Identification of in-sample positivity violations using regression trees: The PoRT algorithm

Background The positivity assumption is crucial when drawing causal inferences from observational studies, but it is often overlooked in practice. A violation of positivity occurs when the sample contains a subgroup of individuals with an extreme relative frequency of experiencing one of the levels of exposure. To correctly estimate the causal effect, we must identify such individuals. For this purpose, we suggest a regression tree-based algorithm. Development Based on a succession of regression trees, the algorithm searches for combinations of covariate levels that result in subgroups of individuals with a low (un)exposed relative frequency. Application We applied the algorithm by reanalyzing four recently published medical studies. We identified the two violations of the positivity reported by the authors. In addition, we identified ten subgroups with a suspicion of violation. Conclusions The PoRT algorithm helps to detect in-sample positivity violations in causal studies. We implemented the algorithm in the R package RISCA to facilitate its use.