Bayesian analysis of an international ELISA comparability study

Immunoassays are biochemical tests applied to measure even very small amounts of substance using the highly specific binding between an antibody and its antigen. They have a wide range of applications. The measurement however, might be associated with substantial uncertainty; this can have significant consequences for any diagnosis, or clinical decision. An international comparability study was thus performed to assess the sources of uncertainty involved in the estimation of a protein cytokine concentration using a fluorescent ELISA.

In contrast to the original publication for this international comparability study, we reanalyse the data using Bayesian inference. This provides a statistically coherent approach to estimate ELISA concentrations and their associated uncertainties.

The Bayesian uncertainties of individual ELISAs and laboratory estimates are considerably larger than previously reported uncertainties. The average concentrations estimated here differ from the ones estimated by each study participant. In general, this leads to different conclusions about the study. In particular, the inter- and intra-laboratory consistency is increased, and repeatability problems occur for fewer laboratories.

Decisions which are based on plausible ranges of measurements (such as credible intervals), are generally superior to those solely based on point estimates (such as the mean). Reliable uncertainties are thus vital, and not only in metrology. In this paper, a general method is developed to derive concentration estimates and valid uncertainties for ELISAs. Guidance on applying this Bayesian method is provided and the importance of reliable uncertainties associated with ELISAs is underlined. The applicability and virtues of the presented method are demonstrated in the context of an international comparability study.