An international team of mathematicians has developed a new predictive method called the Maximum Agreement Linear Predictor (MALP). Unlike traditional techniques that focus only on minimizing average errors, MALP optimizes the Concordance Correlation Coefficient to maximize agreement between predictions and actual outcomes. Credit: Shutterstock

Lehigh researchers create new method that improves consistency between predicted and observed data.

An international team of mathematicians led by Lehigh University statistician Taeho Kim has developed a new method that could greatly enhance predictive modeling in areas such as health, biology, and the social sciences.

This new approach aims to generate predictions that align more closely with actual outcomes. The researchers call it the Maximum Agreement Linear Predictor, or MALP. The method achieves higher consistency by optimizing the Concordance Correlation Coefficient (CCC), a metric that evaluates how well pairs of data points align along the 45-degree line of a scatter plot.

This measure combines both precision, how tightly the data points cluster, and accuracy, how close they are to the reference line. Traditional techniques, such as the least-squares method, primarily focus on minimizing average error. While effective in many applications, those methods may fall short when the goal is to maximize agreement rather than simple proximity, says Kim, assistant professor of mathematics.

“Sometimes, we don’t just want our predictions to be close—we want them to have the highest agreement with the real values,” he says. “The issue is, how can we define the agreement of two objects in a scientifically meaningful way? One way we can conceptualize this is how close the points are aligned with a 45 degree line on a scatter plot between the predicted value and the actual values. So, if the scatter plot of these shows a strong alignment with this 45 degree line, then we could say there is a good level of agreement between these two.”

Why agreement differs from correlation

When people think of agreement, they often recall Pearson’s correlation coefficient, a measure introduced early in most statistics courses. Pearson’s correlation is useful for assessing the strength and direction of a linear relationship between two variables, but it does not specifically measure how well the data align with a 45-degree line. For instance, it can indicate a strong correlation even if the relationship follows a line with a slope of 50 or 75 degrees, Kim notes.

Taeho Kim. Credit: Christine Kreschollek

“In our case, we are specifically interested in alignment with a 45-degree line. For that, we use a different measure: the concordance correlation coefficient, introduced by Lin in 1989. This metric focuses specifically on how well the data align with a 45-degree line. What we’ve developed is a predictor designed to maximize the concordance correlation between predicted values and actual values.”

Testing MALP on real-world data

The team evaluated MALP using both computer simulations and real-world data, including eye scans and body fat measurements. To demonstrate its effectiveness, the researchers applied MALP to data from an ophthalmology study comparing two optical coherence tomography (OCT) devices: the older Stratus OCT and the newer Cirrus OCT. Because clinics are shifting to the Cirrus system, physicians need a reliable way to convert measurements to ensure consistency over time and across devices.

Using high-quality scans from 26 left eyes and 30 right eyes, the researchers tested how well MALP could estimate Stratus OCT readings based on Cirrus OCT data, comparing its performance with the least-squares approach. MALP produced predictions that more closely matched the actual Stratus measurements, while the least-squares method performed slightly better at reducing average error, highlighting the trade-off between accuracy and agreement.

Taeho Kim. Credit: Christine Kreschollek

The team also tested MALP on a body fat data set containing measurements from 252 adults, including weight, abdomen size and other body dimensions. Because direct methods of measuring body fat, such as underwater weighing, are accurate but costly, researchers often rely on estimates from easier measurements. Using these measurements to predict body fat percentage, MALP was compared with the standard least-squares method. The results echoed the eye scan study: MALP delivered predictions that more closely matched actual values, while the least-squares approach produced slightly smaller average errors — underscoring the balance between agreement and error reduction.

Broader applications and next steps

Kim and his colleagues found that MALP often provided predictions that better matched the actual data compared with traditional methods. However, the choice between MALP and conventional methods should depend on the goal and context of individual projects. If minimizing error is most important, the classic methods still perform well; if agreement is key, MALP is the better choice.

The findings could have major implications for improving prediction tools in various fields — from medicine and public health to economics and engineering. For data scientists and researchers working on predictive models, MALP offers a promising new tool, especially when error minimization isn’t just about being close, but about being in full agreement with the truth.

“We need to investigate further,” Kim says. “Currently, our setting is within the class of linear predictors. This set is large enough to be practically used in various fields, but it is still restricted mathematically speaking. So, we wish to extend this to the general class so that our goal is to remove the linear part and so it becomes the Maximum Agreement Predictor.”

References: “Maximum Agreement Linear Predictors” by Taeho Kim, Pierre Chausse, Matteo Bottai, Gheorghe Doros, Mihai Giurcanu, George Luta, and Edsel A. Pena, 5 September 2025, arXiv. DOI: 10.48550/arXiv.2304.04221

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