Comparison of non parallel immunoassay curves resulting from mixtures of competing antigens

Relative potency is a measure that has been used for many years to summarize the comparison of dose-response curves in parallel line bioassays. When response curves for two preparations are not parallel the traditional definition of relative potency no longer applies. We review the concept of relative potency and show that, in some situations, it can be given meaning for non-parallel curves as the ratio of biological activity in full strength assay preparations. Under an assumption that non-parallel curves result from the competition of mixtures of antigens for receptor binding sites, estimation of relative potency for non-parallel curves can be accomplished. We show that estimation of models for both parallel curve and response attenuation situations may be accomplished within the framework of generalized linear models. This estimation depends on the ability to deal with non-linear parameters appearing in the link function, and an iterative algorithm depending on direct parameter updates is outlined. The topics discussed are illustrated with the analysis of data from two immunoassays conducted with veterinary vaccines. The models developed here depend in an essential way on the assumption of response attenuation by competing antigens. Our methods may not be appropriate for non-parallel curves caused by other phenomena.