A segmented measurement error model for modeling and analysis of method comparison data

Method comparison studies are concerned with estimating relationship between two clinical measurement methods. The methods often exhibit a structural change in the relationship over the measurement range. Ignoring this change would lead to an inaccurate estimate of the relationship. Motivated by a study of two digoxin assays where such a change occurs, this article develops a statistical methodology for appropriately analyzing such studies. Specifically, it proposes a segmented extension of the classical measurement error model to allow a piecewise linear relationship between the methods. The changepoint at which the transition takes place is treated as an unknown parameter in the model. An expectation-maximization-type algorithm is developed to fit the model and appropriate extensions of the existing measures are proposed for segment-specific evaluation of similarity and agreement. Bootstrapping and large-sample theory of maximum likelihood estimators are employed to perform the relevant inferences. The proposed methodology is evaluated by simulation and is illustrated by analyzing the digoxin data.