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.
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