Point Prevalence

Point Prevalence in Health Surveys, Costing and Decision Models

Point prevalence answers a head-count question on a fixed date, the share of a defined population that has a condition at that moment, however long ago each case began. In health economics it measures the standing caseload, the number of people a service must treat today, the mix of patients entering a cohort model and the starting size of an eligible population in a budget impact analysis. Because it counts people who are ill at one instant, it gives extra weight to long episodes and says little about how often new cases arise. A one-day survey can still feed annual estimates of cases, deaths and costs, as the European surveys of healthcare-associated infections show, but only through a conversion that rests on assumptions about length of illness.

Counting the existing caseload on one date

The CDC teaching text Principles of Epidemiology in Public Health Practice describes prevalence as the proportion of persons in a population who have a particular disease or attribute at a specified point in time or over a specified period, and calls the first form point prevalence. Its worked example puts the number of persons ill on the date over the population on that date. Unlike incidence, the numerator includes all cases, new and pre-existing.

$$P_t = \frac{C_t}{N_t}$$

Here $P_t$ is the point prevalence at time $t$, $C_t$ is the number of people who have the condition at time $t$ and $N_t$ is the number of people in the defined population at the same time. A person who recovered the day before or falls ill the day after is not a case.

In practice the "point" is often a survey day for each unit. In the third European point prevalence survey of healthcare-associated infections (HAIs), run by the European Centre for Disease Prevention and Control (ECDC) in 2022-2023, data for a single ward were collected on a single day, while covering all wards of one hospital took 11 days on average. Each patient is still assessed once, on that ward's survey day. A survey asking about the past year measures period prevalence instead, which also counts people whose illness began or ended during the window.

Why a snapshot favours long episodes

The CDC text notes that prevalence is based on both incidence and duration of illness. Pearce gives the steady-state link, in which the prevalence odds equal the incidence rate times the average duration, and warns that a difference in prevalence between two groups could depend entirely on differences in disease duration. The derivation and its assumptions are set out on the incidence page.

A direct consequence is that the people found ill on a given day are not a random sample of everyone who ever gets the condition. A patient whose episode lasts 30 days is 15 times as likely to be caught on the survey day as one whose episode lasts two days, at the same rate of onset. Costs, utilities or outcomes measured in a prevalent sample therefore over-represent long episodes, which matters when those values are applied to newly diagnosed patients in a model.

The ECDC figures show the effect at scale. After correction for validation studies, the prevalence of patients with at least one HAI was estimated at 8.0%, while the estimated incidence, the share of hospitalised patients acquiring at least one HAI during the year, was 6.5%. The snapshot exceeds the per-admission risk because the average infection lasts longer than the average hospital stay, so infected patients occupy a larger share of beds on any given day than their share of admissions.

Measurement choices that move the estimate

A point prevalence depends on how people are sampled and on the accuracy of the test or judgement used to classify them, as well as on the case definition. Two adjustments are common in practice, an interval for sampling error and a correction for imperfect case finding.

Sampling error and clustering

Lewis and Torgerson describe the binomial distribution as the model most commonly used to describe sampling error when prevalence is estimated from $r$ positive people out of $n$ tested. Surveys that sample hospitals, practices or households rather than individuals also need a design effect allowance, since cases cluster within units. The ECDC survey adjusted its national 95% confidence intervals for this design effect, to allow for clustering of HAIs within hospitals.

Imperfect tests and true prevalence

Where cases are identified by a test or by surveyors' judgement, the observed proportion is an apparent prevalence. Lewis and Torgerson give the relation between the probability of a positive result and the true prevalence.

$$P(T^{+}) = Se \, \Pi + (1 - Sp)(1 - \Pi)$$

Here $P(T^{+})$ is the probability that a person tests positive (the apparent prevalence), $\Pi$ is the true prevalence, $Se$ is the sensitivity of the test and $Sp$ is its specificity. Rearranging gives the Rogan-Gladen estimator of true prevalence.

$$\hat{\Pi} = \frac{P(T^{+}) + Sp - 1}{Se + Sp - 1}$$

Here $\hat{\Pi}$ is the estimated true prevalence and the other symbols are as above. Lewis and Torgerson note that the estimator needs sensitivity and specificity to be known and constant, and that it can return values above one or below zero, a sign that the assumed accuracy is wrong for that population. The ECDC survey corrected differently, applying the mean shares of false positives and false negatives found by its national validation studies to the estimated numbers of patients with and without HAI, which raised the weighted HAI prevalence of 6.3% to the adjusted 8.0%.

The same relation explains why the positive predictive value of a test depends on prevalence. Lewis and Torgerson give the predictive value as $Se\,\Pi$ divided by the probability of a positive result, so with sensitivity and specificity fixed it falls as true prevalence falls. In the economics of screening, the point prevalence in the population offered the test therefore sets the number of false positives to be followed up, and with it the cost per true case found.

Converting a one-day survey into annual counts and costs

Health economic estimates usually need cases per year, so a snapshot has to be converted. For hospital infections the standard route is the Rhame and Sudderth formula, which the ECDC applies to national prevalence.

$$I = P \times \frac{LA}{LN - INT}$$

Here $I$ is the estimated incidence, the proportion of admissions in which a patient acquires at least one HAI, $P$ is the prevalence of patients with at least one HAI on the survey day, $LA$ is the average length of stay of all patients, $LN$ is the average length of stay of infected patients and $INT$ is the average time between admission and onset of the infection, so $LN - INT$ is the average length of infection. The ratio rescales the snapshot by how long infected patients remain infected relative to an average stay.

The ECDC applied the resulting incidence to the annual number of hospital discharges. Its 2022-2023 report estimates 93,305 patients with at least one HAI on any given day and 4.3 million patients with at least one HAI per year in acute care hospitals in the European Union and European Economic Area. The report keeps the confidence intervals deliberately wide because of the inherent poor precision of the prevalence-to-incidence conversion, and gives a 95% confidence interval of 3.1 to 5.8 million for the annual figure.

These converted counts then enter burden and cost studies. Cassini and colleagues converted prevalence in the 2011-2012 ECDC survey with the Rhame and Sudderth formula and estimated 2,609,911 new cases a year of six common HAIs, causing 501 disability-adjusted life years per 100,000 general population each year, and they list reliance on the formula as a main limitation. In England, Guest and colleagues took an annual HAI incidence of 4.7% among adult inpatients, cited to the 2011-2012 ECDC survey report, and built a cost-of-illness model estimating 653,000 HAIs among adult inpatients in NHS general and teaching hospitals in 2016/2017, at a cost of GBP 2.1 billion. They note that a fixed excess length of stay and the absence of an allowance for time-dependent bias limit the results.

Where the snapshot enters an economic evaluation

Beyond infection surveys, point prevalence mostly enters economic work as a stock at the start of an analysis. A cohort model that represents current patients, such as a Markov model of a chronic disease, starts with the distribution of those patients across health states on the decision date, which is a point prevalence by state. A budget impact analysis begins with the people eligible for treatment on day one, then adds newly eligible people through incidence.

Two cautions follow from the length effect. A prevalent starting cohort contains more long-duration and slower-progressing patients than an incident cohort would, so transition probabilities estimated in newly diagnosed patients may not fit it. A prevalence-based burden of illness estimate for a year needs a count of everyone ill during that year, which is a period prevalence, not a single-date count.

Worked example converting a ward survey to an annual cost

All figures in this example are illustrative. A hospital has an average daily census of 600 inpatients and an average length of stay of 6 days. Its infection team surveys every inpatient once and finds 42 with an active HAI.

1. Apparent point prevalence.

$$P_{app} = \frac{42}{600} = 0.07$$

Here $P_{app}$ is the apparent point prevalence, 42 is the number of patients classified as infected and 600 is the number surveyed.

2. Correct for surveyor accuracy. A validation exercise suggests the team detects 80% of true infections and correctly clears 99% of uninfected patients.

$$\hat{\Pi} = \frac{0.07 + 0.99 - 1}{0.80 + 0.99 - 1} = \frac{0.06}{0.79} = 0.07595$$

Here $\hat{\Pi}$ is the corrected point prevalence, 0.80 is the sensitivity and 0.99 is the specificity. About 0.07595 × 600 = 45.57 patients, or roughly 46, are truly infected on the day.

3. Convert to incidence per admission. Infected patients remain infected for an average of 12 days ($LN - INT$).

$$I = 0.07595 \times \frac{6}{12} = 0.03797$$

Here $I$ is the proportion of admissions acquiring an HAI, 6 is the average length of stay of all patients and 12 is the average length of infection.

4. Annual admissions and cases. With 600 beds occupied and stays of 6 days, the hospital admits 600 × 365 / 6 = 36,500 patients a year. Using the unrounded values, 0.0379747 × 36,500 = 1,386 patients acquire an HAI. A cross-check gives the same answer, since 45.57 infected patients on any day, each infected for 12 days, implies 45.57 × 365 / 12 = 1,386 patients a year.

5. Annual cost. If each HAI adds 5 bed days at GBP 400 per bed day, the excess cost per patient is 5 × 400 = GBP 2,000 and the annual cost is 1,386 × 2,000 = GBP 2,772,000.

6. The error to avoid. Reading the corrected snapshot as a risk per admission gives 0.0759494 × 36,500 = 2,772 patients and about GBP 5.54 million, twice the correct figure, because infections last twice as long as an average stay. Skipping the validation step errs the other way, giving 0.07 × 0.5 × 36,500 = 1,277.5 patients and GBP 2,555,000.

7. Interpretation. The survey describes a typical day, about 46 infected patients. The annual burden depends on the assumed length of infection as much as on the survey count, so a costing built on it should vary that length and the excess stay in sensitivity analysis.

Point prevalence beside neighbouring measures

Period prevalence counts everyone ill at any time in a window and is at least as large as the point prevalence at its start when both use the same denominator. Incidence counts only new cases and is the usual source of transition probabilities, as the cumulative incidence page explains. A prevalence ratio compares point or period prevalence between groups, and the cross-sectional design is the usual way of collecting point prevalence data.

Common misreadings

Most errors with point prevalence come from forgetting that it is a stock measured on one date. The remainder come from treating an observed proportion as exact.

1. Reading the snapshot as annual risk. A prevalence of 8% on a survey day does not mean 8% of patients are affected each year, as the gap between the ECDC prevalence and incidence estimates shows.
2. Comparing prevalence across groups as if it measured risk. A higher prevalence may reflect longer survival or slower recovery, not more frequent onset.
3. Ignoring test accuracy. Apparent prevalence from an imperfect test can sit well above or below true prevalence, particularly when true prevalence is low.
4. Reporting a bare figure. A point prevalence without its date, case definition, denominator and confidence interval cannot be checked or reused in a model.

Sources

• Cassini A, Plachouras D, Eckmanns T, et al. Burden of six healthcare-associated infections on European population health: estimating incidence-based disability-adjusted life years through a population prevalence-based modelling study. PLoS Medicine. 2016;13(10):e1002150. https://doi.org/10.1371/journal.pmed.1002150
• Centers for Disease Control and Prevention. Principles of Epidemiology in Public Health Practice, 3rd ed. Lesson 3: Measures of Risk, Section 2 (Morbidity frequency measures). Atlanta: CDC; 2006, page last reviewed 2012. https://archive.cdc.gov/www_cdc_gov/csels/dsepd/ss1978/lesson3/section2.html
• European Centre for Disease Prevention and Control. Point prevalence survey of healthcare-associated infections and antimicrobial use in European acute care hospitals, 2022-2023. Stockholm: ECDC; 2024. https://doi.org/10.2900/88011
• Guest JF, Keating T, Gould D, Wigglesworth N. Modelling the annual NHS costs and outcomes attributable to healthcare-associated infections in England. BMJ Open. 2020;10(1):e033367. https://doi.org/10.1136/bmjopen-2019-033367
• Lewis FI, Torgerson PR. A tutorial in estimating the prevalence of disease in humans and animals in the absence of a gold standard diagnostic. Emerging Themes in Epidemiology. 2012;9:9. https://doi.org/10.1186/1742-7622-9-9
• Pearce N. Effect measures in prevalence studies. Environmental Health Perspectives. 2004;112(10):1047-1050. https://doi.org/10.1289/ehp.6927