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In the fight against blood doping, the interpretation of the measured levels of blood markers is based on either population-derived reference ranges or the previous test history of the individual under scrutiny. In this report, we demonstrate how an empirical hierarchical Bayesian model can be used to unify both approaches. The aim is to allow anti-doping organizations to bring reliable evidence of blood manipulation in front of a disciplinary panel. Before any tests are performed on an individual, population distributions constitute the priors of a Bayesian network that may depend on heterogeneous factors such as gender, ethnic origin and age. Inferences from the results of a new test are then drawn iteratively. A decision rule can be defined to minimize the expected costs of a decision. Secondly, the same model can be applied to evaluate the evidence of blood doping from a full sequence of individual test results, and not just from a single test result as a function of previous results. We obtained unprecedented sensitivity on a database of 1239 blood samples. Thirdly, if applied to a population of athletes, an extension of the model makes it possible to estimate the prevalence of blood doping for reasonably large populations of athletes. Knowledge of the prevalence allows the decision maker to estimate the prior odds of an athlete being doped. As a consequence, the false-positive fallacy, a form of the prosecutor's fallacy that originates from today multiplication of the number of anti-doping tests, is removed. The joined application of the Bayesian model for (1) the estimation of the prevalence at the population level and (2) the evaluation of the evidence at the individual level will allow anti-doping organizations to prosecute cases for which evidentiary values are derived from indirect blood tests.

A forensic approach to the interpretation of blood doping markers