# Measures of Disease Frequency

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Measures of
Disease Frequency
LEARNING OBJECTIVES
By the end of this chapter, the reader will be able to:
■ Define and provide examples of a population.
■ Distinguish between a fixed and dynamic (or open) population.
■ Explain how epidemiologists create a case definition and discuss how
the definition of acquired immunodeficiency syndrome (AIDS) has
changed over time.
■ Describe the key aspects of measuring disease occurrence.
■ Define and distinguish between cumulative incidence, incidence rate,
and prevalence.
■ Describe the mathematical relationship between the measures of disease
frequency.
■ Provide examples of commonly used measures of disease frequency in
public health.
Introduction
As described in Chapter 1, epidemiologists study the distribution and
determinants of disease frequency in human populations in order to control health problems.1(p1), 2(p62) Thus, the objectives of epidemiology are to
determine the extent of disease in a population, identify patterns and
trends in disease occurrence, identify the causes of disease, and evaluate
the effectiveness of prevention and treatment activities. Measuring how
often a disease arises in a population is usually the first step in achieving
these goals.
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This chapter describes how epidemiologists quantify the occurrence of
disease in a population. Readers will learn that this quantification process
involves developing a definition of a particular disease, counting the number of people who are affected by the disease, determining the size of the
population from which the diseased cases arose, and accounting for the
passage of time.
Definition of a Population
Because epidemiology is concerned with the occurrence of disease in
groups of people rather than in individuals, populations are at the heart of
epidemiologists’ measurements. A population can be defined as a group of
people with a common characteristic such as place of residence, religion,
gender, age, use of hospital services, or life event (such as giving birth).
Location of residence such as a country, state, city, or neighborhood is
one of the most common ways to define a population. For example, the
people who reside in the Brooklyn borough of New York City, the city of
Boston, the state of Oregon, and the country of Sweden are members of distinct populations defined by geopolitical entities ranging in size from a
neighborhood to an entire country. Residence near natural geographic features such as rivers, mountains, lakes, or islands can also be used to define
a population. For example, people who live along the 2350-mile length of
the Mississippi River, around Mount St. Helens in Washington State, and
on Nantucket Island off the coast of Massachusetts are members of populations defined by geographic formations.
Because epidemiology focuses on disease occurrence, populations are
commonly defined in relation to a medical facility such as a doctor’s office,
clinic, or hospital. The service population of a medical facility (also called
catchment population) consists of the people who use the facility’s services.
This population is often difficult to define because an individual’s decision
to use a facility may depend on how far it is from home, the person’s particular medical condition, his or her type of medical insurance, and so forth.
Consider a situation in which a county has only one general hospital,
which provides the complete range of medical services including preventive care, birthing services, and diagnostic and therapeutic services for acute
and chronic conditions. The catchment population for this general hospital
is likely to consist of all people who live in the county where the hospital is
located (see Figure 2–1).
Now suppose that this hospital enhances its cardiology department,
adding many well-trained clinicians and the latest diagnostic equipment. As
the cardiology department’s reputation for excellent care grows, patients
travel from greater distances to receive care. As a result, the catchment population for the cardiology department expands to the surrounding counties
while the catchment population for the other hospital services, particularly
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Measures of Disease Frequency
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Residents
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Public and private hospitals whose catchment populations
vary by socioeconomic status
Public
Poor people
Private
Middle class and
wealthy people
FIGURE 2–1. Types of Hospital Catchment Areas
those dealing with acute conditions requiring prompt treatment, remains
the single county where the hospital is situated (see Figure 2–1).
Socioeconomic status is still another determinant of hospital catchment
populations. Consider a city in which there are two hospitals—one public
and one private—located within a few miles of each other. The private hospital generally treats patients with medical insurance, and the public hospital mainly treats patients without insurance. Even though each catchment
population resides roughly within the same geographic area, the two service groups are distinct in terms of income, and probably many other factors
(see Figure 2–1).
Still another way that a population can be defined is by the occurrence
of a life event such as undergoing a medical procedure, giving birth to a
child, entering or graduating from school, or serving in the military. For
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example, students who graduated from college in 2005 are members of the
population known as the “Class of ’05,” and the men and women who
served in the United States. military during the Persian Gulf War are members of the population known as Gulf War veterans. Populations are often
defined by other characteristics such as age, gender, religion, or type of job.
A unifying framework for thinking about a population is whether its
membership is permanent or transient (see Table 2–1). A population whose
membership is permanent is called a fixed population. Its membership is
always defined by a life event. For example, the people who were in
Hiroshima, Japan, when the atomic bomb exploded at the end of World
War II are members of a fixed population. This population will never gain
any new members because only people who were at this historical event
can be members.
The opposite of a fixed population is a dynamic or open population. Its
membership is defined by a changeable state or condition, and so is transient. A person is a member of a dynamic population only as long as he or
she has the defining state or condition. For example, the population of the
city of Boston is dynamic because people are members only while they
reside within the city limits. Turnover is always occurring because people
enter the city by moving in or by birth, and people leave the city by moving away or by death. The term steady state describes a situation in which
the number of people entering the population is equal to the number leaving. Dynamic populations include groups defined by geographic and hospital catchment areas, religious groups, and occupations.
Regardless of the way in which it is defined, a population can be
divided into subgroups on the basis of any characteristic. For example,
men who undergo coronary bypass surgery are a gender subgroup of a
fixed population defined by a life event, and all children up to six years of
age who live along the Mississippi River are an age subgroup of a dynamic
population defined by a geographic formation.
Definitions of Health and Disease
In 1948, the World Health Organization defined health as “a state of complete physical, mental and social well-being and not merely the absence of
disease or infirmity.”3 More recently, Healthy People 2010, a national plan
TABLE 2–1
Types of Populations
Type of population
Key element
Example
Fixed
Membership is based on
an event and is permanent
Japanese atomic bomb survivors
Dynamic or open
Membership is based on a
condition and is transitory
Residents of a city, hospital
patients
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for improving the health of the American people, stated that health is a key
aspect of the quality of life and that it “reflects a personal sense of physical
and mental health and the ability to react to factors in the physical and
social environments.” The plan also states that the “health-related quality
of life is more subjective than life expectancy and therefore can be more
difficult to measure.”4
Because measurement is a cornerstone of epidemiology, and “health”
and “a sense of well-being” are nonspecific and difficult to quantify, epidemiologists have almost entirely focused their activities on the “absence
of health” such as specific diseases, injuries, disabilities, and death. Consequently, epidemiologists must first compose a definition of the “absence of
health” or “disease” before they can begin measuring its frequency.
The definition of a disease is usually based on a combination of physical and pathological examinations, diagnostic test results, and signs and
symptoms. Which and how many criteria are used to define a “case” (a
person who meets the disease definition) has important implications for
accurately determining who has the disease.
Consider the various criteria that can be used to define a heart attack
“case.” One could use the symptoms of chest pain, the results of diagnostic tests such as electrocardiograms, or blood enzyme tests for cardiac damage. What are the implications of using only chest pain to define heart
attack cases? Using only this nonspecific symptom will capture most but
not all people who have heart attacks because it will miss people who have
“silent” heart attacks that occur without chest pain. In addition, it will
erroneously include many people who have other conditions that produce
chest pain, such as indigestion.
A definition that includes more specific criteria such as the results of
diagnostic tests will be more accurate. For example, if positive blood
enzyme tests are included, silent heart attacks are likely to be picked up
and the other conditions that cause chest pain omitted. In practice, epidemiologists use all available information from physical and pathological
examinations and laboratory and other tests to define a case of a disease as
accurately as possible.
Changes in Disease Definitions
Even when clear-cut criteria are used, disease definitions often change
over time as more is learned about a disease and its various manifestations.
For example, the official definition of acquired immune deficiency syndrome (AIDS) has been changed several times as researchers have gained
knowledge about the disease’s cause and natural course (see Table 2–2).
The story began in the summer of 1981 when the Centers for Disease
Control and Prevention (CDC) reported that Kaposi’s sarcoma and
Pneumocystis carinii pneumonia had been observed among previously
healthy homosexual men.5 Previously, Kaposi’s sarcoma, a malignant neo-
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TABLE 2–2
Changes in the Definition of AIDS over Time
Year
Conditions included in disease definition
1982
Very limited
Only a few conditions including
Kaposi's sarcoma, Pneumocystis carinii
pneumonia, and other severe opportunistic infections
1985
HIV virus discovered as cause of
AIDS; antibody test developed
23 clinical conditions with laboratory
evidence of infection
1993
Discovered importance of CD4
T lymphocytes in monitoring
immunodeficiency and disease
progression
26 clinical conditions and asymptomatic cases with low CD4 T lymphocyte counts
Sources: Data from Centers for Disease Control. Update on acquired immune deficiency syndrome (AIDS)—United States. MMWR. 1982;31:507–514. Centers for Disease Control.
Revision of the case definition of acquired immune deficiency syndrome for national reporting—United States. MMWR. 1985;34:373–375. Centers for Disease Control. 1993 revised classification system for HIV infection and expanded surveillance case definition for AIDS among
plasm of the blood vessels, had been seen primarily among elderly males,
and opportunistic infections such as Pneumocystis carinii pneumonia had
occurred almost exclusively in people with compromised immune systems.
In 1982 the CDC composed the first definition of AIDS for national
reporting as “a disease, at least moderately predictive of a defect in cellmediated immunity, occurring in a person with no known cause for diminished resistance to that disease . . . including Kaposi’s Sarcoma,
Pneumocystis carinii pneumonia, and serious other opportunistic infections.”6 Even then, the CDC acknowledged that the case definition was
imperfect because it could possibly miss the full range of AIDS manifestations and falsely include individuals who were not truly immunodeficient.
However, because the cause of AIDS was unknown at that time, the definition at least served as a consistent tool for monitoring the epidemic.
The CDC made the first major change in the official AIDS case definition in 1985 after the human immunodeficiency virus (HIV) was determined to be the cause of AIDS and a highly accurate laboratory test was
developed to detect the antibody to the HIV virus.7 Because epidemiologists now knew what to look for and how to find its trail, it was possible
to expand the AIDS case definition from a few severe clinical conditions to
a wide range of conditions accompanied by laboratory evidence of HIV
infection. Conversely, it also became possible to exclude patients who had
AIDS-like symptoms but had negative HIV antibody test results.
At the end of 1992, the CDC changed the AIDS case definition again
after natural history studies revealed the importance of lymphocytes in the
HIV infection.8 The new definition was expanded to include individuals
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who had no symptoms of AIDS but had low levels of CD4 T lymphocytes,
a type of white blood cell that is responsible for fighting off infections.
(These cells are the primary target of HIV and are an excellent marker of
disease progression.)
In summary, as epidemiologists discovered the cause of AIDS, learned
more about its different manifestations, and developed a test to detect HIV,
the AIDS case definition was expanded from a few severe diseases to many
varied conditions and the results of sophisticated laboratory tests (see
Table 2–2).
What impact did these changes in case definition have on the number
of reported AIDS cases? In general, any expansion in the case definition
will increase the number of reportable cases and any contraction will
decrease that number. With AIDS, the definition changes increased the
number of people who were officially counted as AIDS cases in national
statistics in the 1980s and early 1990s.8 More recent trends in AIDS incidence are no longer affected by the change in the AIDS case definition.9
Measuring Disease Occurrence
Epidemiologists must always consider three factors when they measure
how commonly a disease occurs in a group of people: (1) the number of
people that are affected by the disease, (2) the size of the population from
which the cases of disease arise, and (3) the length of time that the population is followed. Failure to consider all three components will give a false
impression about the impact of the disease on a population.
Consider the following hypothetical data on the frequency of breast
cancer in two counties. In County A, with a population of 50,000, 100 new
cases of breast cancer occurred over a one year period. In County B, with
a population of 5000, 75 new cases occurred over a three year period.
Which county has a higher frequency of new breast cancer cases? If one
considers only the number of new cases, it appears that County A has a
higher frequency (100 versus 75). However, simply comparing the number
of cases in each town does not provide a full picture because the cases
occurred over different lengths of time (one versus three years) and among
populations of different sizes (50,000 versus 5000) (see Table 2–3).
In order to make a meaningful comparison between the two counties,
it is necessary to convert the data into the same population size and time
period. Let us estimate the frequency of breast cancer in the two counties
over a one year period and as if each population consisted of 100,000 people. The frequency of breast cancer in County A is 100 cases/50,000 population/one year; if the county’s population were 100,000, the frequency
would double to become 200 cases/100,000 population/one year.
Two steps are needed to make a similar conversion for County B. (1) Divide the numerator by three to convert the frequency of breast cancer from
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TABLE 2–3
Hypothetical Data on the Frequency of Breast Cancer in Two
Counties
Type of data
County A
County B
Number of cases
Population size
Follow-up period
Comparable disease frequency
100
50,000
1 year
200/100,000/year
75
5,000
3 years
500/100,000/year
a three to a one year period: 25 cases/5000 population/one year. (2) Multiply
both the numerator and denominator by 20 to estimate the frequency for a
population of 100,000. Thus, the frequency of new cases in County B is 500
cases/100,000 population/one year.
Now it is clear that the “rate” at which new cases are occurring is much
higher in County B than County A (500 cases/100,000 population/one year
versus 200 cases/100,000 population/one year), and that examining only
the number of new cases gives a false impression. Note that the decision to
convert the frequencies to a population size of 100,000 and a one year time
period, while commonly done, is arbitrary. Other population sizes (such as
1000 or 10,000) and time periods (such as one month or five years) could be
used. The guiding principle is that the same population size and time
period should be used for the compared groups.
Types of Calculations:
Ratios, Proportions, and Rates
Three types of calculations are used to describe and compare measures of
disease occurrence: ratios, proportions, and rates (see Table 2–4). A ratio is
simply one number divided by another. The entities represented by the two
numbers are not required to be related to one another. In other words, the
individuals in the numerator can be different from those in the denominator. For example, the “sex ratio” is a ratio of two unrelated numbers: the
number of males divided by the number of females, usually expressed as
the number of males per 100 females. In recent U.S. Census data, the sex
ratio among U.S. residents aged 65 years and older was 73.7 males per 100
females.10
A proportion is also one number divided by another, but the entities represented by these numbers are related to one another. In fact, the numerator of a proportion is always a subset of the denominator. Proportions, also
known as fractions, are often expressed as percentages and range from 0 to
1 or 0% to 100%. For example, the proportion of U.S. residents who are
black is the number of black residents divided by the total number of U.S.
residents of all races. In recent U.S. Census data, the proportion of black
U.S. residents was 0.125 or 12.5%.10 The remaining proportion included
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TABLE 2–4
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Types of Calculations
Type of calculation
Characteristics
Ratio
Division of two unrelated numbers
Proportion
Division of two related numbers; numerator is a subset of
denominator
Rate
Division of two numbers; time is always in denominator
whites (0.762 or 76.2%) and other or multiple races (0.112 or 11.2%). Note
that these three proportions add up to 100% because the three groups
(black, white, and all other races) are collectively exhaustive.
A rate is also one number divided by another, but time is an integral
part of the denominator. We are familiar with rates in our daily travels
since a rate is a measure of how fast we travel. For example, in many areas
of the United States the maximum speed or rate at which cars are permitted to travel is 65 miles per hour. This rate can also be written as 65
miles/one hour. The measure of time in the denominator is what makes
this number a rate. The measures of disease occurrence calculated previously for Counties A and B are also rates (200 cases/100,000 population/
one year and 500 cases/100,000 population/one year, respectively). Unfortunately, the term rate is often incorrectly used to describe ratios and
proportions.11
Measures of Disease Frequency
The two basic measures of disease frequency in epidemiology are incidence
and prevalence. Incidence measures the occurrence of new disease, and
prevalence measures the existence of current disease. Each measure
describes an important part of the natural course of a disease. Incidence
deals with the transition from health to disease, and prevalence focuses on
the period of time that a person lives with a disease.
Incidence
Incidence is defined as the occurrence of new cases of disease that develop
in a candidate population over a specified time period. There are three key
ideas in this definition. First, incidence measures new disease events. For diseases that can occur more than once, it usually measures the first occurrence of the disease.
Second, new cases of disease are measured in a candidate population,
which is a population of people who are “at risk” of getting the disease.
Someone is at risk because he or she has the appropriate body organ, is not
immune, and so forth. For example, a woman who still has an intact uterus
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(that is, she has not undergone a hysterectomy) is a candidate for getting
uterine cancer, and a child who has not been fully immunized against the
polio virus is a candidate for contracting poliomyelitis. Although it is possible to define and measure the incidence of disease in a population not at
risk (for example, the incidence of uterine cancer in women who have
undergone hysterectomies is, by definition, zero), it is not a particularly
interesting pursuit.
Third, incidence takes into account the specific amount of time that the
members of the population are followed until they develop the disease.
Because incidence measures a person’s transition from a healthy to a disease state, time must pass for this change to occur and be observed. As
described in the following sections, there are two types of incidence measures: cumulative incidence and incidence rate. Although closely related,
each measure has different strengths and weaknesses and is used in different settings.
Cumulative Incidence
Cumulative incidence is defined as the proportion of a candidate population that becomes diseased over a specified period of time. Mathematically,
it is expressed as follows:
Number of new cases of disease
Over a specified time period
Number in candidate population
Note that the numerator (new cases of disease) is a subset of the denominator (candidate population), and so the possible value of cumulative incidence ranges from 0 to 1 or, if expressed as a percentage, from 0 to 100%.
Time is not an integral part of this proportion but rather is expressed by the
words that accompany the numbers of the cumulative incidence measure.
Thus, cumulative incidence is dimensionless (see Table 2–5).
TABLE 2–5
Distinguishing Characteristics of Incidence and Prevalence
Measure
Type of
number
Units
Range
Type of
cases
Cumulative
Proportion
None
0 to 1
New
Research on causes,
incidence, prevention,
and treatment of
disease
Incidence rate
True rate
1/time
or t⫺1
0 to
infinity
New
Research on causes,
prevention, and
treatment of disease
Prevalence
Proportion
None
0 to 1
Existing
Resource planning
Major uses
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Cumulative incidence can be thought of as the average risk of getting a
disease over a certain period of time. (A risk is the probability of getting a disease.) A commonly cited measure of cumulative incidence is the “lifetime
risk of breast cancer” among women. Currently estimated at “one in eight”
among U.S. women, it means that 13% of women will develop breast cancer
sometime during the course of their lives.12 Cumulative incidence is influenced by the length of time to which it applies. Generally, the cumulative
incidence over a long period of time (such as a lifetime) will be higher than
that over a few years.
Cumulative incidence is mainly used in fixed populations when there
are no or small losses to follow-up. Consider, for example, the estimated
255,000 residents of Hiroshima, Japan, who were present in the city when
the atomic bomb was dropped on August 6, 1945 (Figure 2–2). During the
blast and in the weeks and months immediately thereafter, an estimated
65,000 people died from physical trauma, burns, and acute radiation sickness resulting in a 25% cumulative incidence of mortality over a fourmonth period.13 Officials estimate that another 21% of the population died
during the year following that initial four-month period. During the subsequent years and decades, the cumulative incidence of death was much
Number of Living Individuals in the Atomic
Bomb Population of Hiroshima, Japan
300,000
270,000
August 1945
240,000
210,000
November 1945
180,000
150,000
November 1946
120,000
90,000
1950
60,000
1991
1997
30,000
0
1945
1952
1959
1966
1973
Year
1980
1987
1994
2001
FIGURE 2–2. Dwindling Size of the Hiroshima Atomic Bomb Population over
Time: 1945–1997
Source: Data from Liebow AA. Encounter with Disaster: A Medical Diary of Hiroshima, pp. 175–176.
New York, NY: WW Norton and Co; 1970. Committee for the Compilation of Materials on
Damage Caused by the Atomic Bombs in Hiroshima and Nagasaki. Hiroshima and Nagasaki: The
Physical, Medical, and Social Effects of the Atomic Bombings. p 113. New York, NY: Basic Books;
1981. Pierce DA, Shimizu Y, Preston DL, Vaeth M, Mabuchi K. Studies of the mortality of atomic
bomb survivors. Report 13: Solid Cancer and Noncancer Disease Mortality: 1950–1997, Radiat
Res. 2003;160:383.
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lower, and different causes of death such as cancer predominated.14 The
cumulative incidence of death was 52% over the 47-year period from 1950
through 1997 among Hiroshima and Nagasaki survivors who were
enrolled in the Life Span Cohort Study of the effects of high-dose radiation
on the incidence of disease and death.14
Note that the cumulative incidence of death during the first 16 months
after the bomb was dropped (25% ⫹ 21% ⫽ 46%) was close to that during
the 47-year follow-up period of the Life Span Cohort Study (52%). This
finding underscores the importance of describing the time period that the
measure covers.
Everyone in the Hiroshima atomic bomb population will eventually die,
and the cumulative incidence of mortality will ultimately be 100%. In addition, the size of the candidate population dwindles as members die. For
example, all 255,000 residents were at risk of dying when the bomb was
dropped in August 1945, while approximately 190,000 survivors of the initial
period were at risk of dying during the subsequent years (see Figure 2–2).
One critical assumption underlies the cumulative incidence measure.
Everyone in the candidate population has been followed for the specified
time period. Thus, the estimate that women have a 13% lifetime risk of breast
cancer assumes that a population was followed for incidence of breast cancer from birth until death, an average of 70 to 80 years. Complete follow-up
is difficult to attain, particularly in a dynamic population where members are
continually entering and exiting. Thus, cumulative incidence is usually
reserved for fixed populations, particularly when there are no or few losses
to follow-up.
Incidence Rate
Incidence rate is defined as the occurrence of new cases of disease that arise
during person-time of observation. Mathematically, the incidence rate is
expressed as follows:
Number of new cases of disease
Person-time of observation in candidate population
Note that the numerator for incidence rate is identical to that of cumulative
incidence. The difference between the two measures lies in the denominator. The incidence rate’s denominator integrates time (t), and so it is a true
rate.11 Thus, its dimension is 1/t or t ⫺1, and its possible values range from
zero to infinity (Table 2–5). An incidence rate of infinity is possible if all
members of a population die instantaneously.
The concept of person-time can be difficult to understand. Person-time
is accrued only among candidates for the disease. Thus, a person con-
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tributes time to the denominator of an incidence rate only up until he or she
is diagnosed with the disease of interest. However, unlike for cumulative
incidence, the incidence rate is not based upon the assumption that everyone in the candidate population has been followed for a specified time
period. Person-time is accrued only while the candidate is being followed.
Accrual of person-time stops when the person dies or is lost to follow-up
(such as when a person moves away from a community). The incidence
rate can be calculated for either a fixed or dynamic population. However,
because it directly takes into account population changes (such as migration, birth, and death), it is especially useful as a measure of the transition
between health and disease in dynamic populations.
Consider the following population of a hypothetical town (Figure 2–3).
This dynamic population of five individuals is followed for the 10-year
period from 1994 to 2004. Person A moved into town in 1995, was diagnosed with disease in 1999, and so accrued four years of person-time.
Person B was a resident of the town at the start of the observation period in
1994, died in 2000, and so accrued six person-years. Person C moved to
town in 1996 and remained healthy until he moved away in 1999. The
investigator could not determine where he moved and so could not learn if
he became diseased later. Person C was considered lost to follow-up as of
the time he moved, and so he accrued three person-years. Person D was a
resident of the town at the start of the observation period, remained
No. Person-Years
Accrued
(Diagnosed with disease)
A
4
B
(Dies)
6
C
(Moves away, lost)
3
D
10
E
7
Total Population (A, B, C, D, E)
S 30
1994
1996 1987
1997 1988
1998 1989
1999 1990
2000 1991
20011992
20021993
20031994
2004
1985 1986
1984 1995
Observation Period
FIGURE 2–3. Measurement of Person–Time in a Hypothetical Population
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healthy for the entire period, and so accrued 10 years of person-time.
Person E was born to Person A in 1997, remained healthy for the entire
observation period, and so accrued seven person-years.
The incidence rate in this hypothetical population is 1/30 person-years.
Only one person became diseased and 30 person-years of observation were
accrued by the population. The denominator of the incidence rate is the
sum of person-time accrued by each member of the population at risk.
Now consider an actual population of 1762 women who were studied
to determine the relationship between radioactive iodine therapy for
hyperthyroidism (an overactive thyroid gland) and the risk of breast cancer.15 The women were treated from 1946 through 1964 and followed until
the end of 1978, the closing date of the study. Each woman’s follow-up time
began with her thyroid treatment and continued until one of the following
events occurred: breast cancer diagnosis, lost to follow-up, or end of follow-up for the study. By 1978, 8% of the women were lost, 32% were
deceased, and 60% were still alive. Investigators identified 61 cases of
breast cancer among the 30,324 person-years of follow-up, and so the incidence rate was 61/30,324 person-years or 201/100,000 person-years.
Although it is most accurate to determine person-time on an individual
basis, as was done in this study, this method is very time consuming and
labor-intensive. Thus, researchers sometimes use shortcuts such as multiplying the number of people under observation by an estimate of the average follow-up time.
In the hypothetical example portrayed in Figure 2–3, five individuals
who were followed for varying amounts of time accrued 30 person-years of
follow-up. However, depending on the size of the population and length
of follow-up, the 30 person-years could have been accrued in many different ways such as five people each contributing six years, three people each
contributing 10 years, and so forth. Regardless of how the person-time is
accrued (for example, from five or 50 people), the person-time units are
assumed to be equivalent. This assumption is usually reasonable, except in
extreme situations where a small number of people are followed for a long
period of time.
The particular time unit used to measure person-time can vary, but
decisions are guided by how long it takes for the disease to develop. For
example, person-years are commonly used for diseases that take many
years to develop (such as cancer), and person-months or person-days are
used for diseases that develop rapidly (such as infection).
The number of person-time units in the denominator is arbitrary. For
example, the same incidence rate can be expressed in terms of one personyear, 10 person-years, or 100 person-years. Epidemiologists generally use
100,000 person-years for rare diseases and those that take a long time to
develop.
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Relationship Between Cumulative
Incidence and Incidence Rate
It is possible to obtain cumulative incidence from an incidence rate. The
simplest situation to demonstrate this relationship is in a fixed population
with a constant incidence rate and small cumulative incidence (less than
10%). Here, the mathematical relationship is as follows:
CI ⫽ IRi ⫻ ti
where CI is cumulative incidence, IRi is incidence rate, and ti is the specified period of time.
When the incidence rate is not constant, it is necessary to take into
account the different rates that prevail during each time period:
CI ⫽ Σ (IRi ⫻ ti)
For example, the mortality rate (a type of incidence rate) among
Hiroshima residents was much higher shortly after the atomic bomb explosion than during subsequent years (see Figure 2–2).
Incidence Summary
In summary, two measures of disease frequency—cumulative incidence and
incidence rate—focus on measuring the transition from health to disease.
These measures have complementary strengths and weaknesses. The cumulative incidence is easy to calculate and understand, although it is less accurate when its assumptions are not met. Although the incidence rate has
greater accuracy, its person-time denominator is more difficult to calculate
and understand. Finally, the incidence rate is most useful for dynamic populations, and cumulative incidence is usually reserved for fixed populations.
Prevalence
While incidence measures the frequency with which new disease develops,
prevalence measures the frequency of existing disease. It is simply defined as
the proportion of the total population that is diseased. There are two types
of prevalence measures—point prevalence and period prevalence—that
relate prevalence to different amounts of time. Point prevalence refers to the
proportion of the population that is diseased at a single point in time and
can be thought of as a single snapshot of the population. The point can be
either a particular calendar date such as December 1, 2005 or a point in
someone’s life such as college graduation. Period prevalence refers to the
proportion of the population that is diseased during a specified duration of
time, such as during the year 2005. The period prevalence includes the
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number of cases that were present at the start of the period (for example,
January 1, 2005) as well as the number that developed during the period
(for example, January 2 through December 31, 2005). It may be helpful to
think of period prevalence as derived from a series of snapshots.
Mathematically, point prevalence is expressed as follows:
Number of existing cases of disease
At a point in time
Number in total population
Period prevalence can be expressed as follows:
Number of existing cases of disease
During a period of time
Number in total population
Note that the numerator (existing cases) is a subset of the denominator
(total population). Unlike the numerator for the two incidence measures, the
prevalence numerator includes all currently living cases regardless of when
they first developed. The denominator includes everyone in the population—
sick, healthy, at risk, and not at risk. Because prevalence is a proportion, it is
dimensionless and its possible values range from zero to one, or 0 to 100% (see
Table 2–5).
Relationship Between Prevalence
and Incidence
Prevalence depends on the rate at which new cases of disease develop (the
incidence rate) as well as the duration or length of time that individuals
have the disease. The duration of a disease starts at the time of diagnosis
and ends when the person either is cured or dies. Mathematically, the relationship between prevalence and incidence is as follows:
P/(1 ⫺ P) ⫽ IR ⫻ D
where P is prevalence (the proportion of the total population with the disease), (1 ⫺ P) is the proportion of the total population without the disease,
IR is incidence rate, and D is the average duration (or length of time) that
an individual has the disease.
This equation assumes that the population is in steady state (that is,
inflow equals outflow) and that the incidence rate and duration do not
change over time. If the frequency of disease is rare (that is, less than 10%),
the equation simplifies to:
P ⫽ IR ⫻ D
To better understand this relationship, think of the variables that influence
the level of water in a sink (see Figure 2–4). The water level is influenced
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Incidence
Prevalence
Cure and Death
FIGURE 2–4. Relationship between Incidence, Prevalence, Mortality and Cure
by both the inflow from the faucet and the outflow down the drain. The
water level will be high if the inflow is large, if the outflow is low, or if both
occur. The water level will be low if inflow is low, outflow is high, or both.
Now consider the water level in the sink as prevalence, the incoming water
as incidence, and the outflowing water as diseased people who either are
cured or die. The number of cases of people currently living with a disease
(prevalence) will be influenced by the rate at which new cases develop as
well as by the rate at which they are eliminated through cure or death.
Consider the real-life example of AIDS, whose prevalence has
increased steadily during the 1990s (see Figure 2–5).8,16 In the early 1990s,
the prevalence of AIDS increased because the AIDS case definition was
expanded and because incidence increased. Thus, prevalence increased
because inflow increased. Since the mid 1990s, prevalence increased because
improvements in treatment resulted in dramatic reductions in the number
of AIDS deaths. Thus, since the mid 1990s, prevalence increased because
outflow decreased. In fact, prevalence increased despite decreasing incidence
during this period.
Uses of Incidence and Prevalence
Epidemiologists and other public health professionals use each measure of
disease frequency for specific purposes (see Table 2–5). Incidence is most
useful for evaluating the effectiveness of programs that try to prevent disease from occurring in the first place. In addition, researchers who study
the causes of disease prefer to study new cases (incidence) over existing
ones (prevalence) because they are usually interested in exposures that lead
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500,000
48,000
Estimated Persons Living with AIDS
400,000
Deaths
300,000
36,000
Prevalence
200,000
24,000
100,000
0
12,000
Estimated Deaths of Persons with AIDS
60,000
0
1991
1993
1995
1997
Year
1999
2001
2003
FIGURE 2–5. Estimated Number of Persons Living with AIDS, and Estimated
Number of AIDS Deaths, 1991–2003, United States
Source: Data from Centers for Disease Control and Prevention. HIV/AIDS Surveillance Report.
1997;19(no 2). Centers for Disease Control and Prevention. HIV/AIDS Surveillance Report.
2001:13(no. 2). Centers for Disease Control and Prevention HIV/AIDS Surveillance Report.
2003:15.
to developing the disease. Prevalence obscures causal relationships because
it combines incidence and survival. In addition, many researchers prefer to
use incidence because the timing of exposures in relation to disease occurrence can be determined more accurately.
On the other hand, prevalence is useful for estimating the needs of
medical facilities and for allocating resources for treating people who
already have a disease. In addition, researchers who study diseases such as
birth defects (where it is difficult to gather information on defects present
in miscarried and aborted fetuses) and chronic conditions such as arthritis
(whose beginnings are difficult to pinpoint) have no choice but to use
prevalence. Unfortunately, results of such studies are difficult to interpret
because it is unclear how much the association is influenced by using a
group of survivors.
Commonly Used Measures of Disease
Frequency in Public Health
There are many measures of disease frequency that are commonly used in
the public health disciplines. Some are incidence measures, some are preva-
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lence measures, some are ratios. Descriptions and examples of the major
measures follow. Note that the word rate is often used incorrectly to
describe a proportion or ratio.
Crude mortality (or death) rate: Total number of deaths from all causes per
100,000 population per year. The term crude means that the rate is based on
raw data. In 2003, 2,448,288 deaths occurred among people residing in the
United States, resulting in a crude mortality rate of 841.9/100,000 population/
year.17
Cause-specific mortality (or death) rate: Number of deaths from a specific
cause per 100,000 population per year. In 2003, there were 685,089 deaths
from heart disease among U.S. residents resulting in a cause-specific mortality rate of 235.6/100,000/year.17
Age-specific mortality (or death) rate: Total number of deaths from all
causes among individuals in a specific age category per 100,000 population
per year in the age category. In 2003, there were 28,025 deaths among U.S.
children under the age of one year, resulting in an age-specific death rate of
700.0/100,000/year.17
Years of potential life lost: The number of years that an individual was
expected to live beyond his or her death. In 2003, 1214 years were lost due
to heart disease, 1628 years were lost due to cancer, and 1086 were lost
due to unintentional injuries before age 75 per 100,000 population younger
than 75 years of age.17 The number of years of potential life lost reflects
both the number of individuals who died of a particular cause and the age
at which the death occurred. For example, a cause of death that is more
common among children and young adults (such as unintentional injuries)
will result in more years of life lost per individual than a cause of death that
is common among the elderly (such as heart disease).
Livebirth rate: Total number of livebirths per 1000 population per year.
A livebirth is a pregnancy that results in a child who, after separation,
breathes or shows any other evidence of life. Sometimes the denominator
includes only women of childbearing age. In 2003, 4,089,950 livebirths
occurred among women that are residents of the United States, and the
crude livebirth rate was 14.1/1000/year.17
Infant mortality rate: Number of deaths of infants less than one year of
age per 1000 livebirths per year. This statistic is often divided into neonatal
deaths (those occurring during the first 27 days following birth) and postneonatal deaths (those occurring from 28 days through 12 months). In 2002,
the infant mortality rate in the United States was 7.0/1000 livebirths/year,
the neonatal mortality rate was 4.7/1000 livebirths/year, and the postneonatal death rate was 2.3/1000 livebirths/year.17
Birth defect (also called congenital anomaly or malformation) rate: Number
of children born with defects per 10,000 births. The numerator and denominator often include both live- and stillbirths. According to a nationwide
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birth defects monitoring program, the prevalence of spina bifida, a central
nervous system malformation, was 4.45/10,000 births from 1986 to 1987.18
Morbidity rate: Number of existing or new cases of a particular disease
or condition per 100 population. The time period that is covered and the
population size in the denominator vary. Morbidity is a general word that
can apply to a disease, condition, or event. For example, from 1999 to 2002,
the prevalence of physician-diagnosed diabetes among U.S. adults aged 60
years and over was 15.1%.17
Attack rate: Number of new cases of disease that develop (usually during a defined and short time period) per the number in a healthy population at risk at the start of the period. This cumulative incidence measure is
usually reserved for infectious disease outbreaks. For example, the 24-hour
attack rate for food poisoning was 50% among people who ate chicken
Case fatality rate: Number of deaths per number of cases of disease.
Note that this measure is a type of cumulative incidence, so it is necessary
to specify the length of time to which it applies. For example, the 5-year
case fatality rates for breast cancer were 9.9% and 21.5%, respectively,
among white and black women in the United States, who were diagnosed
during 1996–2002.12
Survival rate: Number of living cases per number of cases of disease.
This rate is the complement of the case fatality rate; also a cumulative incidence measure. Five-year relative survival rates for cancer compare people
with a particular cancer to similar people in the general population. For
example, from 1988 to 2002, five-year relative survival rates for prostate
cancer were 100% among men diagnosed while the tumor was still confined to the prostate or had spread only to the regional lymph nodes, and
33.5% among men whose tumor had metastasized to distant sites.12
Summary
A population is defined as a group of people with a common characteristic
such as place of residence, age, or the occurrence of an event. There are two
main types of populations, fixed and dynamic (or open). The membership
of a fixed population is defined by a life event and is permanent, whereas
the membership of a dynamic population is defined by a changeable characteristic and is transient.
Three factors should always be considered when measuring how commonly a disease occurs in a population: (1) the number of affected individuals or cases, (2) the size of the population from which the cases arise, and
(3) the amount of time that this population is followed. Before epidemiologists can count the number of affected cases, they must compose a disease
definition that is usually based on physical and pathological examinations,
diagnostic tests, and signs and symptoms. Disease definitions often change
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over time, as more is learned about a disease and its manifestations. For
example, the official case definition of AIDS expanded when its cause was
discovered and improvements in detection were made.
Incidence and prevalence are the two basic measures of disease frequency. Incidence measures the occurrence of new disease and so captures
the transition from health to disease. Cumulative incidence and incidence
rate are the two main types of incidence measures. Cumulative incidence is
defined as the proportion of a candidate population that becomes diseased
over a specified time period. It is a dimensionless proportion that measures
the average risk of contracting a disease over a certain time period. Incidence rate is the occurrence of new cases of disease that arise during person-time of observation, and so it is a true rate. It is important to remember
that person-time accumulates only among candidates for disease. Cumulative incidence and incidence rate are related mathematically. Both measures are most useful for evaluating the effectiveness of disease prevention
activities and for etiological studies of disease.
Prevalence measures existing disease and so focuses on the period when
a person is ill. Prevalence measures the proportion of the total population
that is diseased at a point in time or during a period of time. Its numerator
consists of the number of existing cases, and its denominator includes the
total population, including sick, healthy, at-risk, and immune individuals.
Point prevalence refers to a single point in time and is like a snapshot. Period
prevalence refers to a specific duration of time that may be derived from a
series of snapshots. Prevalence is typically used for estimating the needs of
medical facilities and for allocating resources for treating diseased individuals.
The incidence rate and prevalence are mathematically related.
Many measures of disease frequency are commonly used in public
health, including the crude, cause-specific, and age-specific mortality rates;
morbidity rate; livebirth rate; infant mortality rate; attack rate; case fatality
rate; and survival rate. Note that the term rate is often incorrectly used to
refer to proportions and ratios.
References
1. MacMahon, B, Trichopoulos, D. Epidemiology: Principles and Methods. 2nd ed.
Boston, MA: Little, Brown and Co; 1996.
2. Last, JM. A Dictionary of Epidemiology. 4th ed. New York, NY: Oxford University
Press; 2001.
3. Preamble to the Constitution of the World Health Organization as adopted by the
International Health Conference, New York, 19–22 June 1946; signed on 22 July
by the representatives of 61 States (Official Records of the World Health
Organization p. 100) and entered into force on 4 April 1948.
4. Healthy People 2010: Understanding and Improving Health. 2nd ed. Washington
DC: U.S. Department of Health and Human Services, Public Health Service;
2000.
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5. Centers for Disease Control. Kaposi’s sarcoma and Pneumocystis pneumonia
among homosexual men—New York City and California. MMWR. 1981;30:
305–308.
6. Centers for Disease Control. Update on acquired immune deficiency syndrome
(AIDS)—United States. MMWR. 1982;31:507–514.
7. Centers for Disease Control. Revision of the case definition of acquired immune deficiency syndrome for national reporting—United States. MMWR.
1985;34:373–375.
8. Centers for Disease Control and Prevention. HIV/AIDS Surveillance Report.
1997;9:1–43.
9. Centers for Disease Control and Prevention. HIV/AIDS Surveillance Report 2004.
Vol. 16. 1–46, 2005. Available at: http://www.cdc.gov/hiv/stats/hasrlink.htm.
Accessed August 2006.
10. U.S. Census Bureau. Available at: http://www.census.gov/acs/www/
Products/Profiles/Single/2003/ACS/Tabular/010. Accessed September 2005.
11. Elandt-Johnson, RC. Definition of rates: some remarks on their use and misuse.
Am J Epidmiol. 1975;102:267–271.
12. Ries, LAG, Harkins, D, Krapcho, M, et al. SEER Cancer Statistics Review,
1975–2003, National Cancer Institute, Bethesda, MD. 2006
13. Liebow, AA. Encounter with Disaster: A Medical Diary of Hiroshima. New York,
NY: WW Norton and Co; 1970.
14. Preston, DL, Shimizu, Y, Pierce, DA, Suyama, A, Mabuchi, K. Studies of mortality of atomic bomb survivors. Report 13: Solid Cancer and Noncancer disease mortality: 1950–1997. Radiat Res. 2003;160:381–407.
15. Goldman, MB, Maloof, F, Monson, RR, Aschengrau, A, Cooper, DS, Ridgway,
EC. Radioactive iodine therapy and breast cancer: a follow-up study of hyperthyroid women. Am J Epidemiol. 1988;127:969–980.
16. Centers for Disease Control and Prevention. HIV/AIDS Surveillance Report.
2003;15:1–46.
17. National Center for Health Statistics. Health, United States, 2005 With Chartbook
on Trends in the Health of Americans. Hyattsville, MD: National Center for Health
Statistics, 2005.
18. Centers for Disease Control. Temporal trends in the prevalence of congenital
malformations at birth based on the Birth Defects Monitoring Program, United
States 1979–87. MMWR. 1990;39(SS-4):19–23.
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CHAPTER QUESTIONS
1.
What measure of disease frequency is each of the following?
A. The percentage of freshman girls who become pregnant over the
course of their high school years
B. The percentage of senior boys who are fathers at the time of graduation
C. The number of liveborn babies who die of sudden infant death syndrome during the first year of life per 100,000 baby-years of follow-up
D. The percentage of infants weighing less than 2500 grams at birth
E. The lifetime risk of breast cancer
2.
Briefly describe the main similarities and differences between each of
the following:
A. Prevalence and incidence
B. Incidence rate and cumulative incidence
C. Fixed and dynamic population
3.
In 2005, there were 2900 new cases of breast cancer diagnosed among
women in Alabama and 200 new cases diagnosed among women in
Alaska. Based on these data, is it accurate to say that the incidence rate
of breast cancer is higher in Alabama than Alaska. Why or why not?
4.
Consider a class with 100 enrolled students. None of the students were
ill at the beginning of the school year. On September 30, 5 students
reported having gastroenteritis. All continued to be ill on October 1,
but all 5 recovered within 3 days. On October 14, 3 more students
developed gastroenteritis. All of these students continued to be ill on
October 15, but all 3 recovered 5 days later. In this example, assume
that a person cannot get gastroenteritis more than once.
A. Calculate the prevalence of gastroenteritis in the class on October 1.
B. Calculate the prevalence of gastroenteritis in the class on October 30.
C. Calculate the cumulative incidence of gastroenteritis in the class
during the month of October.
5.
The incidence rate of a nonfatal disease is 500/100,000 person-years. People usually have the disease for an average of 3 years, at which time the
disease resolves spontaneously. Estimate the prevalence of this disease
using this information. Assume that the population is in steady state.
6.
A population of 100 healthy men was followed for the development of
prostate cancer. After being followed for 5 years, 20 men developed
prostate cancer. Ten other men were followed for 1 year and then were
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lost. The remaining men who never developed the disease were followed for 10 years. Calculate the number of person-years of observation accrued by this population.
7. Consider the following hypothetical data on the occurrence of hepatitis in two cities.
City
New cases
Observation period
City A
City B
25
30
January–December 2005
January–December 2005
Starting population at risk
25,000
50,000
A. Calculate the cumulative incidence of hepatitis in each city.
B. Which city has the higher cumulative incidence?
8. Sixty cases of myocardial infarction were reported over a period of two
years in a city with a population of 100,000 people. Using these data,
estimate the incidence rate of myocardial infarction per 100,000 personyears. State any assumptions that are needed.
9. State the type of population (fixed or dynamic) that best describes each
of the following:
A. People who live in New York City
B. Men who had coronary bypass surgery as of 2005
C. Children who were vaccinated against polio in 1955
D. Women who are practicing physicians
10. Indicate whether the following statements are true or false.
A. Only the population at risk contributes to the denominator of the
cumulative incidence.
B. When calculating the incidence rate of a disease, it is necessary to
follow all subjects for the same length of time.
C. If the incidence rate of a very serious disease is 75/100,000 personyears and the prevalence of this disease in the population is
25/100,000, then the average duration of this disease must be three
years.
D. All other things being equal, when a new prevention measure for a
disease is developed, the prevalence of the disease will decrease
over time.
11. An epidemiologic investigation that was started on January 1, 2005,
identified a population of 1000 individuals among whom four were
found to have the disease under study. During the year of the study, six
new cases were found. Among the total of 10 cases, there were six deaths
during the year. For the 10 cases, the diagram indicates the time of case
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Measures of Disease Frequency
recognition, periods of observation during the study, and vital status at
the time of the termination of observation. An arrow at the start of the
diagram (patients 1, 2, 3, 4) indicates that the start of disease occurred
before the study began.
Assume that the 990 remaining individuals in the study did not
become ill or die during the year of observation. From the information
and diagram given, calculate the following:
A. Prevalence of the disease on January 1, 2005; July 1, 2005; and December 31, 2005
B. Cumulative incidence of disease during 2005
C. Cumulative incidence of death during 2005
2005
1999
2006
2000
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan
1
Alive
2
3
4
5
6
Alive
7
8
Alive
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