What the method is for
Prevalence is the proportion of a population that has a condition at a point in time, or over a period. It is estimated by surveys, screening programs, registries and cross-sectional studies, and the estimates differ between studies because the populations, settings, case definitions, diagnostic methods and sampling differ. A prevalence meta-analysis summarizes such studies, to give an overall estimate, to describe how much prevalence varies, and to examine why. It is widely used in epidemiology, public health, psychology and the social sciences, for example to estimate the burden of a disease, the proportion of people with a symptom, or the frequency of a behavior.
It differs from the meta-analysis of treatment effects in several ways. There is no comparison group, so there is no effect to estimate, only a proportion. Heterogeneity is usually far greater, since prevalence legitimately differs between populations. The studies are observational, with sampling methods that range from random population samples to convenience samples. And the usual statistical concerns are sharper, because proportions near zero or one behave badly under simple methods. The general framework is in meta-analysis.
Pooling proportions
A proportion is bounded between zero and one, and its sampling distribution is skewed when it is close to the bounds or when the sample is small, so a simple average with normal-theory intervals can give impossible values such as negative lower limits. The standard remedy is to transform the proportion, pool on the transformed scale, and transform back. The commonly used transformations are the logit, the log of the odds, the Freeman-Tukey double arcsine, and, less often, the log or the untransformed proportion. The logit transformation keeps results within bounds, has a straightforward variance and gives a pooled estimate on the odds scale that is easy to interpret, but it is undefined when the number of cases is zero or equal to the sample size, which needs a continuity correction. The double arcsine stabilizes the variance and handles zeros, but its back-transformation depends on a harmonic mean of the sample sizes, and it has been shown to give misleading results in some circumstances, particularly with very different sample sizes, so its use is now discouraged by many methodologists.
An example shows the logit approach. A study with 24 cases among 200 people has a proportion of 0.12. The logit is ln(0.12/0.88) = -1.992, with variance 1/24 + 1/176 = 0.0473 and standard error 0.218. The 95 percent interval on the logit scale is -2.419 to -1.566, which transforms back to 8.2 to 17.3 percent. A simple normal-theory interval would run from 7.5 to 16.5 percent, and the difference grows as the proportion approaches zero or one. The figures are invented to illustrate the calculation.
Binomial mixed models
An alternative that avoids transformations and continuity corrections is the generalized linear mixed model with a binomial likelihood, in which the number of cases in each study is modeled directly with a random effect on the logit of the proportion. It uses the exact distribution, handles studies with zero or all cases without adjustment, and gives a pooled prevalence and a measure of heterogeneity. It can be fitted in standard software with routines for mixed models or with dedicated meta-analysis functions. It is increasingly recommended as the default for single proportions, with the logit transformation as an acceptable alternative, and with sensitivity analyses comparing approaches. Whichever is used, the results are reported on the proportion scale, with confidence intervals and a prediction interval.
Heterogeneity
Between-study variation in prevalence is often extreme, with I squared values above 90 percent common. This is not necessarily a problem to be fixed, since prevalence legitimately differs by region, age, period and diagnostic criteria. But it changes the interpretation. A single pooled prevalence from studies of very different populations describes an average of limited relevance to any particular population, and the prediction interval, which shows the range of prevalence expected in a new setting, is often very wide and more informative than the pooled estimate. The right response to large heterogeneity is to explore it, by subgroup analysis or meta-regression on region, age group, sex, period, case definition and risk of bias, and to report pooled estimates for meaningful subgroups. See meta-regression.
Risk of bias in prevalence studies
The key question is whether a study's sample represents the target population. The main concerns are the sampling frame and method: a random sample of a defined population is better than a convenience sample or a sample of patients attending a clinic, which cannot give the prevalence in the general population. The response rate and handling of non-response matter, since non-responders may differ systematically. The condition must be defined and measured in a valid, reliable way, using the same criteria for everyone, and the period over which prevalence was measured should be clear. Several critical appraisal tools exist, including one adapted from the Hoy and colleagues checklist and one from the JBI group for prevalence data, and a review of tools has compared them. Whichever is used, the appraisal feeds sensitivity analyses that restrict to studies at lower risk, and it informs the interpretation.
Reporting bias and small studies
Funnel plots and asymmetry tests are of limited use with proportions, since the standard error is mathematically related to the proportion, which produces apparent asymmetry without bias. Specialized approaches exist, and the interpretation is cautious. Small studies may over-represent high prevalence because those with unusual findings were more likely to be published. It is therefore advisable to search broadly, including regional and non-English sources, grey literature and surveys by official bodies, and to discuss the possibility of selection.
Kinds of prevalence and how they differ
The word prevalence covers several quantities, and a review should say which it pools. Point prevalence is the proportion with the condition at a single moment, such as the day of a survey. Period prevalence is the proportion who had the condition at any time during a stated interval, such as a year, and it is always at least as large as the point prevalence. Lifetime prevalence is the proportion who have ever had the condition. They are not interchangeable, and pooling them together without distinction gives a number with no clear meaning. Prevalence also differs from incidence, which is the rate at which new cases arise over time, and from cumulative incidence, the proportion who develop the condition over a period. The review question determines which is needed, and the page on incidence meta-analysis covers rates. Where studies report different types, they are analyzed separately, or the type is used as a subgroup.
Age, sex and standardization
Prevalence of most conditions depends strongly on age and sex, so studies with different age structures are not directly comparable. A study of older adults will report a higher prevalence of many conditions than a study of the general population, and a pooled estimate that mixes them reflects the mix of the studies and not a population of interest. Where studies report prevalence by age and sex groups, pooling within strata gives more meaningful results, and the stratified estimates can be standardized to a reference population if a single figure is wanted. Where only overall figures are reported, the mean age and the proportion of each sex are extracted and used in meta-regression or subgroup analysis, with the limits of study-level inference in mind. The review states the population to which its estimates are meant to apply.
Choosing an approach in practice
| Situation | Suggested approach | Note |
|---|---|---|
| Proportions away from zero and one, moderate samples | Logit transformation with random effects, or a binomial mixed model | Report back-transformed estimate with interval and prediction interval |
| Some studies with zero or all cases | Binomial mixed model | Avoids continuity corrections; compare with a corrected logit analysis |
| Very rare condition | Binomial mixed model, or a rate-based analysis | Wide intervals are expected and should be reported |
| Very different sample sizes | Avoid the double arcsine back-transformation | Use logit or a mixed model and check by sensitivity analysis |
These are starting points. The method is fixed in the protocol, and a second approach is run as a sensitivity analysis to see whether the conclusion depends on the choice.
Presenting the results
Results are shown in a forest plot of the study-specific prevalences with their intervals, the pooled estimate, the prediction interval and the heterogeneity measures. Because prevalence is geographically and temporally structured, subgroup forest plots by region, period or age group are often more informative than a single overall estimate, and for global topics, tables or maps of prevalence by region are common. Each estimate is presented with the number of studies and people it rests on, and with a note on the quality of the underlying studies. Readers should be able to see which regions or groups are poorly covered, because absence of data is itself a finding, and the review should say that the pooled values do not describe places or groups with no studies.
Conducting a review
Define the target population and condition
The population, the case definition, the time frame and the setting are specified, and a decision is made about whether prevalence, incidence or both are the outcome.
Search and select
Searches cover sources that include surveys and official statistics, and eligibility criteria address sampling methods.
Extract and appraise
Cases, sample size, setting, population characteristics, diagnostic method and sampling are extracted, and risk of bias is assessed with a suitable tool.
Pool
The analysis uses a binomial mixed model or a transformation, with random effects, and reports a prediction interval.
Explore and report
Heterogeneity is explored with subgroups and meta-regression, and the review is reported with PRISMA 2020 and MOOSE.
Limitations
Pooled prevalence from heterogeneous studies is an average of uncertain meaning. Studies often use non-representative samples, different diagnostic criteria and different periods, which no analysis can fully harmonize. Small numbers of studies in subgroups limit exploration of heterogeneity. Methods have different properties, and the transformation chosen can change the result. And prevalence at the time of the studies may not describe the present. The pooled estimate should therefore be presented as a summary with its range and its limits, not as the prevalence in any one population. The results are not advice about the care of individuals.
Prevalence reviews describe populations. They do not provide clinical advice.
How we can help
Support for prevalence meta-analysis
The method can be supported at different depths. Choose what you need, and the scope is agreed in writing before work begins.
Feasibility check
A review of your studies and data to confirm that the method is suitable and which approach fits.
Analysis and figures
The analysis run to a prespecified plan, with forest plots and the other figures.
Methods and results text
Written for the manuscript and aligned with PRISMA 2020 or the relevant extension.
Manuscript and submission
Optional: the full paper, the reporting checklist and the submission materials.
Frequently asked questions
Why transform proportions before pooling?
Because proportions are bounded and skewed near zero or one, and simple methods can give impossible intervals. Transformation, or a binomial mixed model, keeps results within bounds.
Is the Freeman-Tukey double arcsine still recommended?
Many methodologists now discourage it as a default, because its back-transformation can give misleading results, especially with very different sample sizes. Logit transformation or a binomial mixed model is often preferred.
What should I do about I-squared of 99 percent?
Treat it as expected and explore it, with subgroup analysis or meta-regression, and report the prediction interval. A single pooled prevalence from very different populations has limited meaning.
Can I pool prevalence from clinic samples and population surveys?
Usually they should be analyzed separately, because clinic samples cannot estimate the prevalence in the general population.
Which tools appraise prevalence studies?
Tools adapted from Hoy and colleagues and the JBI critical appraisal checklist for prevalence data are widely used. The choice should be stated in the protocol.
Which reporting guideline applies?
PRISMA 2020, with MOOSE for observational studies, and guidance from methodological sources for reviews of prevalence.
References
- Barendregt JJ, Doi SA, Lee YY, Norman RE, Vos T. Meta-analysis of prevalence. J Epidemiol Community Health. 2013;67(11):974-978.
- Munn Z, Moola S, Lisy K, Riitano D, Tufanaru C. Methodological guidance for systematic reviews of observational epidemiological studies reporting prevalence and cumulative incidence data. Int J Evid Based Healthc. 2015;13(3):147-153.
- Migliavaca CB, Stein C, Colpani V, et al. Quality assessment of prevalence studies: a systematic review. J Clin Epidemiol. 2020;127:59-68.
- Hoy D, Brooks P, Woolf A, et al. Assessing risk of bias in prevalence studies: modification of an existing tool and evidence of interrater agreement. J Clin Epidemiol. 2012;65(9):934-939.
- Freeman MF, Tukey JW. Transformations related to the angular and the square root. Ann Math Stat. 1950;21(4):607-611.
- Schwarzer G, Chemaitelly H, Abu-Raddad LJ, Rucker G. Seriously misleading results using inverse of Freeman-Tukey double arcsine transformation in meta-analysis of single proportions. Res Synth Methods. 2019;10(3):476-483.
- Lin L, Xu C. Arcsine-based transformations for meta-analysis of proportions: pros, cons, and alternatives. Health Sci Rep. 2020;3(3):e178.
- Stijnen T, Hamza TH, Ozdemir P. Random effects meta-analysis of event outcome in the framework of the generalized linear mixed model with applications in sparse data. Stat Med. 2010;29(29):3046-3067.
- Nyaga VN, Arbyn M, Aerts M. Metaprop: a Stata command to perform meta-analysis of binomial data. Arch Public Health. 2014;72:39.
- Stroup DF, Berlin JA, Morton SC, et al. Meta-analysis of observational studies in epidemiology: a proposal for reporting. JAMA. 2000;283(15):2008-2012.
- Page MJ, McKenzie JE, Bossuyt PM, et al. The PRISMA 2020 statement: an updated guideline for reporting systematic reviews. BMJ. 2021;372:n71. doi:10.1136/bmj.n71