Balanced and Imbalanced Diagnostic-Accuracy Tables: Single-Gate, Two-Gate, and Index-Stratified Sampling

อ่านฉบับภาษาไทย (Thai version)

Abstract

Diagnostic accuracy is shaped by the patients selected for testing and by who receives the reference standard. A balanced table is easy to read, but balance does not remove selection bias. Two-gate studies recruit people with the target condition through one route and people without it through another. This enrichment makes prevalence, positive predictive value, and negative predictive value design-driven. Sensitivity and specificity can also change when disease severity or alternative diagnoses differ from clinical practice. This change is often called a spectrum effect. Index-stratified two-phase sampling offers another route. Investigators first classify everyone by the index test, then sample for reference verification within each index-test stratum. With random sampling within each stratum and complete reference ascertainment, PPV and NPV remain directly estimable. Prevalence, sensitivity, and specificity combine index-test strata, so they require known sampling fractions, weighting, and a defined target population. Design determines interpretation; numerical balance never guarantees validity.

Three diagnostic sampling plans showing single-gate recruitment, reference-status enrichment, and index-stratified verification. — A balanced 2 by 2 table can arise from very different patient-selection mechanisms.

Balance is not a bias cure

A two-gate design recruits participants with and without the target condition through separate routes. It can efficiently fill both reference-status groups.

That efficiency does not make the groups clinically comparable. Different routes may create different disease severity, comorbidity, and alternative diagnoses. Sensitivity and specificity can then shift through spectrum effects.

Which metrics follow the design?

Reference-status enrichment fixes the case and non-case counts by design. Its observed prevalence is therefore artificial.

Positive and negative predictive values depend on that prevalence. They cannot be transported to the target population without valid reweighting. Sensitivity and specificity also need representative clinical spectra and comparable verification.

Three diagnostic sampling plans

The third row is an index-stratified teaching analogy, not a standard epidemiologic case-cohort design.
Plan	Who is sampled	Metrics available without weighting	Main threat
Single-gate population-analogue	One clinical stream	All metrics if verification is complete and the stream represents the target	Verification and referral bias
Reference-status two-gate	Separate affected and unaffected groups	No population predictive values; sensitivity and specificity require comparable spectra	Spectrum effects and artificial prevalence
Index-stratified two-phase	Sample within index-positive and index-negative strata	PPV and NPV under random within-stratum sampling and complete reference ascertainment	Prevalence, sensitivity, and specificity require sampling weights

Index-stratified two-phase sampling

First, apply the index test to the source sample. Second, sample randomly for reference verification within each index-test stratum.

With random sampling within each index-test stratum and complete reference ascertainment of sampled participants, PPV and NPV remain directly estimable. Measures that combine index-test strata - prevalence, sensitivity, and specificity - require the known sampling fraction in each stratum and suitable weights.

Change the recruitment route and verification fractions. See which sample metrics still describe the target population.

Common diagnostic-design errors

Calling two-gate enrichment unbiased

Separate recruitment can create different clinical spectra.

Fix: Describe both routes and compare severity, alternatives, and verification.
Reading predictive values from an enriched table

Reference-status enrichment sets prevalence by design.

Fix: Use a target prevalence or inverse-probability weights from known sampling fractions.
Assuming stratification preserves everything

Index-stratified sampling preserves only specific within-stratum quantities under strict conditions.

Fix: Verify random sampling, complete reference ascertainment, and population weighting.

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

Numerical balance does not cure selection bias.
Two-gate recruitment can change sensitivity and specificity through spectrum effects.
Reference-status enrichment makes prevalence and predictive values design-driven.
Index-stratified sampling preserves within-stratum predictive values only under stated conditions.
Prevalence, sensitivity, and specificity require known sampling fractions, valid weights, and a defined target population.

Related in the wiki: [[cross-sectional-analogue-designs]] [[nested-case-control-design]]