Combining and Comparing Multiple Serial Dilution Assays for Inferring Particle Concentration

• Activity Number: 124
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Jarrett Jay Barber*+
• Companies: Arizona State University
• Keywords: card test ; complement fixation (CF) test ; complete spatial randomness ; method comparison ; homogeneous Poisson process ; latent variables

Abstract

In 1922, R. Fisher used a serial dilution assay to estimate the number of protozoa in a volume of soil---one of the first applications of maximum likelihood. In 1950, W. Cochran reintroduced essentially the same approach for estimating the "most probable number" of organisms in a liquid. More recent studies adopt a similar approach to estimating particle concentration. A serial dilution assay is an indirect method of measuring concentration, or count, of particles in solution whereby only the presence or absence of particles is measured for each dilution in a series of increasingly dilute solutions of the substance of interest. Direct measurement may be impossible or inconvenient. Common assumptions lead to the 'one-hit Poisson' model; it is assumed that single particles are detected---perfect detection. Estimation of particle 'intensity' follows straightforwardly. We discuss a model extension wherein we combine data from multiple types of serial dilution assays to compare the assays via their, now, estimated concentration detection thresholds. We illustrate with synthetic data and data on the bacterial disease, brucellosis, infecting elk in the Greater Yellowstone Ecosystem (GYE).