Four-parameter paired response curve for serial dilution assays

Newer immunoassay platforms offer improved signal-to-noise ratio but are more expensive. Thus, it is more cost efficient to perform these assays at a few selected, rather than a full series of, sample dilutions. We propose a new four-parameter paired response curve to model the relationship between assay outcomes from two sample dilutions and study likelihood-based inference. Given a fitted paired response curve, we can predict assay outcomes for de novo dilutions of samples, which enables cross-protocol comparison of immune response biomarkers even when different protocols use different sample dilutions. Numerical studies on both simulated and real data are presented.