Toxic substances in blood: an analysis of current recommendations under a Bayesian (decision) approach

This paper extends existing discussion in literature on probabilistic inference and decision making with respect to continuous hypotheses, that are prevalent in forensic toxicology. As a main aim, this research investigates the properties of a widely followed approach for quantifying the level of toxic substances in blood samples, and to compare this procedure with a Bayesian probabilistic approach. As an example, attention is confined to the presence of toxic substances, such as THC, in blood from car drivers. In this context, the interpretation of results from laboratory analyses needs to take into account legal requirements for establishing the `presence' of target substances in blood. In a first part, the performance of the proposed Bayesian model for the estimation of an unknown parameter (here, the amount of a toxic substance) is illustrated and compared with the currently used method. The model is then used in a second part to approach -in a rational way- the decision component of the problem, that is judicial questions of the kind `Is the quantity of THC measured in the blood over the legal threshold of 1.5 ug/l?'. This is pointed out through a practical example.