Guides / incidence and prevalence
Incidence and prevalence
Prevalence counts who has a condition now. Incidence counts who is getting it. Two diseases with exactly the same risk of onset can differ forty-fold in prevalence purely because one lasts longer, which is why prevalence answers questions about burden and incidence answers questions about cause. This guide covers both, the person-time version most people skip, and how they relate.
Written and reviewed by Sidra Khan, Lead BiostatisticianPrevalence is the proportion of a population that has the condition at a given moment, so it counts existing cases and includes everyone still living with it. Incidence counts only new cases arising over a period among people who did not already have it. Prevalence depends on both how often the condition starts and how long it lasts, which makes it the right measure for planning services and the wrong one for studying causes.
Existing cases
Prevalence
Prevalence = people with the condition / people in the population. It is a proportion, so it has no units and runs from 0 to 1, usually quoted as a percentage or per 100,000.
| Type | Counts | Used for |
|---|---|---|
| Point prevalence | Cases at a single moment | The usual meaning. Service planning, surveys. |
| Period prevalence | Cases at any time during a window | Conditions that come and go, such as depression over a year. |
| Lifetime prevalence | Anyone who has ever had it | Survey work. Depends heavily on recall. |
Prevalence is what commissioners need, because it tells you how many people require a service. It is also what rises when treatment improves and people live longer with a condition, so a rising prevalence can mean better care rather than worse health.
New cases
Incidence, two versions
Incidence counts onset. There are two forms and they are not interchangeable.
Cumulative incidence, also called risk or attack rate, is new cases divided by the number of people at risk at the start, over a stated period. It is a proportion between 0 and 1 and it assumes everyone was followed for the whole period.
Incidence rate, also called incidence density, is new cases divided by total person-time at risk. It has units, such as per 1,000 person-years, and it handles people who were followed for different lengths of time.
An incidence of 5% is meaningless on its own. Five per cent over a year and five per cent over a decade describe entirely different situations. Cumulative incidence without a time period is the most common error in this area, and it is usually a sign the person did not have complete follow-up either.
The part people skip
Person-time, and why it matters
Real cohorts do not keep everyone for the full period. People join late, move away, die of something else or reach the end of the study. Person-time credits each individual for exactly the time they were actually at risk.
Take 100 people followed for two years, of whom 10 leave after one year on average, with 8 new cases. Cumulative incidence calculated naively is 8 out of 100, or 8%. The true denominator is 90 people for two years plus 10 for one, which is 190 person-years, giving an incidence rate of 42.1 per 1,000 person-years. The naive figure quietly assumed follow-up that never happened.
Worked example one
Both measures from one cohort, step by step
A practice list of 500 adults is followed for two years to study a chronic condition.
Step 1. Point prevalence at baseline
Forty people already have the condition on the day the study opens.
prevalence = 40 / 500 = 0.080, so 8.0%
Those 40 are now removed from everything that follows. You cannot develop a condition you already have, so the population at risk is 500 − 40 = 460.
Step 2. Account for what happened to those 460
Over the two years: 354 reach the end still free of the condition, 46 develop it at a mean of 1.1 years, and 60 leave the practice at a mean of 0.8 years. Those three numbers sum to 460, and if yours do not, something is wrong before any calculation starts.
Step 3. Cumulative incidence, the naive version
cumulative incidence = 46 / 460 = 0.100, so 10.0% over two years
This is a legitimate figure only if everyone was followed for the full two years. Sixty people were not, so it quietly assumes follow-up that did not happen.
Step 4. Person-time, the honest denominator
Credit each person for the time they were actually at risk. People who develop the condition stop contributing at that moment, because they are no longer at risk of developing it.
person-time = (354 × 2.0) + (46 × 1.1) + (60 × 0.8)
= 708 + 50.6 + 48 = 806.6 person-years
The naive calculation credited 460 × 2 = 920 person-years. The real figure is 806.6, so the simple approach inflated the denominator by a factor of 1.14.
Step 5. Incidence rate
incidence rate = 46 / 806.6 = 0.0570 per person-year
Multiply by 1,000 to get a readable figure: 57.0 new cases per 1,000 person-years.
Prevalence 8.0% describes the burden at a moment. Cumulative incidence 10.0% is the risk over two years for someone starting free of the condition. The rate of 57.0 per 1,000 person-years is the speed at which new cases arise. They are not alternative ways of saying the same thing, and a paper that reports one when the question needed another has answered the wrong question.
Worked example two
Age standardisation, and why crude rates deceive
Two areas report the same condition. Area A looks much healthier than Area B. Here is why that conclusion is wrong.
Step 1. The age-specific rates
| Area A | Area B | |||
|---|---|---|---|---|
| Age band | Population | Cases | Population | Cases |
| Under 65 | 8,000 | 16 | 2,000 | 4 |
| 65 and over | 2,000 | 40 | 8,000 | 160 |
| Total | 10,000 | 56 | 10,000 | 164 |
Work out the rate within each band. Area A under 65: 16/8,000 = 2 per 1,000. Area B under 65: 4/2,000 = also 2 per 1,000. Over 65: 40/2,000 = 20 per 1,000 in A, and 160/8,000 = 20 per 1,000 in B. The age-specific rates are identical in both areas.
Step 2. The crude rates
Area A = 56 / 10,000 = 5.6 per 1,000
Area B = 164 / 10,000 = 16.4 per 1,000
Nearly a threefold difference between two areas whose age-specific rates match exactly. The entire gap is age structure: Area B has four times as many older residents, and the condition is ten times commoner in that group.
Step 3. Standardise
Apply each area's age-specific rates to one shared reference population, here a simple 5,000 in each band.
expected cases = (5,000 × 0.002) + (5,000 × 0.020) = 10 + 100 = 110
standardised rate = 110 / 10,000 = 11.0 per 1,000
Both areas give 11.0 per 1,000, because both have the same underlying rates. The apparent difference was never real.
For UK work the European Standard Population is the usual choice and lets your figures be compared with published statistics. A home-made standard is fine for comparing areas within your own study, but it must be stated, because a standardised rate means nothing without the population it was standardised to.
The relationship
How the two relate
In a stable population the two are tied together by how long the condition lasts:
prevalence / (1 − prevalence) = incidence rate × mean duration
When prevalence is low this simplifies to the familiar approximation that prevalence is roughly incidence multiplied by duration. The consequence is the single most important thing on this page.
| Condition | Incidence rate | Mean duration | Prevalence |
|---|---|---|---|
| Rapidly fatal | 10 per 1,000 py | 6 months | 0.50% |
| Chronic, well managed | 10 per 1,000 py | 30 years | 23.1% |
Identical risk of developing the condition. A forty-six-fold difference in how many people have it at any moment, driven entirely by duration. Compare prevalence between two groups and you cannot tell whether you are seeing a difference in who gets ill or a difference in how long they survive.
Recruiting people who currently have a condition over-samples those who have had it longest, and whatever helps people survive with a disease gets mistaken for a cause of the disease. Using newly diagnosed cases avoids it. This is a specific form of the selection problems that affect any study where who you see depends on who lasted.
Comparing groups
Rate ratios and rate differences
A single rate describes one group. To compare two, you need the same two scales the risk measures use, built on person-time instead of people.
The two groups
Continuing the earlier cohort, split by an exposure.
exposed: 46 cases / 806.6 person-years = 57.0 per 1,000 py
unexposed: 28 cases / 1,012.4 person-years = 27.7 per 1,000 py
Rate ratio
rate ratio = 57.0 / 27.7 = 2.06
The interval is built on the log scale, and for rates the standard error has an unusually simple form: the square root of one over each case count, which here is the square root of 1/46 + 1/28 = 0.240. So exp(0.724 ± 1.96 × 0.240) gives 1.29 to 3.30. Note that the person-time does not enter the standard error at all. Precision is driven by how many events you observed, not how long you watched.
Rate difference
rate difference = 57.0 − 27.7 = 29.4 per 1,000 person-years, 95% CI 10.0 to 48.8
This is the absolute measure, and it is the one that scales to a population. Expose 1,000 people for a year and you would expect about 29 extra cases.
Turning it into people
Invert the rate difference and you get the person-time equivalent of number needed to harm.
1 / 0.0294 = 34 person-years of exposure per extra case
Which is to say: 34 people exposed for a year, or 17 people exposed for two, produces roughly one additional case. That sentence does more work in a report than either the ratio or the difference on its own.
Because the standard error depends only on the case counts, doubling your follow-up time while observing the same number of events buys no precision at all. When planning a study, the question is how many events you expect, not how many people or how many years. This is the same principle that governs Cox regression, where power depends on events rather than sample size.
Choosing
Which one answers your question
| Question | Measure |
|---|---|
| How many people need this service? | Prevalence |
| Is this condition becoming more common? | Incidence. Prevalence confounds onset with survival. |
| Does this exposure cause the condition? | Incidence, in people free of it at baseline |
| Did our prevention programme work? | Incidence |
| Did our treatment programme work? | Prevalence may rise if people live longer. Say so. |
| What is the burden on the population? | Prevalence |
Doing it
In R, SPSS and Stata
R
For a rate with an exact Poisson interval, which is what you want when case counts are small:
poisson.test(46, 806.6)
That returns the rate per person-year with its interval; multiply by 1,000 for the usual units. For a prevalence proportion use binom.test(40, 500) or DescTools::BinomCI(40, 500, method = "wilson"). Direct standardisation is handled by epitools::ageadjust.direct(count, pop, stdpop = std), and PHEindicatormethods::phe_dsr() implements the method used in English public health reporting.
SPSS
SPSS has no native incidence rate procedure, so compute person-time as a variable and derive the rate.
COMPUTE persontime = (exitdate - entrydate) / 365.25.
EXECUTE.
AGGREGATE /OUTFILE = * /BREAK = group /cases = SUM(event) /pt = SUM(persontime).
COMPUTE rate = cases / pt * 1000.
Prevalence comes straight from FREQUENCIES. For standardisation you will need to compute the expected counts by hand against a reference population, since there is no built-in command.
Stata
Stata handles this best of the three. stset declares the survival-time structure once and everything else follows.
stset exitdate, origin(entrydate) failure(event) scale(365.25)
stptime, per(1000)
That gives the incidence rate per 1,000 person-years with an exact interval. Add by(group) to compare groups. For immediate calculation without a dataset, iri takes counts and person-time directly. Direct standardisation is dstdize.
Person-time ends at the event, at loss to follow-up, at death, or at the end of the study, whichever comes first. Every package needs you to state that explicitly, and getting it wrong changes the denominator without changing anything visible in the output.
Avoid these
Six mistakes that cost marks
| Mistake | Why it matters |
|---|---|
| Quoting incidence with no time period | "An incidence of 5%" is meaningless. Over a year and over a decade are different claims entirely. |
| Leaving prevalent cases in the denominator | People who already have the condition cannot develop it. Including them understates the rate. |
| Using cumulative incidence with incomplete follow-up | It assumes everyone was followed the whole time. Use person-time whenever follow-up varies, which is almost always. |
| Comparing crude rates between populations | Two areas with identical age-specific rates can differ threefold on crude figures. Standardise, and say to what. |
| Reading rising prevalence as worsening health | Better survival raises prevalence while incidence falls. Prevalence confounds onset with duration. |
| Using prevalent cases in a case-control study | It over-samples long survivors, so anything that prolongs the illness is mistaken for a cause of it. |
Writing it up
How to report them
Age standardisation matters more than people expect. Two areas with identical age-specific rates will show different crude figures if one has an older population, and comparing crude rates between regions is a reliable way to reach a wrong conclusion.
Common questions
Frequently asked questions
What is the difference between incidence and prevalence?
Prevalence is the share of a population with the condition at a point in time, counting existing cases. Incidence counts only new cases arising over a period among people who did not already have it. Prevalence reflects both how often the condition starts and how long it lasts; incidence reflects only how often it starts.
What is prevalence?
The proportion of a defined population that has a condition at a given moment, expressed as a percentage or per 100,000. Point prevalence is a single moment, period prevalence covers a window, and lifetime prevalence counts anyone who has ever had it. It is the measure used for estimating how many people need a service.
Can prevalence rise while incidence falls?
Yes, and it happens often. If fewer people develop a condition but those who have it survive much longer, prevalence rises while incidence falls. Reading a rising prevalence as worsening health is a common error, since it can equally reflect better treatment.
What is person-time?
The total time each person was actually at risk, summed across everyone. It lets you handle varying follow-up: someone followed for six months contributes half a person-year. Dividing new cases by person-time gives an incidence rate, usually expressed per 1,000 person-years.
Why should case-control studies use new cases?
Because people who currently have a condition over-represent those who have had it longest. Anything that prolongs survival then looks like a cause of the disease. Recruiting newly diagnosed cases removes that distortion.
Should I use crude or standardised rates?
Standardised whenever you compare populations that differ in age or another strong determinant. Two areas with identical age-specific rates will show different crude rates if one population is older, so comparing crude figures across regions reliably produces misleading conclusions. State which you used and the reference population.