*! version 2.1.0 30mar2026

Title

midas bvsroc -- Bivariate summary ROC plot with confidence and prediction regions

Syntax

midas bvsroc
[, options]

Regions
cellipse confidence ellipse (line only)

pellipse prediction ellipse (line only)

cregion confidence region (shaded area)

pregion prediction region (shaded area)

Display
mean display summary operating point with Se/Sp values

data overlay individual study points

labeldata label study points with IDs

weighted size study points by bivariate weight

lgnd show legend

lgnpos(#) legend position; default is 6

Analysis
area compute and display region area indices

Appearance
level(#) confidence level; default is 95

confcolor(color) confidence region colour

predcolor(color) prediction region colour

summcolor(color) summary point colour

pointopts(string) marker options for study points

summopts(string) marker options for summary diamond

midas bvsroc is a post-estimation command. Run midas mle,
midas mh, midas hmc, or midas inla first.

pregion and pellipse are mutually exclusive.
cregion and cellipse are mutually exclusive.

Description

midas bvsroc plots the bivariate summary ROC curve in
sensitivity-by-specificity space. It displays the summary operating
point (pooled Se and Sp) together with confidence and prediction
regions derived from the bivariate normal model on the logit scale,
back-transformed to probability space.

The confidence region reflects uncertainty in the pooled estimate
(analogous to a confidence interval). The prediction region reflects
between-study heterogeneity and shows where a new study's Se-Sp pair
is expected to fall.

Options

cellipse / cregion displays the confidence region as a line
or shaded area.

pellipse / pregion displays the prediction region as a line
or shaded area.

mean displays the summary operating point with numeric Se and Sp
values and credible/confidence intervals.

data overlays individual study-specific (Se, Sp) points.

weighted sizes study points proportional to their bivariate weight
from e(studywgts).

area computes and displays five heterogeneity indices based on the
prediction and confidence region areas. See Area analysis
below for details.

Area analysis

When area is specified, midas bvsroc computes the area of the
prediction and confidence regions using the Shoelace (Surveyor's) formula
via the polyarea helper, then derives five heterogeneity indices:

Index Description

Overlap Coefficient ACR / APR. Ranges (0, 1]. Value of 1 means
identical regions (no excess heterogeneity); smaller values indicate greater
heterogeneity.

Heterogeneity Area Index APR - ACR. Absolute excess area in the
Se x Sp unit square attributable to between-study variability.

Log Area Ratio (LAR) ln(APR / ACR). Unbounded, log-scale symmetric.
Value of 0 means no excess heterogeneity; exp(LAR) gives the multiplicative
factor by which the prediction region exceeds the confidence region. This is
the recommended primary index.

Standardized Area Difference Cohen's d analog computed on the
square-root-area scale: 2(sqrt(APR) - sqrt(ACR)) / (sqrt(APR) + sqrt(ACR)).
Treats sqrt(area) as an effective "radius" for standardized comparison.

Area Ratio (APR - ACR) / APR. Legacy index, retained for backward
compatibility. Ranges [0, 1).

Interpretation thresholds (based on LAR):

LAR < 1.5 -- LOW heterogeneity. Prediction region
is less than 4.5x larger than confidence region. Summary point is reliable.

1.5 < LAR < 2.5 -- MODERATE heterogeneity. Consider
subgroup analysis or meta-regression.

LAR > 2.5 -- HIGH heterogeneity. Prediction region
is more than 12x larger. Summary point may not represent individual
settings.

Stored results

midas bvsroc stores the following in r():

Scalars

r(summ_sens) pooled sensitivity

r(summ_spec) pooled specificity

r(summ_sens_lb) sensitivity lower bound

r(summ_sens_ub) sensitivity upper bound

r(summ_spec_lb) specificity lower bound

r(summ_spec_ub) specificity upper bound

When area is specified:

r(pred_area) prediction region area (APR)

r(conf_area) confidence region area (ACR)

r(overlap_coef) overlap coefficient (ACR/APR)

r(het_area_index) heterogeneity area index (APR-ACR)

r(log_area_ratio) log area ratio ln(APR/ACR)

r(std_area_diff) standardized area difference

r(area_ratio) legacy area ratio (APR-ACR)/APR

Examples

Basic bivariate SROC with ellipses

. midas mle tp fp fn tn, id(author)

. midas bvsroc, cellipse pellipse data mean

With weighted points and region areas

. midas bvsroc, cellipse pellipse data mean weighted area

Shaded regions with legend

. midas bvsroc, cregion pregion data mean lgnd

Custom colours

. midas bvsroc, cregion pregion mean confcolor(navy%40) predcolor(orange%30)

Retrieve area indices after estimation

. midas bvsroc, cellipse pellipse mean area

. display "LAR = " r(log_area_ratio)

. display "Prediction " exp(r(log_area_ratio)) "x larger than confidence"

References

Reitsma JB, Glas AS, Rutjes AWS, Scholten RJPM, Bossuyt PM, Zwinderman AH.
2005. Bivariate analysis of sensitivity and specificity produces informative
summary measures in diagnostic reviews.
Journal of Clinical Epidemiology 58: 982-990.

Harbord RM, Deeks JJ, Egger M, Whiting P, Sterne JAC. 2007.
A unification of models for meta-analysis of diagnostic test accuracy
studies. Biostatistics 8: 239-251.

Author

Ben Adarkwa Dwamena, MD

University of Michigan / BennyBeauBooks

ben@bennybeaubooks.com