Addressing Unmeasured Confounders in Cox Hazard Models Using Nonparametric Bayesian Approaches

Oregon Convention Center 

In observational studies, presence of unmeasured confounders is a crucial challenge in accurately estimating desired causal effects. To calculate the hazard ratio (HR) in Cox proportional hazard models, instrumental variable methods such as Two-Stage Residual Inclusion (Martinez-Camblor et al., 2019) and Limited Information Maximum Likelihood (Orihara, 2022) are typically employed. However, these methods have several concerns, including the potential for biased HR estimates and issues with parameter identification. In this presentation, we introduce a novel nonparametric Bayesian method designed to estimate an unbiased HR, addressing concerns related to parameter identification. Our proposed method consists of two phases: 1) detecting clusters based on the likelihood of the exposure variable, and 2) estimating the hazard ratio within each cluster. Although it is implicitly assumed that unmeasured confounders affect outcomes through cluster effects, our algorithm is well-suited for such data structures. We will present simulation results to evaluate the performance of our method.

general Bayes

instrumental variable

Mendelian randomization

nonparametric Bayes

unmeasured confounders 

Biometrics Section