Error Field Concordance Analysis: A New Statistical Method and Python Package to Assess Cardiac Output Concordance

Determining the concordance between different cardiac output (CO) measurement methods is important in perioperative and intensive care medicine. Two frequently used statistical methods are 4-quadrant plot and polar plot analyses, but these methods have limitations (eg, 4-quadrant plot cannot distinguish well between tight concordance and loose concordance, while polar plot analysis requires complex transformation of data and does not quantify discordance). We propose a new approach, error field concordance analysis, which uses the strengths of the 4-quadrant plot and polar plot analyses while removing their main weaknesses. This tool aims to intuitively use the Cartesian plane to provide an easily interpretable score for concordance assessment. In addition, we provide a Python package available through the Package Installer for Python (PIP) to offer easy access for applying this new method.

We propose and explain error field concordance analysis, which uses a color-coded Cartesian approach, weighs the magnitude of concordance, and allows calculation of the concordance angle. We also develop the mathematical basis for computing concordance using error field concordance analysis. We compare error field concordance analysis with 4-quadrant plot and polar plot analyses using simulated data to demonstrate strong concordance, loose concordance, total noise, and strong discordance to compare these strategies and identify potential pitfalls.

Error field concordance analysis can clearly differentiate strong concordance, loose concordance, total noise, and strong discordance without excluding data. Error field concordance analysis outperforms 4-quadrant plot analysis by detecting loss of concordance, discordance, and noise. As a result of having no exclusion zone, the data are not subject to artificial inflation of the metric in the presence of little observed change in the underlying data. We again demonstrate that the polar plot method has poor discriminant capacity compared to other methods and additionally has a critical flaw that renders it unreliable.

Error field concordance analysis intuitively displays color-coded data on a Cartesian plane and provides an easily interpretable score for both concordance and discordance.