  Root causes of disease intuitively correspond to root vertices that increase
the likelihood of a diagnosis. This description of a root cause nevertheless
lacks the rigorous mathematical formulation needed for the development of
computer algorithms designed to automatically detect root causes from data.
Prior work defined patient-specific root causes of disease using an
interventionalist account that only climbs to the second rung of Pearl's Ladder
of Causation. In this theoretical piece, we climb to the third rung by
proposing a counterfactual definition matching clinical intuition based on
fixed factual data alone. We then show how to assign a root causal contribution
score to each variable using Shapley values from explainable artificial
intelligence. The proposed counterfactual formulation of patient-specific root
causes of disease accounts for noisy labels, adapts to disease prevalence and
admits fast computation without the need for counterfactual simulation.
