Robust multiple method comparison and transformation

A generalization of Passing-Bablok regression for the simultaneous comparison of multiple methods is proposed. Possible applications include assay migration studies or interlaboratory trials. The method is shown to reduce to the usual Passing--Bablok estimator if only two methods are compared. It is close in spirit to reduced major axis regression, which is, however, not robust. To obtain a robust estimator, the major axis is replaced by the (hyper-)spherical median axis. The method is applied to the comparison of SARS-CoV-2 serological tests, bilirubin in neonates, and to a clinical test using different instruments, sample preparations and reagent lots. Plots, similar to the well known Bland-Altman plots, are developed for a posteriori checks of the assumed variance structure.