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Propensity score analysis
In Orihara and Hamada (2021), we propose a novel method for selecting the optimal number of strata for subclassification on the propensity score. The proposed method can estimate the optimal number of strata in the sense that it minimizes the mean squared error (MSE) of the estimated causal effect. The proposed method can estimate the "true" optimal number of strata, where the true optimal strata are detected using the true MSE for each dataset, which cannot be directly estimated from the data.
The manuscript is cited in the "Handbook of matching and weighting adjustments for causal inference" (Zubizarreta et al., 2023).
In Orihara and Momozaki (2024), we propose a novel Bayesian-based subclassification estimator. In the proposed model, we account for uncertainty arising from the estimation of the propensity score, subclassification, and the causal effect of interest. In our framework, it is not necessary to determine the exact number of strata, which distinguishes it from previous methods; this is achieved by incorporating subclassification uncertainty. In the proposed method, the subclassification estimator can be viewed as Bayesian model averaging over the number of subclasses. This approach enables accurate estimation of the causal effect, and it is expected that credible intervals can be constructed appropriately.
In Orihara et al. (2025), we propose a novel Bayesian doubly robust (DR) estimator using entropic tilting techniques. While several previous studies have addressed Bayesian DR inference, our manuscript presents a new approach in which the posterior distribution is explicitly characterized. Because our method couples the posterior distributions of the propensity score and outcome models, it allows for flexible choices of likelihood functions and prior distributions. Additionally, we believe that our method can effectively address the so-called feedback problem. For these reasons, we consider our Bayesian DR approach to be an important contribution to the field of Bayesian causal inference.
Unmeasured confounder problems
In Orihara et al. (2024), we propose a valid instrumental variable (IV) selection method using auxiliary variables such as negative control outcomes. While selecting these variables, we can construct a semiparametric efficient estimator for the causal effects of interest. Essentially, it is important to capture the variability of unmeasured confounders through the auxiliary variable. The proposed procedure can robustly estimate causal effects using a smaller number of IVs compared to previous methods, which may fail in certain scenarios.
In Orihara et al. (2024), we propose a novel IV method applicable to Cox proportional hazard models (CPHM). Unlike previous methods, our proposed method can be applied to various types of exposure and instrumental variables. However, the proposed method requires the direct specification of the unmeasured confounder distribution. To overcome this problem, we introduce a novel nonparametric Bayesian method as a direct extension of the previous method (Orihara et al., 2024). This new Bayesian method also accounts for unmeasured confounder distributions that can vary between subjects, allowing for cluster construction without any prior information on the number of clusters. The proposed Bayesian method performs well compared to the most efficient estimation methods.
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