Editverse Free Calculator
Diagnostic Meta-Analysis Calculator (HSROC & Bivariate)
Pool diagnostic accuracy across studies — summary sensitivity and specificity from a bivariate random-effects model, with an HSROC curve — and copy the exact R command behind the result. A full guide follows below. Validated against R 4.3.3.
In Simple Words
A diagnostic meta-analysis combines studies that each report how well a test detects a condition, summarised in a 2×2 of true/false positives and negatives. The challenge is that sensitivity and specificity trade off against each other as the test’s threshold varies, so they cannot simply be pooled separately.
The bivariate model estimates summary sensitivity and specificity together while respecting their correlation, and the HSROC (hierarchical summary ROC) approach models the underlying accuracy and threshold across studies. Both give a defensible summary point and a summary ROC curve, which separate pooling of the two measures cannot.
When to Use Diagnostic Meta-Analysis
Use it when several studies evaluate the same diagnostic test against a reference standard and you want a pooled estimate of its accuracy. It is the diagnostic counterpart to an intervention meta-analysis and underpins evidence-based testing guidelines.
Prefer a bivariate or HSROC model over pooling sensitivity and specificity independently, which ignores their correlation and the threshold effect. Report the summary point with its confidence region and the HSROC curve, and assess between-study heterogeneity. For a single study’s test performance, use our diagnostic accuracy calculator. Unsure which model fits? Our Test Selector can help.
Expected: one row per record, TP, FP, FN, TN
Drop a CSV here or click to choose. Parsed in your browser: nothing is uploaded.
Expected: one row per record, TP, FP, FN, TN
library(mada)
dat <- read.csv(text = "TP,FP,FN,TN
{dm_csv}")
madad(dat); reitsma(dat)User guide
When to use. Pool diagnostic accuracy (sensitivity and specificity) across studies with a random-effects model.
Assumptions. Each study reports a 2×2 of test result vs reference standard.
Common mistakes. Pooling sensitivity and specificity separately ignores their correlation; a bivariate/HSROC model is preferred when feasible.
Worked example
Click Load example data above, then Run Analysis to see a fully worked result with figure, formula and interpretation for this test.
References
- Reitsma JB, et al. Bivariate analysis of sensitivity and specificity. J Clin Epidemiol. 2005;58:982-990.
Worked Examples
Example 1 — Pooling four studies
Four studies report 2×2 counts of true/false positives and negatives. A bivariate model returns a summary sensitivity near 0.84 and specificity near 0.86, with a confidence region around the summary point and an HSROC curve through the studies — a coherent overall estimate of test accuracy.
Example 2 — Why not pool separately
If you averaged sensitivity and specificity independently across studies that used different thresholds, you would ignore the trade-off between them and produce a misleadingly optimistic summary. The bivariate and HSROC models avoid this by modelling both measures jointly.
Assumptions to Check
Each study reports a full 2×2. The method needs true positives, false positives, false negatives, and true negatives per study, against a consistent reference standard.
A common target condition and reference standard. Studies must be diagnosing the same condition with comparable reference standards; mixing them produces an uninterpretable summary.
Enough studies for a hierarchical model. Bivariate and HSROC models estimate between-study variance, which needs a reasonable number of studies; with very few, simpler summaries may be all that is supportable.
Common Mistakes
Pooling sensitivity and specificity separately
Independent pooling ignores the threshold effect and their correlation, biasing the summary. Use a bivariate or HSROC model.
Combining tests with different reference standards
If the “truth” differs between studies, the pooled accuracy is not interpretable. Restrict to a consistent reference standard.
Ignoring threshold variation
Studies often use different positivity thresholds; the HSROC curve captures this, whereas a single pooled pair of values hides it.
Overlooking heterogeneity
Diagnostic meta-analyses are often highly heterogeneous. Report and explore that heterogeneity rather than quoting a summary point alone.
Frequently Asked Questions
Why is diagnostic meta-analysis different from intervention meta-analysis?
It must summarise two correlated measures — sensitivity and specificity — that trade off with the test threshold, so it uses bivariate or HSROC models rather than pooling a single effect.
What is the HSROC curve?
It is a hierarchical summary ROC curve that models test accuracy and threshold across studies, giving a curve rather than a single point.
Should I report a summary point or a curve?
Report both where possible: the summary operating point with its confidence region and the HSROC curve, which conveys performance across thresholds.
Does the result match R?
Yes. The calculator uses standard bivariate/Reitsma modelling and shows the R command (mada package) so you can reproduce the summary estimates.
Related Calculators
References
- Reitsma JB, Glas AS, Rutjes AWS, Scholten RJPM, Bossuyt PM, et al. Bivariate analysis of sensitivity and specificity produces informative summary measures in diagnostic reviews. J Clin Epidemiol. 2005;58(10):982–990. PMID 16168343.
- Reitsma JB, Moons KGM, Bossuyt PMM, Linnet K. Systematic reviews of studies quantifying the accuracy of diagnostic tests and markers. Clin Chem. 2012;58(11):1534–1545. PMID 22991421.
- Rutter CM, Gatsonis CA. A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations. Stat Med. 2001;20(19):2865–2884.
Need This Analysis Done for Your Manuscript?
Our PhD biostatisticians run diagnostic meta-analyses — bivariate and HSROC models, summary ROC curves, and heterogeneity assessment — with reproducible R output.