Dilution assay statistics
Myers, L., McQuay, L., & Hollinger, F. B. (1994). Dilution assay statistics. Journal of Clinical Microbiology, 32(3), 732-739.
A parametric method of statistical analysis for dilution assays is developed in detail from first principles of probability and statistics. The method is based on a simple product binomial model for the experiment and produces an estimate for the concentration of target entities, a confidence interval for this concentration, and an indicator of the quality of the assay called the p value for goodness of fit. The procedure is illustrated with data from a virologic quantitative micrococulture assay used to quantify free human immunodeficiency virus in clinical trials. The merits of the procedure versus those of nonparametric methods of estimating the dilution inducing a 50% response rate are discussed. Advantages of the proposed approach include plausibility of the underlying assumptions, ability to assess plausibility of specific experimental outcomes through their likelihood, and plausibility of confidence intervals