  Complex diseases are caused by a multitude of factors that may differ between
patients. As a result, hypothesis tests comparing all patients to all healthy
controls can detect many significant variables with inconsequential effect
sizes. A few highly predictive root causes may nevertheless generate disease
within each patient. In this paper, we define patient-specific root causes as
variables subject to exogenous "shocks" which go on to perturb an otherwise
healthy system and induce disease. In other words, the variables are associated
with the exogenous errors of a structural equation model (SEM), and these
errors predict a downstream diagnostic label. We quantify predictivity using
sample-specific Shapley values. This derivation allows us to develop a fast
algorithm called Root Causal Inference for identifying patient-specific root
causes by extracting the error terms of a linear SEM and then computing the
Shapley value associated with each error. Experiments highlight considerable
improvements in accuracy because the method uncovers root causes that may have
large effect sizes at the individual level but clinically insignificant effect
sizes at the group level. An R implementation is available at
github.com/ericstrobl/RCI.
