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Conditional Method Agreement Trees (COAT)

Subject Area Medical Informatics and Medical Bioinformatics
Cardiology, Angiology
Term from 2021 to 2025
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 447467169
 
Final Report Year 2025

Final Report Abstract

Method comparison studies are relevant in all scientific fields when the agreement of continuously scaled measurements of two or more methods is investigated. In medicine, taking measurements can be time-consuming, expensive, invasive or stressful for patients. Therefore, methods are constantly developed and improved. However, agreement between a new method and a standard method needs to be shown in order to replace the latter. A well-established analysis method is the Bland-Altman plot, which illustrates the differences against the mean values of paired measurements made by two methods. Here, two quantities of interest are the mean difference, referred to as ‘bias’, and the standard deviation of the differences, which is used to determine the ‘Limits of Agreement’ (LoA). The bias is a measure of overall deviation but, as a summary measure, has limited interpretability concerning the expected agreement of single measurements. Therefore, Bland and Altman proposed the LoA, that is a prediction interval in which about 95% of individual differences are expected to lie. We assume that the underlying assumption of a Bland-Altman analysis, that the agreement of methods is identically distributed for all observational units or subjects, may not be valid in any case. The basic idea is that measurements can be affected by internal and external factors, such as the subjects’ characteristics and measurement settings, with direct implications on the agreement. Previous studies used heuristic approaches to address this issue, for example through post-hoc fitting of additional regression models and subgroup analyses. An early example is the regression of mean values on differences as originally suggested by Bland and Altman. We introduce a unifying methodological framework and analysis approach for conditional method agreement, that is for covariate-dependent method agreement. All relevant cases of single measurements and paired or unpaired multiple measurements per subject or observational unit are covered. The machine learning method of recursive partitioning is used to simultaneously explore relations between covariates and agreement and to define corresponding subgroups with heterogeneous agreement in terms of bias and/or LoA, taking advantage of the fact that a Bland-Altman analysis can be parameterized accordingly. We propose three modelling approaches, based on conditional inference trees with an appropriate transformation of the outcome, distributional regression trees, and model-based trees. Preceding data processing is necessary in case of repeated measurements to model subject-specific biases and variance components. The ability of the novel approach to control the type-I error, the power to detect given subgroups, and the ability to accurately define these subgroups is shown in simulation studies. We also demonstrate the practical relevance through applications to real data examples of accelerometer measurements and cardiac output measurements made by different devices. In addition, we propose a two-sample test suitable for exploratory or confirmatory hypothesis testing of differences in agreement between two groups. To our knowledge, there is no comparable method of analysis available today. The research findings are published open access and an implementation of the novel modelling approach is publicly available through the R package “coat” on the Comprehensive R Archive Network (CRAN).

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