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In the absence of a randomized experiment, a key assumption for drawingcausal inference about treatment effects is the ignorable treatment assignment.Violations of the ignorability assumption may lead to biased treatment effectestimates. Sensitivity analysis helps gauge how causal conclusions will bealtered in response to the potential magnitude of departure from theignorability assumption. However, sensitivity analysis approaches forunmeasured confounding in the context of multiple treatments and binaryoutcomes are scarce. We propose a flexible Monte Carlo sensitivity analysisapproach for causal inference in such settings. We first derive the generalform of the bias introduced by unmeasured confounding, with emphasis ontheoretical properties uniquely relevant to multiple treatments. We thenpropose methods to encode the impact of unmeasured confounding on potentialoutcomes and adjust the estimates of causal effects in which the presumedunmeasured confounding is removed. Our proposed methods embed nested multipleimputation within the Bayesian framework, which allow for seamless integrationof the uncertainty about the values of the sensitivity parameters and thesampling variability, as well as use of the Bayesian Additive Regression Treesfor modeling flexibility. Expansive simulations validate our methods and gaininsight into sensitivity analysis with multiple treatments. We use theSEER-Medicare data to demonstrate sensitivity analysis using three treatmentsfor early stage non-small cell lung cancer. The methods developed in this workare readily available in the R package SAMTx.

A flexible sensitivity analysis approach for unmeasured confounding with  multiple treatments and a binary outcome with application to SEER-Medicare  lung cancer data