Robust Propagation-Integrated Inference for Observational Studies with Network Interference

In observational studies with network interference, the treatment-propensity error can affect exposure probabilities through the network, creating additional challenges for point estimation and uncertainty quantification. We propose Propagation-Integrated Inference (PIN), which constructs observable propagation directions through cross-fitting and uses the propagation directions for both point estimation and uncertainty quantification. PIN incorporates the propagation directions into a first-order estimator and then uses second-order propagation correction to adjust the remaining propensity–outcome product error. PIN further constructs a propagation-integrated standard error that simultaneously accounts for network dependence and the adjustment used in point estimation. We derive an upper bound on the approximation error of the propagation directions, prove that second-order propagation correction does not increase the upper bound of the remaining propensity–outcome product error, and establish asymptotic normality of the final PIN point estimator and conservative coverage of confidence intervals. Across three treatment-propensity shift simulations, PIN maintains 97–98% average coverage, with 5–12-point higher coverage than the state-of-the-art baseline and only 5–9% longer intervals, while reducing absolute bias by 32–78%. In a real-network study under high treatment-propensity shift, PIN achieves 97% average direct-effect coverage and reduces absolute bias by approximately 85–89% relative to the baseline.