arXiv subjects

Tomohiro Ohigashi

Publications and source records attributed to Tomohiro Ohigashi.

8 recordsLinked to original sources

arXiv2026

Efficient Prior Sensitivity and Tipping-point Analysis for Medical Research: Revisiting Sampling Importance Resampling

Bayesian methods have received increasing attention in medical research, where sensitivity analysis of prior distributions is essential. Such analyses typically require the evaluation of the posterior distribution of a parameter under multiple alternative prior settings. When the posterior distribution of the parameter of interest cannot be derived analytically, the standard approach is to re-fit the model using Markov chain Monte Carlo (MCMC) for each setting, which incurs substantial computational costs. This issue is particularly relevant in tipping-point analysis, in which the posterior must be evaluated across gradually changing degrees of borrowing. Sampling-importance resampling (SIR) provides an efficient alternative by approximating posterior samples under new settings without MCMC re-fitting. Despite its potential computational advantages, the practical performance of SIR in repeated prior-sensitivity analyses, including tipping-point analysis, and in complex Bayesian models used in medical research has not been sufficiently illustrated. In this study, we illustrate the practical utility of SIR through two case studies: one involving tipping-point analysis under external data borrowing and another involving sensitivity analysis for a Bayesian nonparametric model in meta-analysis. In both examples, SIR substantially reduced computation time and produced posterior summaries similar to those obtained by MCMC re-fitting.

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arXiv2026

Modification and extension of the Bayesian clinical trial design using external data for single-arm and hybrid-controlled trials

Limited patient availability complicates sample size determination in pediatric clinical trials. Although Bayesian methods incorporating external data offer a solution, rigorously controlling the type I error rate remains difficult. Psioda and Ibrahim (2019) proposed a simulation-based framework as a practical solution. However, although their framework was designed to relax the type I error control, this relaxation fails when the external data exhibit a large treatment effect, making it difficult to design clinical trials that incorporate external data. Furthermore, restricting the support of sampling priors can cause trial outcomes to fall outside of this support, leading to lower power. Additionally, their analytic prior formulation may induce bias, and their method is not applicable to hybrid-controlled trials involving two-group comparisons. Thus, we propose modifications to both the sampling and analytic prior specifications and extend the framework to hybrid-controlled trials. We redefine the null sampling prior as a normal distribution centered at the null boundary, ensuring a Bayesian type I error evaluation. For the analytic prior, we employ a weakly informative prior for the second component of a robust mixture prior to mitigate bias under prior-data conflict. Furthermore, we extend this methodology to hybrid-controlled trials. Simulation studies and a pediatric case study of cutaneous lupus erythematosus demonstrate that our method substantially reduces the required sample size compared with both frequentist and original Bayesian methods, while maintaining the target operating characteristics and controlling estimation bias under prior-data conflict. This framework provides a reliable and efficient approach for designing clinical trials that incorporate external information.

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arXiv2026

Posterior Quantification of Borrowing from Multiple Historical Control Data in Bayesian Dynamic Borrowing Methods: A Scoping Review

Bayesian dynamic borrowing methods incorporate historical control data into current clinical trial analyses while allowing the degree of borrowing to depend on the compatibility between historical and current data. Although many methods have been proposed, the degree of borrowing is often difficult to interpret, especially when multiple historical control sources are available. This scoping review focuses on posterior quantification of borrowing from multiple historical controls. We discuss overall borrowing summaries based on effective historical sample size, together with method-specific source-level summaries of borrowing, information contribution, or compatibility arising from power priors, unit information priors, multisource exchangeability models, Dirichlet process mixture models, and potential bias models. We distinguish posterior borrowing measures from quantities describing prior information allocation or source-specific conflict. Two case studies, one with a binary endpoint and one with a continuous endpoint, illustrate that methods with broadly similar posterior treatment effect estimates may differ in both the overall amount and source-specific pattern of borrowing. These examples show that large overall borrowing may reflect selective borrowing from compatible historical sources rather than uniform borrowing from all sources. We recommend reporting treatment effect estimates together with overall and source-specific borrowing summaries, when available, to improve transparency in posterior inference.

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arXiv2026

Efficient Bayesian Inference in the Cox Model via Rank-Ordered Likelihood

In Bayesian inference for the Cox proportional hazards model, modeling the baseline hazard function is challenging. Recently, direct Bayesian inference using the partial likelihood is considered in the framework of general Bayesian inference. In terms of posterior computation, several studies have examined sampling algorithms under the Cox model. In this study, we propose two Gibbs sampling algorithms for Bayesian inference in the Cox proportional hazards model, motivated by a rank-ordered data representation and based on the Plackett--Luce and generalized Plackett--Luce models with P'{o}lya--Gamma data augmentation, referred to as PL-Cox and GPL-Cox, respectively. The two proposed methods offer practical advantages, as they do not require correction of posterior samples, naturally handle tied event times, and are readily extensible to shared frailty models. In simulation study, we considered multiple survival model settings, including continuous and discrete survival time models, as well as scenarios with varying degrees of ties, and found that the PL-Cox model exhibited relatively stable performance. In analyses of a large real dataset, the proposed methods remained computationally feasible, and the GPL-Cox model showed more favorable computational scalability than the PL-Cox model. In analyses of real data incorporating shared frailty, both methods demonstrated good computational efficiency.

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arXiv2025

Sample size re-estimation in blinded hybrid-control design using inverse probability weighting

With the increasing availability of data from historical studies and real-world data sources, hybrid control designs that incorporate external data into the evaluation of current studies are being increasingly adopted. In these designs, it is necessary to pre-specify during the planning phase the extent to which information will be borrowed from historical control data. However, if substantial differences in baseline covariate distributions between the current and historical studies are identified at the final analysis, the amount of effective borrowing may be limited, potentially resulting in lower actual power than originally targeted. In this paper, we propose two sample size re-estimation strategies that can be applied during the course of the blinded current study. Both strategies utilize inverse probability weighting (IPW) based on the probability of assignment to either the current or historical study. When large discrepancies in baseline covariates are detected, the proposed strategies adjust the sample size upward to prevent a loss of statistical power. The performance of the proposed strategies is evaluated through simulation studies, and their practical implementation is demonstrated using a case study based on two actual randomized clinical studies.

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arXiv2024

Evaluating marginal likelihood approximations of dose-response relationship models in Bayesian benchmark dose methods for risk assessment

Benchmark dose (BMD; a dose associated with a specified change in response) is used to determine the point of departure for the acceptable daily intake of substances for humans. Multiple dose-response relationship models are considered in the BMD method. Bayesian model averaging (BMA) is commonly used, where several models are averaged based on their posterior probabilities, which are determined by calculating the marginal likelihood (ML). Several ML approximation methods are employed in standard software packages, such as BBMD, \texttt{ToxicR}, and Bayesian BMD for the BMD method, because the ML cannot be analytically calculated. Although ML values differ among approximation methods, resulting in different posterior probabilities and BMD estimates, this phenomenon is neither widely recognized nor quantitatively evaluated. In this study, we evaluated the performance of five ML approximation methods: (1) maximum likelihood estimation (MLE)-based Schwarz criterion, (2) Markov chain Monte Carlo (MCMC)-based Schwarz criterion, (3) Laplace approximation, (4) density estimation, and (5) bridge sampling through numerical examples using four real experimental datasets. Eight models and three prior distributions used in BBMD and \texttt{ToxicR} were assumed. The approximation and estimation biases of bridge sampling were the smallest regardless of the dataset or prior distributions. Both the approximation and estimation biases of MCMC-based Schwarz criterion and Laplace approximation were large for some datasets. Thus, the approximation biases of the density estimation were relatively small but were large for some datasets. In terms of the accuracy of ML approximation methods, using Bayesian BMD, in which the bridge sampling is available, is preferred.

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arXiv2024

Nonparametric Bayesian approach for dynamic borrowing of historical control data

When incorporating historical control data into the analysis of current randomized controlled trial data, it is critical to account for differences between the datasets. When the cause of the difference is an unmeasured factor and adjustment for observed covariates only is insufficient, it is desirable to use a dynamic borrowing method that reduces the impact of heterogeneous historical controls. We propose a nonparametric Bayesian approach for borrowing historical controls that are homogeneous with the current control. Additionally, to emphasize the resolution of conflicts between the historical controls and current control, we introduce a method based on the dependent Dirichlet process mixture. The proposed methods can be implemented using the same procedure, regardless of whether the outcome data comprise aggregated study-level data or individual participant data. We also develop a novel index of similarity between the historical and current control data, based on the posterior distribution of the parameter of interest. We conduct a simulation study and analyze clinical trial examples to evaluate the performance of the proposed methods compared to existing methods. The proposed method based on the dependent Dirichlet process mixture can more accurately borrow from homogeneous historical controls while reducing the impact of heterogeneous historical controls compared to the typical Dirichlet process mixture. The proposed methods outperform existing methods in scenarios with heterogeneous historical controls, in which the meta-analytic approach is ineffective.

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arXiv2024

Nonparametric Bayesian Adjustment of Unmeasured Confounders in Cox Proportional Hazards Models

In observational studies, unmeasured confounders present a crucial challenge in accurately estimating desired causal effects. To calculate the hazard ratio (HR) in Cox proportional hazard models for time-to-event outcomes, two-stage residual inclusion and limited information maximum likelihood are typically employed. However, these methods are known to entail difficulty in terms of potential bias of HR estimates and parameter identification. This study introduces a novel nonparametric Bayesian method designed to estimate an unbiased HR, addressing concerns that previous research methods have had. Our proposed method consists of two phases: 1) detecting clusters based on the likelihood of the exposure and outcome variables, 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. The proposed Bayesian estimator has good performance compared with some competitors.

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