Why Cohort Eligibility Defines the Inference
A GWAS result is an estimate from people who met specified eligibility rules and contributed usable data. Those rules are therefore more than administrative details: they help define the population described by the result. A study of adults recruited at specialist clinics, for example, does not automatically estimate the same association that would be found among all adults with the phenotype in the community.
Eligibility should be designed in relation to a clearly stated target population: the group about which the investigators intend to make an inference. The target population need not be identical to the people who can be recruited, but differences must be recognized. Age limits, recruitment setting, disease history, and requirements for available data can all narrow the population. They can also change an estimated association if eligibility is related to genotype, phenotype, or factors associated with both.
Writing Eligibility Criteria Precisely
An inclusion criterion specifies a feature a person must have to enter the cohort; an exclusion criterion specifies a feature that prevents entry. Criteria should be operational: a reader should be able to determine consistently whether a particular person qualifies. “Adults with the condition” leaves important questions unanswered. An age range needs a defined age and date, the condition needs a usable case definition, and the setting or recruitment source needs to be stated if it limits who can enter.
Eligibility is best specified before examining genetic association results. Otherwise, choices about age boundaries, prior diagnoses, or data availability can be influenced—consciously or not—by the results. The rules should also distinguish scientific eligibility from later reasons data are unavailable or unusable. For example, requiring a particular phenotype measurement at enrollment is an eligibility rule; a failed genotype call discovered during quality control is an analysis-data issue. Both affect who is analyzed, but they arise at different stages and should be reported separately.
A useful specification states the target population first, then gives criteria that define the study population and identifies foreseeable gaps. It should make clear whether the intended inference concerns a particular age range, disease stage, care setting, or other defined group. These details are especially important when age affects the phenotype or when access to recruitment differs across settings.
State the group of people, setting, and period to which the intended conclusion refers. Avoid defining the target merely as “the study participants.”
Specify age boundaries, phenotype requirements, recruitment sources, and relevant history in terms that can be applied consistently.
Separate people who fail eligibility from eligible people who are not recruited, lack required measurements, or are omitted from analysis.
Ask which parts of the target are absent or sparse, and whether inclusion could depend on genotype, phenotype, or shared causes of them.
How Age and Setting Shape the Target
Age restrictions can be scientifically justified: a phenotype may be defined only after a particular age, or the study question may concern disease occurring in a specific life stage. But a result among older adults does not, without further assumptions, establish the same association among younger adults. Genetic effects may differ by age, phenotype definitions may operate differently across ages, and an age-restricted cohort has a different age distribution from a broader target population.
Recruitment setting also matters. A tertiary clinic may see people with more severe or unusual disease than a community service. A workplace cohort may not include people unable to work. These differences do not automatically make an association estimate invalid for the analyzed cohort. They do limit what can be inferred about people outside it, and they can affect the estimate itself if selection into the setting is related to genotype and phenotype, or to factors related to both.
The distinction is between scope and selection effects. Scope concerns where a result is intended to apply. Selection effects concern whether the process of eligibility or recruitment changes the association being estimated. A difference in age composition alone does not prove bias; it may simply define a narrower population. If genetic effects vary with age, however, changing the age composition can change a population-level association even when selection is otherwise unrelated to genotype within age groups.
Worked Examples
Worked Example: An Age Criterion Changes the Population-Level Association
Suppose a hypothetical quantitative-trait GWAS studies an allele dosage \(G\), coded 0, 1, or 2, and a trait \(Y\). Investigators intend to describe adults aged 20–80, but the available cohort includes only people younger than 50. Hypothetical summaries from two age groups are:
| Age group | Population weight | \(\operatorname{Var}(G)\) | Within-group slope of \(Y\) on \(G\) |
|---|---|---|---|
| 20–49 years | 0.50 | 0.25 | 0.20 trait units per allele |
| 50–80 years | 0.50 | 0.25 | 0.60 trait units per allele |
For this example, assume that the mean dosage is the same in both age groups, and that the within-group slopes are the stated linear-regression slopes. The equal mean dosage means there is no between-age-group covariance between \(G\) and the group-specific mean of \(Y\). With equal genotype variances, the pooled slope is the weighted average of the within-group slopes:
Thus the hypothetical slope for the full 20–80 target is 0.40 trait units per allele, whereas the younger-only cohort estimates 0.20 trait units per allele. The difference follows from the specified age-varying slopes and the target’s age composition; it does not show that either estimate is erroneous. The younger-only estimate directly describes the younger population under this model, not the stated full-age target.
This comparison assumes the summaries are population quantities and that the linear slopes are meaningful within each age group. In real data, uncertainty would also need to be reported. The example illustrates why age boundaries and the intended age range belong in the design description.
Worked Example: Eligibility Can Induce an Association
Consider a deliberately simplified hypothetical setting. Let \(G\) be a binary genetic indicator and \(U\) a binary health-related factor. In the target population, assume \(G\) and \(U\) are independent, with each having probability 0.5 of being 1. Let the binary outcome be \(Y=U\), and suppose eligibility \(E=1\) occurs only when \(G=U\).
In the target population, independence gives \(P(Y=1\mid G=1)=P(U=1)=0.5\), and likewise \(P(Y=1\mid G=0)=0.5\). The target-population risk difference is therefore:
Among eligible people, only the combinations \((G,U)=(0,0)\) and \((1,1)\) occur. Each has probability 0.25 before selection, so each has conditional probability \(0.25/(0.25+0.25)=0.5\) among eligible people. Since \(Y=U\), eligible people with \(G=0\) all have \(Y=0\), while eligible people with \(G=1\) all have \(Y=1\). The eligible-group risk difference is:
Eligibility has created an association in this constructed example, even though \(G\) and \(Y\) were unassociated in the target. The rule is intentionally extreme, but it demonstrates a general concern: conditioning on selection can associate variables that influence selection. In practice, eligibility rarely uses genotype directly; selection may nevertheless depend on health, participation, or care factors that relate to genotype and phenotype. This example is a warning to examine the selection process, not a claim that every restricted cohort is biased.
Worked Example: Auditing a Recruitment Plan
A hypothetical study states that its target is adults aged 18 or older with a newly diagnosed condition in community clinics. Its planned cohort recruits only from tertiary referral centers and includes people aged 45–75. In a screening frame of 1,200 referral records, 180 are younger than 45, 120 are older than 75, and 150 are outside the specified referral-center setting. Assume these three categories are disjoint. A further 90 otherwise qualifying records lack the required phenotype measurement.
The count meeting the age and setting criteria is:
After excluding those without the required measurement, the number eligible is \(750-90=660\). Thus \(660/1{,}200=0.55\), or 55.0% of the screening frame, meets the stated criteria. If 528 of the 660 eligible people ultimately contribute data, the analyzed fraction of the eligible group is \(528/660=0.80\), or 80.0%.
These calculations describe the screening and analysis flow; they do not show that 55.0% of all people in the target population are eligible, because the screening frame consists of referral records rather than a census of the target. More importantly, the plan’s age and setting criteria do not match its stated target. The study can directly describe the analyzed participants, and may be intended to describe adults aged 45–75 at referral centers, but broader claims about all adults with newly diagnosed disease in community clinics need additional justification. A clear design would either narrow the stated target or change recruitment and eligibility to better represent it.
A Short Justification: Why Population Composition Can Matter
For a quantitative trait, the unadjusted linear-regression slope of \(Y\) on dosage \(G\) in a population is \(\operatorname{Cov}(G,Y)/\operatorname{Var}(G)\), provided the genotype variance is positive. Let \(A\) denote an age or setting group. The law of total covariance decomposes the numerator into within-group and between-group components:
The denominator has the corresponding variance decomposition:
These identities follow by writing each variable as its deviation from its group-specific mean plus that mean, then taking expectations; the cross-products between a within-group deviation and a group-specific mean have expectation zero conditional on \(A\). Changing eligibility can change the weights of the groups and, therefore, the expectations and between-group terms in these expressions. It can change the pooled slope even if the within-group slopes stay fixed. If genotype distributions or group-specific trait means differ across groups, the between-group covariance term also matters. This is why a pooled association is not generally just an unweighted average of group-specific effects.
This justification concerns a marginal linear-regression slope. A covariate-adjusted coefficient is defined by its particular regression model and need not equal the marginal slope. Adjusting for age or setting may be appropriate for a stated estimand, but it does not by itself guarantee that an estimate from a selected cohort applies to people who were never eligible or recruited.
Common Mistakes and Practical Checks
- Equating the target with the cohort. Saying “the target is our participants” avoids specifying the population of interest. State the intended group independently, then describe how the analyzed group differs.
- Assuming a narrow age range is automatically biased. A restriction can define a legitimate, narrower target. The problem is claiming that result applies to other ages without justification, or overlooking age-related differences relevant to the association.
- Treating recruitment setting as incidental. A specialist setting may differ from community care in severity, referral, or access. Describe the setting and consider whether selection could relate to the genetic and phenotypic variables.
- Assuming adjustment repairs every eligibility problem. Covariate adjustment can address specified differences under a suitable model, but it cannot automatically recover information about groups absent from the study or remove every selection effect.
- Combining all exclusions into one count. Separate ineligible people, eligible nonparticipants, missing required measurements, and analysis-stage data exclusions. Their causes and implications may differ.
Before finalizing a GWAS cohort, ask whether the target is named precisely, whether each rule is reproducible, whether the age and setting limits match the scientific question, and which people those rules systematically omit. Report the resulting population in the interpretation of the association. This discipline keeps an estimate’s scope aligned with the evidence without claiming that a cohort represents people it did not include.
Check Your Understanding
Use the definitions and reasoning in this tutorial to answer the following questions.
- How does the target population differ from the eligible population and the analyzed population?
- A GWAS recruits only adults aged 60–80 from specialist clinics. Name two aspects of the intended inference that should be made explicit.
- In the worked age example, why did the pooled slope change when the older group was excluded?
- In the eligibility example, what changed when analysis was restricted to \(E=1\), and why did this create an association?
- Why does a screening-frame eligibility percentage not necessarily estimate the proportion eligible in the target population?
- Give one reason a cohort can be valid for a narrow target but not automatically informative about a broader population.