Cross-Sectional Analogue Designs: Population-Analogue, Cohort-Analogue & Case-Control-Analogue Sampling for Rare Exposure vs Rare Outcome
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Abstract
Cross-sectional studies observe predictors and outcomes within one measurement window, but sampling gates change which quantities remain direct. This article uses three analogues as a teaching framework, not a standard design taxonomy. A population-analogue sample has no deliberate gate on X or Y. A cohort-analogue sample enriches rare X. When selection is random within X strata, Y given X remains direct - including risk only if Y is an incident event over a defined interval - while raw X prevalence changes. A case-control-analogue sample enriches rare Y. Random sampling within Y strata preserves X given Y, but raw Y prevalence and predictive values are design-driven. Population-standardized marginal quantities require known sampling fractions, valid weights, and clear target-population assumptions. The practical rule is simple: identify the gate, say which conditional distribution the sample preserves, define any risk interval, and state which denominator each sampled group represents before calculating a measure.
Start here: what is rare?
The three analogues are a teaching map. They are not standard named designs in methods literature.
When neither exposure nor outcome is deliberately enriched, call the sample population-analogue. When exposure is rare, sampling more exposed people is cohort-analogue. When outcome is rare, sampling more affected people is case-control-analogue.
The gate changes the denominator
A sampling gate is the eligibility and selection rule that determines who can enter the analytic sample. The sampling fraction is the proportion selected from each eligible group. The estimand is the population quantity the study aims to learn; the estimator is the rule applied to sampled data to estimate it. Transportability asks whether that estimate validly applies to the stated target population.
Deliberate enrichment changes the sample margins. Therefore, naive prevalence and other marginal measures belong to the sample. They reach the target population only after valid weighting and clear target-population assumptions.
Three analogue sampling plans
| Teaching label | Sampling gate | Efficiency target | What needs weighting |
|---|---|---|---|
| Population-analogue | No deliberate gate on X or Y | Broad representation | Use design weights if selection probabilities still differ |
| Cohort-analogue | Enrich rare X | More exposed observations | Marginal exposure prevalence and population totals |
| Case-control-analogue | Enrich rare Y | More affected observations | Outcome prevalence and predictive values; risk only for a defined cumulative-incidence outcome |
What can survive selection?
A conditional measure can survive when selection is random inside every conditioning stratum. Complete and comparable measurement must also hold within those strata.
This is a property of the selection mechanism. The analogue label alone proves nothing. Write the sampling fractions and target-population assumptions beside the 2 by 2 table.
Common interpretation errors
-
Treating the analogues as official taxonomy
The labels organize a lesson. Methods papers may use different names.
Fix: Describe the actual sampling rule after using the teaching label.
-
Reporting the enriched prevalence
The observed prevalence reflects the designed sample margins.
Fix: Use known sampling fractions and suitable weights for the stated target population.
-
Assuming efficiency removes bias
More rare observations improve precision only under a valid selection and analysis plan.
Fix: State selection probabilities, measurement rules, and target-population assumptions.
References
- Rutjes AWS, Reitsma JB, Vandenbroucke JP, Glas AS, Bossuyt PMM. Case-control and two-gate designs in diagnostic accuracy studies. Clinical Chemistry 2005;51:1335 to 1341. https://doi.org/10.1373/clinchem.2005.048595
- Cohen JF, Korevaar DA, Altman DG, et al. STARD 2015 guidelines for reporting diagnostic accuracy studies: explanation and elaboration. BMJ Open 2016;6:e012799. https://doi.org/10.1136/bmjopen-2016-012799
- Kohn MA. Studies of diagnostic test accuracy: partial verification bias and test result-based sampling. Journal of Clinical Epidemiology 2022;145:179 to 182. https://doi.org/10.1016/j.jclinepi.2022.01.022
Key takeaways
- Use the three analogues as a teaching framework, then describe the actual sampling rule.
- Ask whether exposure, outcome, or neither was deliberately enriched.
- Enrichment improves efficiency but changes the sample margins.
- Naive prevalence and other marginal measures need known sampling fractions and valid weighting.
- State the target population and the denominator represented by every sampled group.
Related in the wiki: [[balanced-vs-imbalanced-diagnostic]] [[nested-case-control-design]]