Analyzing bioassay data using Bayesian methods -- A primer

The classical statistics approach used in health physics for the interpretation of measurements is deficient in that it does not take into account needle in a haystack effects, that is, correct identification of events that are rare in a population. This is often the case in health physics measurements, and the false positive fraction (the fraction of results measuring positive that are actually zero) is often very large using the prescriptions of classical statistics. Bayesian statistics provides a methodology to minimize the number of incorrect decisions (wrong calls): false positives and false negatives. The authors present the basic method and a heuristic discussion. Examples are given using numerically generated and real bioassay data for tritium. Various analytical models are used to fit the prior probability distribution in order to test the sensitivity to choice of model. Parametric studies show that for typical situations involving rare events the normalized Bayesian decision level kα = Lc/σ0, where σ0 is the measurement uncertainty for zero true amount, is in the range of 3 to 5 depending on the true positive rate. Four times σ0 rather than approximately two times σ0, as in classical statistics, would seem a better choice for the decision level in these situations