Nonparametric Bayesian Adjustment of Unmeasured Confounders in Cox Proportional Hazards Models

Unmeasured confounders pose a major challenge in accurately estimating causal effects in observational studies. To address this issue when estimating hazard ratios (HRs) using Cox proportional hazards models, several methods, including instrumental variables (IVs) approaches, have been proposed. However, these methods often face limitations, such as weak IV problems and restrictive assumptions regarding unmeasured confounder distributions. In this study, we introduce a novel nonparametric Bayesian procedure that provides accurate HR estimates while addressing these limitations. A key assumption of our approach is that unmeasured confounders exhibit a cluster structure. Under this assumption, we integrate two remarkable Bayesian techniques, the Dirichlet process mixture (DPM) and general Bayes (GB), to simultaneously (1) detect latent clusters based on the likelihood of exposure and outcome variables and (2) estimate HRs using the likelihood constructed within each cluster. Notably, leveraging DPM, our procedure eliminates the need for IVs by identifying unmeasured confounders under an alternative condition. Additionally, GB techniques remove the need for explicit modeling of the baseline hazard function, distinguishing our procedure from traditional Bayesian approaches. Simulation experiments demonstrate that the proposed Bayesian procedure outperforms existing methods in some performance metrics. Moreover, it achieves statistical efficiency comparable to the efficient estimator while accurately identifying cluster structures. These features highlight its ability to overcome challenges associated with traditional IV approaches for time-to-event data.