Core concepts in pharmacoepidemiology: Violations of the positivity assumption in the causal analysis of observational data: Consequences and statistical approaches.

In the causal analysis of observational data, the positivity assumption requires that all treatments of interest be observed in every patient subgroup. Violations of this assumption are indicated by nonoverlap in the data in the sense that patients with certain covariate combinations are not observed to receive a treatment of interest, which may arise from contraindications to treatment or small sample size. In this paper, we emphasize the importance and implications of this often-overlooked assumption. Further, we elaborate on the challenges nonoverlap poses to estimation and inference and discuss previously proposed methods. We distinguish between structural and practical violations and provide insight into which methods are appropriate for each. To demonstrate alternative approaches and relevant considerations (including how overlap is defined and the target population to which results may be generalized) when addressing positivity violations, we employ an electronic health record-derived data set to assess the effects of metformin on colon cancer recurrence among diabetic patients.