Learning the Ranking of Causal Effects with Confounded Data

Carlos Fernández-Loría, Jorge Loría

Abstract: Decision makers often want to identify the individuals for whom some intervention or treatment will be most effective in order to decide who to treat. In such cases, decision makers would ideally like to rank potential recipients of the treatment according to their individual causal effects. However, the available data may be completely inadequate to estimate causal effects accurately. We formalize a new assumption -- the rank preservation assumption (RPA) -- that defines when data are suitable to learn how to rank individuals according to their causal effects, even if the effects themselves cannot be accurately estimated. The RPA holds when there is data to estimate a scoring variable that induces the same ranking of individuals as the causal effect of interest. Some of the scoring variables we consider are confounded estimates, proxy causal effects, and non-causal quantities. We show that such scoring variables can work well for treatment assignment if the RPA is met, and potentially even better than using causal effects as scores. We also show that the RPA holds under conditions that are more general and weaker than the typical assumptions made in observational studies. Finally, we showcase how practitioners can apply and evaluate alternative scoring models (including non-causal models) to maximize the causal impact of their targeting decisions.