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Bivariate DTA / HSROC

Meta-analysis of diagnostic test accuracy: bivariate random-effects model on logit(Se) and logit(FPR = 1−Sp), with a parametric HSROC curve and summary operating point. Fitted by full maximum-likelihood bivariate random effects (Reitsma), matching R's mada::reitsma for k ≥ 4; a DerSimonian-Laird per-margin approximation is retained only as a small-sample fallback when k < 4.

Study data

Data CSV: label, TP, FP, FN, TN TP = true positives, FP = false positives, FN = false negatives, TN = true negatives. Continuity correction (+0.5 to all cells) applied only if any cell is zero (advanced-stats.md).

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Per study (Clopper-Pearson 95% CI)

Summary estimates

SROC plot

Model: bivariate random-effects on logit-Se, logit-FPR, correlation ρ — Reitsma JB et al. J Clin Epidemiol 2005;58:982–990; Rutter CM, Gatsonis CA. Stat Med 2001;20:2865–2884 (HSROC). Fitted by maximum-likelihood bivariate random effects for k ≥ 4 via the shared Reitsma engine (the IGLS start and BFGS optimisation of mvmeta; parity with mada::reitsma(method = "ml") on all six mada example datasets). The prediction region is that of mada::plot.reitsma(predict = TRUE) (between-study plus estimation uncertainty). A univariate DerSimonian-Laird per-margin approximation (Harbord RM et al. Biostatistics 2007;8:239–251) is retained only as a k < 4 fallback where Σ is not identifiable. 0.5 continuity correction when any cell is zero. HSROC curve = locus of (FPR, Se) pairs from the conditional mean linear predictor. Choosing a tool: for the Moses SROC line and a Spearman threshold-effect check (e.g. k<5 or when bivariate fails to converge), use Moses DTA-SROC →.