Methods for the analysis and design of limiting dilution assays

Limiting dilution assays are a useful device for extracting quantitative information when the underlying analytical tool can only provide information on presence or absence. Analysis by maximum likelihood is advocated and some alternative methods are discussed. Several interval estimators, including one based directly on the log-likelihood are presented. Methods for determining designs which permit efficient estimation are considered and some of their weaknesses are mentioned. Opportunities for further methodological development are outlined.