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In observational studies, unmeasured confounders present a crucial challengein accurately estimating desired causal effects. To calculate the hazard ratio(HR) in Cox proportional hazard models for time-to-event outcomes, two-stageresidual inclusion and limited information maximum likelihood are typicallyemployed. However, these methods are known to entail difficulty in terms ofpotential bias of HR estimates and parameter identification. This studyintroduces a novel nonparametric Bayesian method designed to estimate anunbiased HR, addressing concerns that previous research methods have had. Ourproposed method consists of two phases: 1) detecting clusters based on thelikelihood of the exposure and outcome variables, and 2) estimating the hazardratio within each cluster. Although it is implicitly assumed that unmeasuredconfounders affect outcomes through cluster effects, our algorithm iswell-suited for such data structures. The proposed Bayesian estimator has goodperformance compared with some competitors.

Nonparametric Bayesian Adjustment of Unmeasured Confounders in Cox Proportional Hazards Models