Statistical estimation of antibody concentration using multiple dilutions

In medicine and chemistry, measurement of concentrations usually involves calibration that maps the observed responses to the underlying concentration using inversion of a standard curve. The Enzyme-linked ImmunoSorbent Assay (ELISA) is one example of such methods that is commonly used to measure antibody concentration. A problem in this and similar type of technology is that an accurate measurement is obtainable only if the observations fall within the optimal, near-linear range of the standard curve. It is common to conduct a series of doubling or tripling dilutions of the samples, so that at least some of the diluted samples are within the optimal range. A single dilution may then be selected for statistical analysis. This common practice does not fully utilize the data from multiple dilutions and reduces accuracy. We consider two weighted average estimators for fully utilizing the information from multiple dilutions. The first uses weights inversely proportional to the variances of the dilution-specific calibrated values; the second is a simplified form of the first. Simulation results demonstrated the superiority of this weighted estimation approach over the conventional approach of analyzing a single selected dilution. We apply the methods to an experimental study of malaria vaccine candidates.