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The Stata Journal
Volume 16 Number 2: pp. 316-330

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Implementing weighted-average estimation of substance concentration using multiple dilutions

Ying Xu
Center for Quantitative Medicine
Duke–NUS Graduate Medical School
Singapore, Singapore
Paul Milligan
Department of Infectious Disease Epidemiology
London School of Hygiene and Tropical Medicine
London, UK
Edmond J. Remarque
Department of Parasitology
Biomedical Primate Research Centre
Rijswijk, The Netherlands
Yin Bun Cheung
Center for Quantitative Medicine
Duke–NUS Graduate Medical School
Singapore, Singapore
and Department for International Health
University of Tampere
Tampere, Finland
Abstract.  In medicine and chemistry, immunoassays are often used to measure substance concentration. These tests use an S-shaped standard curve to map the observed optical responses to the underlying concentration. The enzyme-linked immunosorbent assay is one such test that is commonly used to measure antibody concentration in vaccine and infectious disease research. The enzyme-linked immunosorbent assay and other immunoassays usually involve a series of doubling or tripling dilutions of the test samples so that some of the diluted samples fall within the near-linear range in the center of the standard curve. The dilution that falls within or is nearest to the center of the near-linear range may then be selected for statistical analysis. This common practice of using one dilution does not fully use the information from multiple dilutions and reduces accuracy. We describe a recently proposed weighted-average estimation approach for analyzing multiple-dilution data (Cheung et al. 2015, Journal of Immunological Methods 417: 115–123), and we present the new wavemid command, which carries out the approach. We also present the new command midreshape, which processes raw data in text format exported from some microplate readers into analyzable data format. We use data from an experimental study of malaria vaccine candidates to demonstrate use of the two commands.
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