Individual causation with biased data

The field of causal statistical inference subsumes two quite distinct general activities: inference about “Effects of Causes" (EoC), and inference about “Causes of Effects" (CoE). While related, these are very different enterprises. Indeed, even if we have full knowledge of the probabilities of outcomes under different exposures, that doesn’t directly address the question of whether a specific exposure caused a particular outcome in an individual case. For this we require the “probability of causation" (PC), but PC is typically not identifiable based solely on the EoC probabilities. Nevertheless, these probabilities do enable us to establish bounds on PC, and these can be refined with additional information about the causal process, such as data on covariates or mediators. In such scenarios, it becomes apparent that ignoring or lacking relevant information about the causal process can introduce bias into our analyses. In this article we compare results obtained with and without proper consideration of the causal process, so as to better understand the implications of such oversights.