Modelling method comparison data

We explore a range of linear regression models that might be useful for either: (a) the relative calibration of two or more methods or (b) to evaluate their precisions relative to each other. Ideally, one should be able to use a single data set to carry out the jobs (a) and (b) together. Throughout this review we consider the constraints (assumptions) needed to attain identifiability of the models and the possible pitfalls to the unwary in having to introduce them. We also pay particular attention to the possible problems arising from the presence of random matrix effects (reproducible random measurement 'errors' that are characteristic of a given method when being used on a given specimen or sample, i.e. specimen specific biases or subject by method interactions). Finally, we stress the importance of a fully-informative design (using replicate measurements on each subject using at least three independent methods) and large sample sizes.