Measuring agreement in method comparison studies with heteroscedastic measurements

We propose a methodology for evaluation of agreement between two methods of measuring a continuous variable whose variability changes with magnitude. This problem routinely arises in method comparison studies that are common in health-related disciplines. Assuming replicated measurements, we first model the data using a heteroscedastic mixed-effects model, wherein a suitably defined true measurement serves as the variance covariate. Fitting this model poses some computational difficulties as the likelihood function is not available in a closed form. We deal with this issue by suggesting four estimation methods to obtain approximate maximum likelihood estimates. Two of these methods are based on numerical approximation of the likelihood, and the other two are based on approximation of the model. Next, we extend the existing agreement evaluation methodology designed for homoscedastic data to work under the proposed heteroscedastic model. This methodology can be used with any scalar measure of agreement. Simulations show that the suggested inference procedures generally work well for moderately large samples. They are illustrated by analyzing a data set of cholesterol measurements.