Primer 6 · Measuring disease
Prevalence, risk, rate, person-time: and which one your question needs
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Epidemiology begins with counting. The hard part is not the arithmetic. It is knowing what belongs in the denominator, and what that choice means.
A count is not a measure
“Kolar reported 480 tuberculosis cases last year; Tumkur reported 210.”
You cannot compare those. Kolar might be 3 times the size. A bare count answers “how much work is there”, which matters for planning drugs and beds. It does not answer “how bad is it here”, which needs a denominator.
Every measure below is the same count divided by something different. Choosing that something is the whole job. Divide 312 cases by everyone, and you get prevalence. Divide the same 312 by only those who could fall ill, and you get a risk. Divide them by time instead of people, and you get a rate. Three different answers from one numerator.
Prevalence: how many have it now
\[\text{Prevalence} = \frac{\text{people with the disease at a point in time}}{\text{people in the population at that time}}\]
Prevalence is a proportion. It has no units and it sits between 0 and 1, usually reported as a percentage or per 1000.
The answer is 0.13, or 13.0%.
Prevalence describes a snapshot. It tells a health service how many people need treatment today. It does not tell you how fast the disease is appearing, because a case counted today may have started ten years ago.
NotePoint prevalence and period prevalence
Point prevalence is at one moment: “on 1 March, 312 of 2,400 adults had hypertension.”
Period prevalence is over a stretch: “during 2026, 410 of 2,400 adults had hypertension at some point.”
Period prevalence counts people who recovered in March and people who fell ill in November. It is always at least as large as point prevalence.
Say which one you mean. Look at the 2 examples above. Same 2,400 people, same year, same disease. One gives 13%. The other gives 17%.
So if one paper reports “17%” and another reports “13%”, and neither says which it measured, you cannot compare them. You may spend an afternoon hunting for a difference between the two populations when the only difference is the definition.
Risk: what fraction fell ill over a period
Also called cumulative incidence. Now the denominator changes: only people who could get the disease, counted at the start.
\[\text{Risk} = \frac{\text{new cases during the period}}{\text{people free of disease at the start}}\]
The answer is 0.06, or 6% over two years.
Risk is also a proportion between 0 and 1. Two things make it different from prevalence:
- Only new cases count. Someone who already had asthma is excluded from the numerator and from the denominator; they were never at risk.
- It is meaningless without a time period. “A 6% risk” says nothing. “A 6% risk over two years” says something. Always attach the period.
Rate: how fast, per unit of time at risk
Risk has a problem. It assumes everyone was followed for the whole period.
In a real study people leave, die of other things, or join late. Counting them as if they were followed for 2 years overstates the denominator.
Person-time fixes this. Each person contributes exactly as much time as they were actually observed and still at risk.
\[\text{Incidence rate} = \frac{\text{new cases}}{\text{total person-time at risk}}\]
16.5 person-years, 2 events, so a rate of 12.1 per 100 person-years.
3 things about a rate catch people out:
- It has units. Per person-year, per 1000 person-years. A rate without units is not a number you can interpret.
- It is not a proportion. It can exceed 1, and it can exceed 100%, because the denominator is time, not people. A rate of 150 per 100 person-years is perfectly possible.
- Person-time stops when the person stops being at risk. D contributed 1.5 years, not 5. B contributed 2 years, not 5, because after the event they are no longer at risk of a first event.
WarningPerson-time assumes the rate is steady
Ten people followed for 1 year and one person followed for 10 years both give 10 person-years, and the formula treats them as equivalent. If the risk changes with age, or with time since exposure, they are not equivalent at all. This is why rates are usually calculated within age bands rather than over a whole population at once.
Which measure answers which question
| The question | The measure | Denominator |
|---|---|---|
| How many patients need treatment today? | Prevalence | everyone, now |
| How likely is this person to fall ill in 5 years? | Risk | those at risk, at the start |
| How fast is disease appearing in this population? | Rate | person-time at risk |
| How much work will the clinic have? | Count | none |
How the three relate
For a stable condition, prevalence rises both when disease appears more often and when it lasts longer:
\[\text{Prevalence} \approx \text{Incidence rate} \times \text{Average duration}\]
About 0.04, or 4% prevalent.
That has a consequence people find surprising. A treatment that keeps patients alive without curing them raises prevalence.
Antiretroviral therapy cut HIV incidence and it cut HIV deaths. The prevalence of people living with HIV went up. Nothing went wrong. Prevalence was never measuring what people assumed it was.
NoteThe approximation has conditions
It holds when incidence and duration have been roughly steady for long enough, and when the disease is not common. In an outbreak, or for a condition affecting a large share of the population, it breaks down. Use it to reason, not to compute a number you will publish.
What you should now be able to do
- Say why a count without a denominator cannot be compared between places.
- Compute a prevalence, and say whether it is point or period prevalence.
- Compute a risk, excluding from the denominator anyone who was not at risk.
- Compute an incidence rate from person-time, and state its units.
- Explain why a rate can exceed 100% and a risk cannot.
- Explain why a life-extending treatment raises prevalence.
→ Primer 7: measuring association