present.

The case-fatality rate is a proportion, not a true rate. As a result, some epidemiologists prefer the term case-fatality ratio.

The concept behind the case-fatality rate and the death-to-case ratio is similar, but the formulations are different. The death-to-case ratio is simply the number of cause-specific deaths that occurred during a specified time divided by the number of new cases of that disease that occurred during the same time. The deaths included in the numerator of the death-to-case ratio are not restricted to the new cases in the denominator; in fact, for many diseases, the deaths are among persons whose onset of disease was years earlier. In contrast, in the case-fatality rate, the deaths included in the numerator are restricted to the cases in the denominator.

Proportionate mortality

Definition of proportionate mortality

Proportionate mortality describes the proportion of deaths in a specified population over a period of time attributable to different causes. Each cause is expressed as a percentage of all deaths, and the sum of the causes must add to 100%. These proportions are not mortality rates, because the denominator is all deaths rather than the population in which the deaths occurred.

Method for calculating proportionate mortality

For a specified population over a specified period,

Deaths caused by a particular cause Deaths from all causes

× 100

The distribution of primary causes of death in the United States in 2003 for the entire population (all ages) and for persons ages 25–44 years are provided in Table 3.1. As illustrated in that table, accidents (unintentional injuries) accounted for 4.3% of all deaths, but 21.6% of deaths among 25–44 year olds.8

Sometimes, particularly in occupational epidemiology, proportionate mortality is used to compare deaths in a population of interest (say, a workplace) with the proportionate mortality in the broader population. This comparison of two proportionate mortalities is called a proportionate mortality ratio,or PMR for short. A PMR greater than 1.0 indicates that a particular cause accounts for a greater proportion of deaths in the population of interest than you might expect. For example, construction workers may be more likely to die of injuries than the general population.

However, PMRs can be misleading, because they are not based on mortality rates. A low cause-specific mortality rate in the population of interest can elevate the proportionate mortalities for all of the other causes, because they must add up to 100%. Those workers with a high injury-related proportionate mortality very likely have lower proportionate mortalities for chronic or disabling conditions that keep people out of the workforce. In other words, people who work are more likely to be healthier than the population as a whole — this is known as the healthy worker effect.

Exercise 3.5

Using the data in Table 3.8, calculate the missing proportionate mortalities for persons ages 25—44 years for diseases of the heart and assaults (homicide).

Table 3.8 Number, Proportion (Percentage), and Ranking of Deaths for Leading Causes of Death, All Ages and 25–44 Year Age Group — United States, 2003

	All ages			Ages 25–44 Years
	Number	Percentage	Rank	Number	Percentage	Rank
All causes	2,443,930	100		128,924	100
Diseases of heart	684,462	28	1	16,283		3
Malignant neoplasms	554,643	22.7	2	19,041	14.8	2
Cerebrovascular_disease	157,803	6.5	3	3,004	2.3	8
Chronic lower respiratory_diseases	126,128	5.2	4	401	0.3	*
Accidents (unintentional injuries)	105,695	4.3	5	27,844	21.6	1
Diabetes mellitus	73,965	3	6	2,662	2.1	9
Influenza & pneumonia	64,847	2.6	7	1,337	1	10
Alzheimer’s_disease	63,343	2.6	8	0	0	*
Nephritis, nephrotic syndrome, nephrosis	33,615	1.4	9	305	0.2	*
Septicemia	34,243	1.4	10	328	0.2	*
Intentional self-harm (suicide)	30,642	1.3	11	11,251	8.7	4
Chronic liver_disease and cirrhosis	27,201	1.1	12	3,288	2.6	7
Assault (homicide)	17,096	0.7	13	7,367		5
HIV_disease	13,544	0.5	*	6,879	5.3	6
All_other	456,703	18.7		29,480	22.9

* Not among top ranked causes

Data Sources: CDC. Summary of notifiable diseases, United States, 2003. MMWR 2005;2(No. 54).
Hoyert DL, Kung HC, Smith BL. Deaths: Preliminary data for 2003. National Vital Statistics Reports; vol. 53 no 15. Hyattsville, MD: National Center for Health Statistics 2005: 15, 27.

Check your answer.

Years of potential life lost

Definition of years of potential life lost

Years of potential life lost (YPLL) is one measure of the impact of premature mortality on a population. Additional measures incorporate disability and other measures of quality of life. YPLL is calculated as the sum of the differences between a predetermined end point and the ages of death for those who died before that end point. The two most commonly used end points are age 65 years and average life expectancy.

The use of YPLL is affected by this calculation, which implies a value system in which more weight is given to a death when it occurs at an earlier age. Thus, deaths at older ages are “devalued.” However, the YPLL before age 65 (YPLL₆₅) places much more emphasis on deaths at early ages than does YPLL based on remaining life expectancy (YPLL_LE). In 2000, the remaining life expectancy was 21.6 years for a 60-year-old, 11.3 years for a 70-year-old, and 8.6 for an 80-year-old. YPLL65 is based on the fewer than 30% of deaths that occur among persons younger than 65. In contrast, YPLL for life expectancy (YPLL_LE) is based on deaths among persons of all ages, so it more closely resembles crude mortality rates.(10)

YPLL rates can be used to compare YPLL among populations of different sizes. Because different populations may also have different age distributions, YPLL rates are usually age-adjusted to eliminate the effect of differing age distributions.

Method for calculating YPLL from a line listing

1. Step 1. Decide on end point (65 years, average life expectancy, or other).
2. Step 2. Exclude records of all persons who died at or after the end point.
3. Step 3. For each person who died before the end point, calculate that person’s YPLL by subtracting the age at death from the end point.
   YPLL _individual = end point − age at death
4. Step 3. Sum the individual YPLLs.
   YPLL = ∑ YPLL _individual

Method for calculating YPLL from a frequency

1. Step 1. Ensure that age groups break at the identified end point (e.g., 65 years). Eliminate all age groups older than the endpoint.
2. Step 2. For each age group younger than the end point, identify the midpoint of the age group, where midpoint =
   age group’s youngest age in years + oldest age + 1 2
3. Step 3. For each age group younger than the end point, identify that age group’s YPLL by subtracting the midpoint from the end point.
4. Step 4. Calculate age-specific YPLL by multiplying the age group’s YPLL times the number of persons in that age group.
5. Step 5. Sum the age-specific YPLL’s.

The YPLL rate represents years of potential life lost per 1,000 population below the end-point age, such as 65 years. YPLL rates should be used to compare premature mortality in different populations, because YPLL does not take into account differences in population sizes.

The formula for a YPLL rate is as follows:

Years of potential life lost Population under age 65 years

× 10 ⁿ

Table 3.10 Deaths and Years of Potential Life Lost Attributed to Leukemia by Age Group — United States, 2002

Column 1 Age Group (years)	Column 2 Deaths	Column 3 Age Midpoint	Column 4 Years to 65	Column 5 YPLL
Total	21,498			117,033
0–4	125	2.5	62.5	7,813
5–14	316	10	55	17,380
15–24	472	20	45	21,240
25–34	471	30	35	16,485
35–44	767	40	25	19,175
45–54	1,459	50	15	21,885
55–64	2,611	60	5	13,055
65+	15,277
Not stated	0

Data Source: Web-based Injury Statistics Query and Reporting System (WISQARS) [online database] Atlanta; National Center for Injury Prevention and Control. Available from: https://www.cdc.gov/injury/wisqars.

References (This Section)

8. Web-based Injury Statistics Query and Reporting System (WISQARS) [online database] Atlanta; National Center for Injury Prevention and Control. [cited 2006 Feb 1]. Available from: https://www.cdc.gov/injury/wisqars.
9. Centers for Disease Control and Prevention. Health, United States, 2004. Hyattsville, MD.; 2004.
10. Wise RP, Livengood JR, Berkelman RL, Goodman RA. Methodologic alternatives for measuring premature mortality. Am J Prev Med 1988;4:268–273.