Measuring Disease: Incidence, Prevalence and Attack Rates
Epidemiological measures convert case counts into meaningful comparisons by relating disease to the population and time at risk. The three core measures are incidence, prevalence and attack rate.
Learning objectives
- Calculate incidence proportion, incidence rate and prevalence.
- Calculate attack rate and secondary attack rate.
- Select the correct denominator and multiplier.
- Interpret relationships between incidence, prevalence and disease duration.
- Avoid common calculation and examination errors.
Start with the population at risk
The denominator should include people who could develop the outcome during the period. People who already have the disease at baseline are usually excluded from the denominator for first-occurrence incidence, but included among existing cases when prevalence is measured.
| Measure | Numerator | Denominator | Time |
|---|---|---|---|
| Incidence proportion | New cases | People disease-free and at risk at start | Specified period |
| Incidence rate | New cases | Total person-time at risk | Built into denominator |
| Point prevalence | All existing cases | Total population at that point | One point |
| Period prevalence | People with disease at any time in period | Average or specified population | Defined period |
| Attack rate | New outbreak cases | Exposed population at risk | Outbreak period |
1. Incidence proportion or cumulative incidence
Incidence proportion is the probability or risk that a disease-free person develops the condition during a specified period.
Incidence proportion = New cases during the period ÷ Population at risk at the beginning × multiplier
Worked example
At the start of one year, 2,000 adults are free from diabetes. During the year, 50 are newly diagnosed.
Incidence proportion = 50 ÷ 2,000 × 1,000 = 25 per 1,000 persons per year, or 2.5% over the year.
It assumes a reasonably closed cohort and similar follow-up. Losses and varying observation time can make an incidence rate more appropriate.
2. Incidence rate or incidence density
Incidence rate describes the speed at which new cases occur and uses person-time contributed while individuals remain disease-free and under observation.
Incidence rate = New cases ÷ Total person-time at risk × multiplier
Person-time may be person-days, person-months or person-years. Ten people followed for one year contribute ten person-years, as do five people followed for two years, assuming all remain at risk for those periods.
Worked example
A cohort contributes 4,800 person-years and 24 new tuberculosis cases occur.
Incidence rate = 24 ÷ 4,800 × 1,000 = 5 cases per 1,000 person-years.
3. Prevalence
Prevalence measures all existing cases—new and previously diagnosed—in a population. It describes burden rather than the rate of becoming ill.
Point prevalence
Point prevalence = Existing cases at a specified point ÷ Total population at that point × multiplier
Period prevalence
Period prevalence = Persons who had the disease at any time during the period ÷ Population during the period × multiplier
Worked example
On 30 June, 360 of 12,000 residents are living with epilepsy.
Point prevalence = 360 ÷ 12,000 × 100 = 3%.
Relationship between incidence and prevalence
In a stable population with a relatively uncommon condition:
Prevalence ≈ Incidence × Average duration
Prevalence rises when
- Incidence increases
- Disease lasts longer
- Survival improves without cure
- Cases move into the population
- Detection improves
Prevalence falls when
- Incidence decreases
- Recovery becomes faster
- Case fatality increases
- Cases leave the population
- Case definition becomes narrower
Improved treatment may reduce incidence of complications but increase prevalence of people living with a chronic disease because survival improves. High prevalence therefore does not always mean prevention has failed.
4. Attack rate
An attack rate is a cumulative incidence proportion used during a limited outbreak. It is commonly expressed as a percentage.
Attack rate = New cases among an exposed group ÷ Number of exposed people at risk × 100
Food-specific attack rate example
At a function, 80 people ate chicken and 40 became ill. Of 120 who did not eat chicken, 12 became ill.
- Attack rate among exposed = 40 ÷ 80 × 100 = 50%.
- Attack rate among unexposed = 12 ÷ 120 × 100 = 10%.
- Risk ratio = 50% ÷ 10% = 5.
The chicken eaters had five times the risk, supporting chicken as a possible vehicle, though other evidence is still required.
5. Secondary attack rate
Secondary attack rate measures spread among susceptible close contacts after exposure to primary cases, commonly in households, dormitories or institutions.
Secondary attack rate = New cases among susceptible contacts within an incubation period ÷ Susceptible contacts exposed, excluding primary cases × 100
If two primary cases occur in a household of ten and three of the remaining eight susceptible contacts later become ill, the secondary attack rate is 3 ÷ 8 × 100 = 37.5%.
Choosing the right measure
| Question | Best measure |
|---|---|
| What is the risk of developing disease over one year? | Incidence proportion |
| How rapidly are new cases occurring with unequal follow-up? | Incidence rate |
| How many people currently need long-term services? | Point prevalence |
| How much illness occurred during a defined period? | Period prevalence |
| What proportion of exposed people became ill in an outbreak? | Attack rate |
| How effectively did infection spread among close contacts? | Secondary attack rate |
Worked mixed example
A population of 10,000 has 500 existing hypertension cases on 1 January. During the year, 190 new cases are found among the 9,500 initially free of diagnosed hypertension. At year-end, 650 residents are living with hypertension after allowing for recovery classification, deaths and migration.
- Beginning point prevalence: 500 ÷ 10,000 × 100 = 5%.
- Annual incidence proportion: 190 ÷ 9,500 × 1,000 = 20 per 1,000 at-risk persons.
- Year-end point prevalence: use the year-end cases and year-end population, not automatically the January denominator.
Common errors
- Counting old cases in the incidence numerator.
- Including existing cases in the incidence population at risk.
- Calling a proportion a rate without stating a time period.
- Using total population instead of the exposed population for attack rate.
- Including primary cases in a secondary attack-rate denominator.
- Mixing persons and episodes when recurrent events are possible.
- Reporting a number without units, multiplier or time.
Interpretation checklist
- State the case definition.
- Specify new or existing cases.
- Identify the population at risk.
- State the time point or period.
- Show the formula and substitution.
- Use an appropriate multiplier.
- Report units clearly.
- Interpret the result in words.
Exam-focused summary
- Incidence measures new disease; prevalence measures all existing disease.
- Incidence proportion estimates risk; incidence rate measures speed using person-time.
- Attack rate is an outbreak-specific cumulative incidence.
- Prevalence depends on both incidence and duration.
- Correct denominators and clear units are essential.
Review questions
- Differentiate incidence proportion and incidence rate.
- Calculate point prevalence from a short dataset.
- Explain five reasons prevalence may increase.
- Calculate food-specific attack rates and interpret them.
- Define secondary attack rate and state who is excluded from its denominator.
- Choose the appropriate measure for five public-health scenarios.
References and further reading
- CDC Field Epidemiology Manual: Epidemiologic measures.
- WHO indicator definitions.
- Clinical Medicine Year 2 curriculum.
Educational use only. Apply current national case definitions and reporting standards.
