A Simple Diagnostic for the Positivity Assumption for Continuous Exposures

The positivity or experimental treatment assignment assumption is a fundamental requirement in causal analyses, invoked to ensure that identifiability holds without extrapolating beyond what the observed data can reveal. Positivity is well understood in the context of binary and categorical treatments, and has been thoroughly discussed-from how the assumption can be assessed to approaches that may be used when the assumption is suspected not to hold. Positivity extends to the context of continuous exposures, such as doses, however it has been given very little formal consideration. In this manuscript, we propose a method for assessing whether the positivity assumption is violated in a given dataset, relying on a principled concept in regression analysis. We demonstrate the diagnostic tool in various simulated settings, as well as in an application involving warfarin dosing.