1. 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
Slides supporting chapter 7 of the book:
Bhopal R S.
Concepts of Epidemiology. Oxford,
Oxford University Press, 2002, pp317

2. Risk and frequency: incidence and prevalence- educational objectives
You should understand:
Risk is the likelihood of an individual developing a disease/problem
Epidemiology measures risk (actual or absolute measures) and how this compares with other populations (relative measures).
A risk factor is a characteristic associated with disease.
The meaning of the words rate, ratio and proportion in everyday and epidemiological language.
The principal measures of risk- the incidence and prevalence rates.
The differences and similarities between incidence (density) using a person-time denominator and cumulative incidence using a population denominator.
The challenges in accurately measuring the events (numerator) and populations at risk (denominator)
The interrelationship between incidence and prevalence.
The advantages of using specific as opposed to overall rates

3. Risk Risk in everyday language and in epidemiology Risk markers
Associations
Risk factors
Causes

4. Numbers, proportions, ratios and rates
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.
In epidemiology rate is usually reserved for a ratio where the numerator and denominator have different qualities, e.g. deaths/population alive at a point in time.
A proportion in epidemiology is usually a ratio where the numerator is a part of the denominator, so both have the same qualities, e.g. deaths due to one cause/deaths due to all causes.

5. Measures in Epidemiology
Numbers of cases
Proportional mortality
Proportional mortality ratio
Actual/Crude prevalence and incidence rates
Specific prevalence and incidence rates
Standardised rates
Standardised ratios
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)

6. Incidence rate
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
Time spent by the study population at-risk

7. Denominator
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?

8. Incidence rates: a variety of names
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)

9. Incidence: shifting population at risk
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

10. very short time span approaching zero
Figure 7.1
very short time span approaching zero
Incidence density
time

11. Figure 7.2 Numerator: Denominator: (years of observation
0 cases 1 2 3
Denominator:
(years of observation
assuming each case
occurs at mid-point of
interval and contributes
0.5 years) 10 10
19.5
19.5 28 28
35.5
study start - year 1
- year 2
- year 3
- year 4
time

12. Incidence density and a person-time denominator
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 (disease-free, or alive, in the case of mortality studies)
When would this approach be either inappropriate or unnecessary?

13. Person denominator (cumulative incidence rate)
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

14. Time denominator (estimate of incidence density)
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

15. Prevalence rate
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

16. Types of prevalence
For prevalence, unlike incidence, include those people who have the disease in the denominator
The point prevalence rate comprises all the cases of a disease that exist at a point in time
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 mid-point estimate)
Lifetime prevalence is the proportion of the population who have ever had the disease

17. Figure 7.4
Incident cases
Prevalent cases
Deaths, emigrations and recovery

18. Emigrant and non-measured cases, deaths
Figure 7.7
Births
Recoveries
Population reservoir
Immigration
Incident cases
Emigrant cases, unmeasured cases occurring abroad, and deaths
Prevalent cases
Emigrant and non-measured cases, deaths
Recoveries

19. Incidence and prevalence and preferences
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?

20. Overall and specific rates
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?

21. Prevalence and incidence
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.

22. Entering diagnosis on a death certificate: exercise
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)

23. 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

24. Death certificate Compare your completed certificate with mine below.
1a Pulmonary embolus
b Pneumonia
c Influenza
11 Deep venous thrombosis

25. Coding of diagnosis: exercise
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).

26. 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)

27. Lower limb amputation: measurement
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?

28. Hospital discharge data Operating theatre records
Figure 7.1
Hospital discharge data
N = 165
Limb fitting centre
N = 66 65 26 8 17 75 15 85
Operating theatre records
N = 192

29. Class exercise: angina
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.

30. Summary 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
Rates are most accurately presented by age and sex groups ('specific' rates), but for ease of interpretation they may be grouped as overall (crude) rates, which can be adjusted for age and sex differences between compared populations