Risk and frequency:
incidence and prevalence
Raj Bhopal,
Bruce and John Usher Professor of Public Health,
Public Health Sciences Section,
Division of Community Health Sciences,
University of Edinburgh, Edinburgh EH89AG
Raj.Bhopal@ed.ac.uk
Risk and frequency: incidence and
prevalence- educational objectives
You should understand:
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Risk is the likelihood of an individual
developing a disease/problem
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Epidemiology measures risk (actual or absolute
measures) and how this compares with other
populations (relative measures).
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A risk factor is a characteristic associated with
disease.
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The meaning of the words rate, ratio and
proportion in everyday and epidemiological
language.
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The principal measures of risk- the incidence
and prevalence rates.
Risk
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Risk in everyday language and in
epidemiology
Risk markers
Associations
Risk factors
Causes
Numbers, proportions,
ratios and rates
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Epidemiology needs the number and
characteristics of disease cases, of people
with risk factors, and of the population from
which the above people derive.
Numbers of cases, or people with the risk
factors comprise the numerator-the top half of
the fraction- the population from which they
come is the denominator-the bottom part in of
factions
The fraction, numerator divided by the
denominator, is usually called the rate in
epidemiology
A ratio is one number in relation to another,
and a rate is a ratio.
Measures in Epidemiology
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Numbers of cases
Proportional mortality
Proportional mortality
ratio
Actual/Crude
prevalence and
incidence rates
Specific prevalence
and incidence rates
Standardised rates
Standardised ratios
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Relative risk
Odds ratio
Attributable risks
Numbers needed to
treat and prevent
Life years lost
Disability adjusted life
year (DALY)
Quality adjusted life
year (QALY)
Incidence rate
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Dictionary definition: the act of
happening, and, the occurrence or the
extent or frequency of occurrence
Count of new cases over a period of time
in a population size defined by
characteristics (age, sex, etc), and place
and time boundaries
Obtain from disease register or cohort
study or trial
The two key formulae are:
New cases
Population-at-risk, or
New cases
Time spent by the study population at-risk
Denominator
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What might be your denominator for a
study defining the incidence of (a)
infant mortality (b) the sudden infant
death syndrome (‘cot’ death) and (c)
myocardial infarction?
What information would you need to
make a rational choice?
Incidence rates:
a variety of names
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Incidence density is also known as
incidence rate, person-time incidence
rate, instantaneous incidence rate, hazard
rate and force of morbidity or mortality
Cumulative incidence is usually simply
referred to as incidence rate (or rarely,
cumulative proportion)
Incidence: shifting
population at risk
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Assume that the incidence rate of a disease is
20% per year and we follow up 100 people
How many people at an six months, on
average, will develop the disease?
For diseases that occur only once how many
are at risk after six months, or a day, or in the
first hour?
How many are at risk after one month?
How should we take into account this shifting
denominator in large studies?
Incidence density is a measure of the
occurrence of disease over a period of time
approaching zero
Figure 7.1
very short time span
approaching zero
Incidence density
time
Figure 7.2
Numerator:
0 cases
1
2
3
Denominator:
(years of
observation
0
10
assuming each
case
occurs at midstudy start - year 1
point of
interval and
contributes
0.5 years)
10
19.5
- year 2
19.5
28
- year 3
28
35.5
- year 4
time
Incidence density and a person-time
denominator
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If the incidence is constant over time then the
incidence density is estimated by the probability
that a person well at that time will develop the
disease in a moderate interval of time, i.e. not a
period approaching zero.
When might this assumption of constant incidence
be true?
In this circumstance using a person-time
denominator estimates the average value of the
incidence density.
The person-time denominator is the amount of time
that the study population has spent at risk (diseasefree, or alive, in the case of mortality studies)
When would this approach be either inappropriate
or unnecessary?
Person denominator
(cumulative incidence rate)
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Ranges from 0 to 1
Measures absolute risk (probability) of
disease e.g. cases/10,000 people = 5%
Can be used to construct relative risks
Incidence rates can be calculated with
population estimates, e.g., from a census,
and disease from a register
Can only be used with cohort studies where
study participants are enrolled at about the
same time
Time denominator (estimate of
incidence density)
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Ranges from zero to infinity
Not clearly interpreted as a measure of absolute
risk e.g. 50 cases per 1,000 person-years
Can be used to construct relative risks
Migration loss to follow-up and migration data
are not usually available in population
estimates so person-time cannot be calculated
Can be used either when enrolment is at about
the same time or when enrolment is spread
over time
Prevalence rate
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Count of cases (new and old) at a point in
time in a population size defined by
characteristics (age, sex, etc) and place
Obtained from cross-sectional studies or
disease registers
The formula is:
All cases
Population-at-risk
Types of prevalence
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For prevalence, unlike incidence, include those
people who have the disease in the
denominator
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The point prevalence rate comprises all the
cases of a disease that exist at a point in time
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Period prevalence is all cases whether old,
new or recurrent, arising over a defined period,
say a year or two. The denominator is the
average population over the period (or midpoint estimate)
Lifetime prevalence is the proportion of the
population who have ever had the disease
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Figure 7.4
Incident cases
Prevalent cases
Deaths, emigrations and recovery
Figure 7.7
Recoveries
Births
Population reservoir
Immigration
Incident cases
Emigrant cases,
unmeasured cases
Prevalent cases
occurring abroad,
and deaths
Emigrant and nonmeasured cases,
Recoveries
deaths
Incidence and prevalence and
preferences
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For studies of the causes of disease the
incidence rate is preferred. Why?
For studies of the burden of diseases of short
duration e.g. measles incidence is also
preferred. Why?
The prevalence rate is generally preferred as
the measure of burden for long-lasting
diseases. Why?
For health behaviours and other disease risk
factors prevalence is the preferred measure
(even in studies of disease causation). Why?
Overall and specific rates
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The rate can be subdivided by any
characteristic of epidemiological interest eg
age, sex, place and time.
Such rates are called specific rates, e.g. age or
sex specific rates
Specific rates permit rational and easy
comparison of disease patterns in different
places and times for they can be directly
compared with each other
Why is this not true for overall rates?
Prevalence and incidence
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In fixed populations, the prevalence is equal to
the incidence rate x average duration of disease
It follows that incidence rate = point prevalence
rate  duration; and duration = point prevalence
rate ÷ incidence rate.
In a dynamic population, however, the prevalence
of a disease cannot be predicted from knowledge
of the incidence (or vice versa) because of
migration into and out of the population, deaths,
changing disease rates, changes in prognosis
and error in measuring the incidence (or
prevalence) accurately.
In practice, either the prevalence and incidence
are both measured or a choice of one is made.
Entering diagnosis on a death
certificate: exercise
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A person who has a feverish illness diagnosed
on laboratory tests as influenza, develops
cough and shortness of breath shown to be
pneumonia, followed by a deep venous
thrombosis. The doctors suspect that
pulmonary embolus has occurred but before it
can be confirmed by tests, the patient
collapses and dies unexpectedly. Assume that
there is no post-mortem because the relatives
refuse permission
Complete the specimen death certificate in
table 7.5 for the above person. Take care to
order the causes as instructed and note that as
the death certificate states that the underlying
cause of death goes on line 1(c)
Table 7.5 Specimen death
certificate: exercise
I (a) Disease or condition directly leading
to death (b) Other disease or condition,
if any, leading to I(a) (c) Other disease or
condition, if any, leading to I(b)
II Other significant conditions
CONTRIBUTING TO THE DEATH but not
related to the Disease or condition
causing it
CAUSE OF DEATH
The condition thought to be the "Underlying
Cause of Death" should appear in the
lowest completed line of Part
Death certificate
Compare your completed certificate with
mine below.
 1a Pulmonary embolus
 b Pneumonia
 c Influenza
 11 Deep venous thrombosis
Coding of diagnosis: exercise
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Based on your completed death
certificate code the causes of death
(see table 7.6).
Reconsider your choice of order of
causes of death after reading the coding
rule from the ICD (see table 7.6).
Death certificate: coded
Compare your completed certificate with
mine below.
 1a Pulmonary embolus (I26)
 b Pneumonia (J18)
 c Influenza (J10.0)
 11 Deep venous thrombosis (I80.1)
Lower limb amputation:
measurement
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To calculate the frequency of disease we need
rules to judge whether a case is a case, whether it
is new or old and to decide whether to include
recurrences
Each study will need to make this decision in the
light of its aims
Decisions are not easy except for the incidence of
mortality, diseases which are irreversible e.g.
amputation of a limb, disease which usually
occur only once e.g. measles, or diseases agreed
by definition or convention to be lifelong
diseases, e.g. diabetes
So how will we define lower limb amputation and
measure its prevalence? Where will the data
come from?
Figure 7.1
Hospital discharge
data
N = 165
Limb fitting centre
N = 66
65
26
8
75
17
15
85
Operating theatre records
N = 192
Class exercise: angina
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A health authority (or an equivalent body such
as an insurance agency or a managed care
organisation) serving 500,000 people wishes to
cost and plan a service for the medical and
surgical management of angina of the
population, with particular emphasis on the
numbers of cases requiring surgery.
You are invited to assist. Consider the general
principles that you would apply to the task.
Consider the relative merits of incidence, point
prevalence, period prevalence and lifetime
prevalence.
Summary
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Risk is the possibility of harm
In epidemiology risk is the likelihood of an
individual in a defined population developing a
disease or other adverse health problem
In epidemiology the association between risk of
disease and both individual and social
characteristics (risk factors) is often the starting
point for causal analysis
Measures of risk include incidence and
prevalence rates.
The incidence rate focuses on new cases
prevalence on all cases
In a fixed population prevalence rate is equal to
the incidence rate multiplied by the duration of
the disease