Theory put into practice: probabilistic approach to propranolol as the cause of death

Post-mortem forensic toxicology aims to assist in cause-of-death investigations, especially in suspected toxicity cases. Utilizing a large toxicology database derived from routine medico-legal autopsies, we tested a probabilistic approach in assessing the contribution of a toxicological finding to the underlying cause of death. In this retrospective study, theoretical general prior odds for a poisoning death were calculated for three different groups of cases based on the laboratory referral issued by the forensic pathologist. The groups were, in descending order according to the likelihood of poisoning: (i) suspected poisoning (N = 6356), (ii) exclusion of poisoning (N = 12 641), and (iii) for background information only (N = 15 018). Propranolol was selected as a model compound with 548 propranolol-positive cases in the database. First, the detected propranolol concentrations were divided into concentration ranges. Then, a likelihood ratio (LR) for each concentration range was calculated as the probability of observing a propranolol concentration within a certain concentration range given that propranolol poisoning was the cause of death, divided by the probability of observing a propranolol concentration within the same concentration range given that propranolol poisoning was not the cause of death. To showcase the practical applicability, posterior odds for fatal propranolol poisoning were derived using the odds form of Bayes' theorem (posterior odds = prior odds × LR) for a selection of propranolol-positive cases (N = 5) and compared with the cause of death recorded on the death certificate. In our dataset, the point estimate for LR exceeded 1 for propranolol concentrations ≥1.0 mg/L. The LR proved useful in assisting in the cause-of-death determination and making the interpretive process more systematic and transparent. Despite some limitations, this study added to the evidence of the usefulness of a probabilistic approach in assessing the relevance of a toxicology finding in autopsy cases.