Nonparametric Inference on Dose-Response Curves Without the Positivity Condition

Music City Center 

Statistical methods in causal inference often assume the positivity condition that every individual has some chance of receiving any treatment level, regardless of covariates. However, this assumption could be violated in observational studies with continuous treatments. In this talk, we introduce a novel integral estimator for dose-response curve without requiring the positivity condition. Our approach estimates the derivative of the treatment effect at each observed data point and integrates it to the treatment level of interest, addressing bias stemming from violations of the positivity condition. The validity of our approach relies on a weaker assumption, satisfied by additive confounding models in spatial confounding settings. We further propose a fast and reliable numerical recipe for computing our integral estimator in practice and derive its asymptotic properties. To enable valid inference on the dose-response curve and its derivative, we use the nonparametric bootstrap and establish its consistency. The performances of our proposed estimators are validated through an application assessing the impact of air pollution (PM2.5 exposure) on cardiovascular mortality rates.

Causal inference

Dose-Response Curve

Positivity

Kernel Smoothing 

Section on Nonparametric Statistics