Ascertainment, Prevalence, and Case Definition

Why the Case Fraction Is Not Prevalence

In a population-based cohort, the fraction of participants meeting a disease definition may approximate the prevalence in the population from which they were sampled, provided selection is representative and the disease status is measured appropriately. A genome-wide association study (GWAS), however, may recruit cases deliberately and select controls separately. Its observed case fraction then reflects the recruitment design as well as disease occurrence. Confusing that fraction with population prevalence can lead to incorrect descriptions of the study population and inappropriate interpretations of genetic effects.

The issue is not only a matter of reporting. The disease definition determines who counts as a case, while the control definition determines the comparison group. Together with the sampling scheme, these choices specify the population and disease contrast to which the association result refers.

A prevalence statement therefore needs a population, a case definition, and a time reference. For example, “the point prevalence of condition X among eligible adults in region Y on date Z” has a defined denominator. “The percentage of cases in this GWAS” describes the sample, not necessarily that population quantity. Even in a population-based study, prevalence estimates can be distorted if participation depends on disease status or related characteristics.

How Outcome-Based Sampling Changes the Case Fraction

Suppose a target population has prevalence \(K=P(D=1)\), where \(D=1\) means that a person meets the disease definition. Let \(s_1\) be the probability that an eligible case is sampled and \(s_0\) the probability that an eligible noncase is sampled. If sampling is otherwise random within these two groups, the expected case fraction \(f\) in the ascertained sample is

The numerator represents the sampled cases per member of the target population, and the denominator represents all sampled cases and noncases per member. If cases are sampled at a higher rate than noncases, \(f\) can be much larger than \(K\). When \(s_1=s_0\), the formula reduces to \(f=K\); otherwise the sample fraction generally differs from prevalence.

If the sampling probabilities are known, the relationship can also be inverted to recover prevalence from a case fraction under the stated sampling model:

This inversion requires correct sampling probabilities and a compatible target population and disease definition. In practice, those probabilities may not be known precisely. A case-control sample’s case fraction alone cannot identify population prevalence.

Which Association Does Case-Control Sampling Estimate?

A key distinction is between an association measured by a disease odds ratio and an association measured by population risk or prevalence. Under a particular case-control sampling model, an odds ratio for genotype and disease is preserved, even though the sample case fraction is changed. This property does not make the sample representative for estimating disease probability.

For a simple derivation, compare two genotype values, \(G=1\) and \(G=0\). Write the population disease odds at genotype value \(g\) as \(P(D=1\mid G=g)/P(D=0\mid G=g)\). Suppose cases are sampled with probability \(s_1\), noncases with probability \(s_0\), and, within each disease group, selection does not depend on genotype. Then the odds of being a case rather than a noncase in the sample, conditional on genotype \(g\), are

Taking the ratio of these sample odds for \(G=1\) versus \(G=0\) cancels the common factor \(s_1/s_0\). Consequently, the disease odds ratio comparing the two genotype values is the same in the sampled data as in the target population, under these assumptions. In a logistic model, this corresponds to a change in the intercept from outcome-based sampling, while the genotype slope can remain the same.

The result depends on selection being independent of genotype within disease status. It does not say that every sampling scheme preserves every association parameter. Selection related to genotype within cases or controls can bias the comparison. Sampling based on covariates may require those covariates and the sampling structure to be handled correctly. Further, the preserved quantity is an odds ratio: the sample does not by itself provide population risks, risk differences, or prevalence. Converting an odds ratio into absolute risk requires additional information, including a suitable baseline risk.

Case Definitions Specify the Disease Contrast

A case definition is the operational rule that classifies participants as having the disease. It may combine clinical criteria, diagnostic codes, laboratory thresholds, records, or participant reports. The rule should be established for the intended scientific question, rather than chosen only because it produces more cases. Decisions may include which disease subtypes count, whether a single recorded event is sufficient, what time window applies, and how uncertain diagnoses are treated.

The control definition is equally consequential. A control group might consist of people with no evidence of the disease, people who are disease-free at recruitment, or people sampled from the same source population as cases without regard to their disease status. These choices create different contrasts. For example, including controls who are too young to have reached the age at which a condition is usually diagnosed can mix unaffected people with people who may later become cases. Conversely, defining controls as unusually healthy may compare cases with a selected subgroup rather than with the general source population.

A case definition can also change the composition of cases. A narrow definition may identify a relatively homogeneous subtype, while a broad definition may include milder, less certain, or biologically different forms. An association for the broad definition is then an association with that mixture, not automatically the association for the narrow subtype. This concern is distinct from the accuracy of recording: even consistently applied criteria can answer a different question when they include a different disease spectrum.

Planning Around the Intended Estimand

Before recruitment, state what the association is meant to describe. Is the target the odds of meeting a particular diagnosis in a defined population, the occurrence of new cases over a follow-up period, or the prevalence of existing disease at recruitment? The disease definition, eligible population, time reference, and sampling scheme should be consistent with that target. This makes the result interpretable even when the sample is deliberately enriched for cases.

A related caution is whether cases are incident or prevalent. Incident cases are identified as they develop during a defined observation period; prevalent cases already have the disease when recruited. Existing cases must remain alive, available, and eligible to be enrolled. If genotype or other factors affect survival or duration with disease, sampling prevalent cases can alter the case group. The resulting association may describe disease prevalence among recruited survivors rather than susceptibility to developing the disease. Thus the timing of ascertainment is part of the estimand, not merely an administrative detail.

Common Mistakes

• Calling the recruited case fraction prevalence. This is wrong when cases and noncases have different sampling probabilities. Report the sample composition as such, and estimate prevalence only with a representative design or a justified correction.
• Assuming an odds ratio means the same thing as a risk ratio. Case-control sampling can preserve an odds ratio under specified assumptions, but it does not recover absolute risks or make the odds ratio a risk ratio.
• Treating a broader diagnosis as only a larger sample. Adding cases can change the disease phenotype being studied and the association’s meaning, especially when added cases differ from the original cases.
• Ignoring control eligibility. Controls who do not represent the relevant source population, or whose disease status is defined inconsistently, can change the comparison and undermine interpretation.
• Overlooking prevalent-case selection. A study of existing cases may reflect disease duration and survival as well as disease onset. State which target the sampling process can support.