Tree models for assessing covariate-dependent method agreement

Method comparison studies explore the agreement of measurements made by two or more methods. Commonly, agreement is evaluated by the well-established Bland-Altman analysis. However, the underlying assumption is that differences between measurements are identically distributed for all observational units and in all application settings. We introduce the concept of conditional method agreement and propose a respective modeling approach to alleviate this constraint. Therefore, the Bland-Altman analysis is embedded in the framework of recursive partitioning to explicitly define subgroups with heterogeneous agreement in dependence of covariates in an exploratory analysis. Three different modeling approaches, conditional inference trees with an appropriate transformation of the modeled differences (CTreeTrafo), distributional regression trees (DistTree), and model-based trees (MOB) are considered. The performance of these models is evaluated in terms of type-I error probability and power in several simulation studies. Further, the adjusted rand index (ARI) is used to quantify the models' ability to uncover given subgroups. An application example to real data of accelerometer device measurements is used to demonstrate the applicability. Additionally, a two-sample Bland-Altman test is proposed for exploratory or confirmatory hypothesis testing of differences in agreement between subgroups. Results indicate that all models were able to detect given subgroups with high accuracy as the sample size increased. Relevant covariates that may affect agreement could be detected in the application to accelerometer data. We conclude that conditional method agreement trees (COAT) enable the exploratory analysis of method agreement in dependence of covariates and the respective exploratory or confirmatory hypothesis testing of group differences. It is made publicly available through the R package coat.