Bayesian Measures of the Minimum Detectable Concentration of an Immunoassay

The minimum detectable concentration (MDC) is one of the most important properties of an assay. It is a statement about the smallest physical quantity an assay can reliably measure, and is used in assay design and quality control assessments. A plethora of measures of the MDC have been reported in a widely scattered literature. Many of these were developed at a time when accuracy and relevance had to be sacrificed for computational feasibility. This paper identifies limitations of existing measures and demonstrates how Bayesian inference may be used to overcome these limitations. Several new measures of the MDC are developed. These are conceptually simpler than existing measures, and are free of analytical approximations. The recent advances in Bayesian computation make them efficient to evaluate. A procedure developed in this paper measures the difference in the quality of two assays and shows that the new Bayesian measures perform better than existing measures.