Detection probability models for bacteria, and how to obtain them from heterogeneous spiking data. An application to Bacillus anthracis.

Efficient and correct evaluation of sampling results with respect to hypotheses about the concentration or distribution of bacteria generally requires knowledge about the performance of the detection method. To assess the sensitivity of the detection method an experiment is usually performed where the target matrix is spiked (i.e. artificially contaminated) with different concentrations of the bacteria, followed by analyses of the samples using the pre-enrichment method and the analytical detection method of interest. For safety reasons or because of economic or time limits it is not always possible to perform exactly such an experiment, with the desired number of samples. In this paper, we show how heterogeneous data from diverse sources may be combined within a single model to obtain not only estimates of detection probabilities, but also, crucially, uncertainty estimates. We indicate how such results can then be used to obtain optimal conclusions about presence of bacteria, and illustrate how strongly the sampling results speak in favour of or against contamination.