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In this chapter, three basic measures to assess the frequency
of health events are introduced. These measures, which play key
roles in medicine, epidemiology, and public health, are
risk (the likelihood that an individual
will contract a disease),
prevalence (the
amount of disease already present in a population), and
incidence rate (how fast new occurrences
of disease arise). In addition, these measures can be used to assess
the prognosis and mortality of patients with disease.
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Risk, or cumulative incidence, is a measure of the occurrence
of new cases of the disease of interest in the population. More
precisely,
risk is the proportion of unaffected
individuals who, on average, will contract the disease of interest
over a specified period of time. Risk is estimated by observing
a particular population for a defined period of time-the risk period.
The estimated risk (
R) is a proportion;
the numerator is the number of newly affected persons (
A), called
cases by
epidemiologists, and the denominator is the size (
N) of the unaffected population under
observation:
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All members of the population, or cohort, are free of disease
at the start of observation. Risk, which has no units, lies between
0 (when no new occurrences arise) and 1 (when, at the other extreme,
the entire population becomes affected during the risk period).
Alternatively, risk can be expressed as a percentage by multiplying
the proportion by 100.
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In Figure 2–1 a hypothetical study of six subjects illustrates
the calculation of risk. This study began in 1995 and concluded
in 2004. Individual subjects entered the study at various times,
were all free of the disease of interest at the time of enrollment,
and were followed up for at least 2 years. For example, Patient
A was enrolled in 1995, was diagnosed with the disease just prior
to 1997, and was followed up until death in 2002. Patient B was
enrolled in 1997, was followed up until 1999 without developing
the disease, and then discontinued participation in the study. Patient
C was enrolled in 1999, was diagnosed with the disease just prior
to 2002, and survived through the end of the observation period
in 2004. Patients D, E, and F entered the study in 1997, 2002, and
1998, respectively; each patient was followed through 2004 without
developing the disease.
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Of the six subjects under observation (N = 6),
only one (A = 1) developed
the disease within 2 years of entry into the study. The 2-year risk
of disease, therefore, is estimated by
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These same data are also summarized in Figure 2–2, where
the time scale on the horizontal axis represents the duration of
observation for each subject. In other words, observation of a particular individual
begins at time zero and continues until that person dies or is lost
from the study or until the study is concluded. The format used
in Figure 2–2 is sometimes preferred as a matter of convenience,
because it may be easier to visualize the actual lengths of observation
for individual subjects. The following example further illustrates
the use of risks and how they are estimated.
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Example 1. In deciding whether
to treat the patient in the Patient Profile with antibiotics prior
to determining the cause of the fever, the clinician had to address
this key question: How likely is it that the patient has a bacterial
infection? The answer can be based on experience with similar patients.
For example, to estimate a cancer patient’s risk of acquiring
an infection in the hospital (a nosocomial infection), a study was
conducted of 5031 patients admitted to a comprehensive cancer center. The
investigators carefully defined a nosocomial infection as an infection
that (1) is documented by cultures, (2) was not incubating at admission,
(3) occurred at least 48 hours after admission, and (4) occurred
no more than 48 hours following discharge (somewhat longer for surgical
wound infections). Of the 5031 patients, 596 developed an infection
that met these criteria. The risk was
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In this example, the risk period for each patient began 48 hours
after hospitalization and ended 48 hours after discharge. This equation
indicates that about 12% of cancer patients similar to
those studied will develop a nosocomial infection during or soon
after hospitalization. The risk is greater than would be expected
for the average hospitalized patient, suggesting that cancer patients
are at an unusually high risk of developing a hospital-acquired
infection.
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A broad range of hospitalized cancer patients were involved in
this study. The woman in the Patient Profile, however, had a fever
and a low granulocyte count. A more refined estimate of the likelihood
of infection could be derived from a study of patients with similar
conditions. In one such study, 1022 cancer patients with fever and
granulocytopenia were studied according to a defined protocol. Of
these patients, 530 had a clinically or microbiologically documented
bacterial infection. Thus, the risk of infection in granulocytopenic,
febrile cancer patients is estimated to be
++
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This result suggests that patients similar to the one described
in the Patient Profile have a very high risk of a bacterial infection,
thus supporting the decision to treat the patient with antibiotics even
before an infection is diagnosed.
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Prevalence indicates the number of existing
cases of the disease of interest in a population. Specifically,
the point prevalence (
P) is the proportion
of a population that has the disease of interest at a particular
time, eg, on a given day. This value is estimated by dividing the
number of existing affected individuals, or cases (
C), by the number of persons in the
population (
N):
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Prevalence, like risk, ranges between 0 and 1 and has no units.
The calculation of prevalence can be illustrated using the data
summarized in Figure 2–1. For example, to calculate the
prevalence of the disease of interest in 2001, it is necessary to
know (1) the number of persons under observation in 2001 and (2)
the number of individuals affected at that time. First, four persons
are under observation in 2001 (Patients A, C, D, and F) (N = 4). Second, at that time
one of these persons (Patient A) is affected (C = 1).
Thus, the prevalence in 2001 is
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Example 2. An important question
in deciding whether to administer antibiotics to the patient described
in the Patient Profile is the type of infection involved. As indicated
earlier, individuals with low neutrophil counts are susceptible
to a wide variety of bacterial infections. Therefore, broad-spectrum antibiotics
are used empirically in these patients until the specific infecting
organism is identified.
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These bacteria often can be cultured from persons without symptomatic
illness. For example, the prevalence of skin colonization with S aureus was estimated among 96 people
attending an outpatient clinic for the first time. Patients with
skin infections were excluded from the study. S
aureus was cultured from specimens from 62 patients. The prevalence
of colonization with S aureus in this
group was
++
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From this equation, it is estimated that in a group of patients
similar to the patients studied, the prevalence of skin colonization
with S aureus is about 65%.
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The incidence rate (
IR), like risk,
reflects occurrence of new cases of the disease of interest. Thus,
incidence rate measures the rapidity with
which newly diagnosed cases of the disease of interest develop. The
incidence rate is estimated by observing a population, counting
the number of new cases of disease in that population (
A), and measuring the net time, called
person-time (
PT), that individuals
in the population at risk for developing disease are observed. A
subject at risk of disease followed for 1 year contributes 1 person-year
of observation. The incidence rate is
++
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To illustrate calculation of person-time and incidence rate,
consider the small hypothetical cohort illustrated schematically
in Figure 2–2. Patient A developed the disease 2 years
after entry into the study. Because subjects contribute person-time
only while eligible to develop the disease, the person-time for
Patient A was 2 years. Similarly, Patients B, C, D, E, and F contributed
2, 3, 7, 2, and 6 years, respectively. Patients A and C developed
disease. Thus, A (the number of new
cases of disease in the population) = 2, the total PT = 2 + 2 + 3 + 7 + 2 + 6 = 22
person-years, and the incidence rate is
++
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Note that the total person-years of observation is obtained simply
by addition of the years contributed by each subject. Alternatively,
this rate can be expressed as 9 cases/100 person-years
by multiplying the numerator and denominator by 100. Although these
two expressions are equivalent, the latter might be preferred since
it does not require use of decimal points.
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Example 3. Returning to the study
cited in Example 1, the incidence rate of nosocomial infections
can be calculated from additional data reported in that investigation.
The 5031 patients remained under observation for a total of 127,859
patient-days (or an average length of stay of 127,859/5031 = 25.4
days). Since 596 patients developed an infection that met the definition
for a hospital-acquired infection, the incidence rate can be estimated
as
++
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This means that among patients similar to those studied, on average,
about 0.47% of patients would be expected to develop a
nosocomial infection per day.
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Calculation of incidence rates for a large population, such as
that in a city, by separately enumerating the person-years at risk
for each individual, as described above, would require a tremendous amount
of work. Fortunately, person-time for a large population can often
be calculated by multiplying the average size of the population
at risk by the length of time the population is observed:
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In many instances, relatively few people in the population develop
the disease, and the population undergoes no major demographic shifts
during the time period of observation. In such situations, the average
size of the population at risk can be estimated by the size of the
entire population, using census or other data. The person-time of
a large, stable population can often be estimated by
++
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Example 4 illustrates calculation of incidence rates using this
alternative approach to estimating person-time.
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Example 4. In the United States,
the National Cancer Institute maintains a network of registries
that collect information on all new occurrences of cancer within
populations residing in specific geographic areas. Collectively,
these registries cover about 14% of the population of the
United States, and between 1996 and 2000, 2957 females were newly
diagnosed with acute myelocytic leukemia in these areas. An estimated
19,185,836 females lived in these combined areas on average during this
5-year period. Thus, the number of woman-years of observation for
this population was 19,185,836 women × 5 years = 95,929,180
woman-years. Therefore, the average annual incidence rate of acute
myelocytic leukemia among females was 3.1 cases for every 100,000
woman-years of observation in these specific study areas.