Assays for recombinant proteins: a problem in non-linear calibration

Quantification of protein levels in biological matrices such as serum or plasma frequently relies on the techniques of immunoassay or bioassay. The relevant statistical problem is that of non-linear calibration, where one estimates analyte concentration in an unknown sample from a calibration curve fit to known standard concentrations. This paper discusses a general framework for calibration curve fit to known standard concentrations. This paper discusses a general framework for calibration inference, that of the non-linear mixed effects model. Within this framework, we consider two issues in depth: accurate characterization of intra-assay variation, and the use of empirical Bayes methods in calibration. We show that proper characterization of intra-assay variability requires pooling of information across several assay runs. Simulation work indicates that use of empirical Bayes methods may afford considerable gain in efficiency; one must weigh this gain against practical considerations in the implementation of Bayesian techniques. We illustrate the methods discussed using a cell-based bioassay for the recombinant hormone relaxin.