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When drawing causal inferences about the effects of multiple treatments onclustered survival outcomes using observational data, we need to addressimplications of the multilevel data structure, multiple treatments, censoringand unmeasured confounding for causal analyses. Few off-the-shelf causalinference tools are available to simultaneously tackle these issues. We developa flexible random-intercept accelerated failure time model, in which we useBayesian additive regression trees to capture arbitrarily complex relationshipsbetween censored survival times and pre-treatment covariates and use the randomintercepts to capture cluster-specific main effects. We develop an efficientMarkov chain Monte Carlo algorithm to draw posterior inferences about thepopulation survival effects of multiple treatments and examine the variabilityin cluster-level effects. We further propose an interpretable sensitivityanalysis approach to evaluate the sensitivity of drawn causal inferences abouttreatment effect to the potential magnitude of departure from the causalassumption of no unmeasured confounding. Expansive simulations empiricallyvalidate and demonstrate good practical operating characteristics of ourproposed methods. Applying the proposed methods to a dataset on older high-risklocalized prostate cancer patients drawn from the National Cancer Database, weevaluate the comparative effects of three treatment approaches on patientsurvival, and assess the ramifications of potential unmeasured confounding. Themethods developed in this work are readily available in the $\textsf{R}$package $\textsf{riAFTBART}$.

A flexible approach for causal inference with multiple treatments and clustered survival outcomes