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Signal Acquisition, Score Interpretation, and Economics of a Non-Invasive Point-of-Care Test for Coronary Artery Disease

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System of Linear Equations to Derive Unreported Test Accuracy Counts for Meta-Analysis.

Xuanqian Xie¹, Myra Wang¹, Jesmin Antony¹

¹Acute and Hospital-Based Care, Ontario Health, Toronto, Ontario, Canada.

Statistics in Medicine

|December 3, 2025

Summary

This study presents methods to estimate missing diagnostic test accuracy counts (true positives, false negatives, false positives, true negatives) from published research. It enables more comprehensive meta-analyses by solving linear equations and handling data imperfections.

Keywords:

2 × 2 table meta‐analysis system of linear equations test accuracy

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Area of Science:

Biostatistics
Medical Informatics
Diagnostic Test Evaluation

Background:

Meta-analyses of diagnostic test accuracy studies often lack complete 2x2 contingency tables (TP, FN, FP, TN).
Incomplete data limits the comprehensive assessment of screening and diagnostic accuracy in meta-analyses.

Purpose of the Study:

To develop and demonstrate methods for estimating unreported counts (TP, FN, FP, TN) in test accuracy studies.
To enhance the completeness of data for meta-analyses by utilizing reported parameters like sensitivity and specificity.

Main Methods:

Formulating systems of linear equations based on reported test accuracy parameters (sensitivity, specificity).
Applying matrix methods to solve for unknown TP, FN, FP, and TN counts.
Addressing rounding errors and exploring bound solutions for underdetermined systems.

Main Results:

Demonstrated mathematical approaches to derive missing counts from available data.
Provided practical guidance and code (Excel, SAS, R) for implementing these estimation methods.
Simulation studies validated the performance of the proposed techniques.

Conclusions:

The proposed methods enable the recovery of essential data for more robust meta-analyses of diagnostic test accuracy.
Researchers can improve the completeness of their meta-analytic data by applying these techniques to published studies.