title: Statistical estimation of antibody concentration using multiple dilutions.
abstract: 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.
authors.affiliation: Center for Quantitative Medicine, Duke-NUS Graduate Medical School, 8 College Road, Singapore 169857, Singapore; Department of International Health, University of Tampere, ARVO Building, FIN-33014, Finland. Electronic address: yinbun.cheung@duke-nus.edu.sg.
authors.forename: Yin Bun
authors.initials: YB
authors.lastname: Cheung
authors.affiliation: Center for Quantitative Medicine, Duke-NUS Graduate Medical School, 8 College Road, Singapore 169857, Singapore.
authors.forename: Ying
authors.initials: Y
authors.lastname: Xu
authors.affiliation: Department of Parasitology, Biomedical Primate Research Centre, Postbox 3306, 2280 GH Rijswijk, The Netherlands.
authors.forename: Edmond J
authors.initials: EJ
authors.lastname: Remarque
authors.affiliation: Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, Keppel Street, WC1E 7HT London, UK.
authors.forename: Paul
authors.initials: P
authors.lastname: Milligan
mesh_terms: D000465:Algorithms; D000818:Animals; D000906:Antibodies / Q000097:blood*; D002138:Calibration; D004797:Enzyme-Linked Immunosorbent Assay / Q000379:methods*; D008288:Malaria / Q000097:blood / Q000276:immunology; D017780:Malaria Vaccines / Q000276:immunology*; D011817:Rabbits
chemical_list: D000906:Antibodies; D017780:Malaria Vaccines
keywords: Calibration model; ELISA; Laboratory assays; Multivariate data analysis; Weighted average estimation