The + Files: Disentangling Different Aspects Of Positivity

Positivity is a crucial identification assumption concerning a possible zero density/probability. It is central to most epidemiological studies pursuing causal goals, yet discourse around it is limited and sometimes contradictory. Using the causal roadmap, we identify two issues often considered positivity issues, neither of which coincides with the original density/probability-based definition: the target issue, which stems from logical problems with the scientific question, and the estimation issue, which is often referred to as sparsity or practical positivity violation. Both are related to positivity, but treating them as purely density/probability-driven phenomena often leads to suboptimal handling. We also question whether true positivity violations at the identification stage can even meaningfully arise in real-world settings. We propose a workflow enabling researchers to identify and address all issues discussed under the positivity umbrella adequately. A fictitious study serves as a running example, developing the central insights in an accessible, step-by-step manner.