A flexible sensitivity analysis approach for unmeasured confounding with multiple treatments and a binary outcome

In the absence of a randomized experiment, a key assumption for drawing causal inference about treatment effects is the ignorable treatment assignment. Violations of the ignorability assumption may lead to biased treatment effect estimates. Sensitivity analysis helps gauge how causal conclusions will be altered in response to different magnitude of departure from the ignorability assumption. However, sensitivity analysis approaches for causal inference with multiple treatments and binary outcomes are scarce. We propose a flexible Monte Carlo sensitivity analysis approach for the complex multiple treatment settings with binary outcomes. We first derive the general bias form introduced by unmeasured confounding (UMC), with emphasis on theoretical properties uniquely relevant to multiple treatments. We then propose methods to encode the impact of UMC on potential outcomes and adjust the estimates of causal effects in which the presumed UMC is removed. Our proposed methods embed nested multiple imputation within the Bayesian framework, which allow for seamless integration of the uncertainty about the sensitivity parameters and sampling variability, as well as use of reputable Bayesian machine learning techniques for modeling flexibility. Expansive simulations validate our methods and gain insight into sensitivity analysis with multiple treatments, and we use the SEER-Medicare data to demonstrate sensitivity analysis using three treatments for early stage non-small cell lung cancer. The methods developed in this work are readily available in the R package SAMTx.