Bayesian Optimal INterval (BOIN) Design for Single-Agent and Drug- Combination Phase I Clinical Trials

The Bayesian optimal interval (BOIN) design is a novel phase I clinical trial design for finding the maximum tolerated dose (MTD). It can be used to design both single-agent and drug-combination trials. The BOIN design is motivated by the top priority and concern of clinicians when testing a new drug, which is to effectively treat patients and minimize the chance of exposing them to subtherapeutic or overly toxic doses. The prominent advantage of the BOIN design is that it achieves simplicity and superior performance at the same time. The BOIN design is algorithm-based and can be implemented in a simple way similar to the traditional 3+3 design. The BOIN design yields an average performance that is comparable to that of the continual reassessment method (CRM, one of the best model-based designs) in terms of selecting the MTD, but has a substantially lower risk of assigning patients to subtherapeutic or overly toxic doses. For tutorial, please check Yan et al. (2020) .

Tidy Methods for Bayesian Treatment Effect Models

Functions for extracting tidy data from Bayesian treatment effect models, in particular BART, but extensions are possible. Functionality includes extracting tidy posterior summaries as in 'tidybayes' < https://github.com/mjskay/tidybayes>, estimating (average) treatment effects, common support calculations, and plotting useful summaries of these.

Estimate Causal Effects with Borrowing Between Data Sources

Estimate population average treatment effects from a primary data source with borrowing from supplemental sources. Causal estimation is done with either a Bayesian linear model or with Bayesian additive regression trees (BART) to adjust for confounding. Borrowing is done with multisource exchangeability models (MEMs). For information on BART, see Chipman, George, & McCulloch (2010) . For information on MEMs, see Kaizer, Koopmeiners, & Hobbs (2018) .

Bayesian Model for CACE Analysis

Performs CACE (Complier Average Causal Effect analysis) on either a single study or meta-analysis of datasets with binary outcomes, using either complete or incomplete noncompliance information. Our package implements the Bayesian methods proposed in Zhou et al. (2019) , which introduces a Bayesian hierarchical model for estimating CACE in meta-analysis of clinical trials with noncompliance, and Zhou et al. (2021) , with an application example on Epidural Analgesia.

Variational Mixture Models for Clustering Categorical Data

A variational Bayesian finite mixture model for the clustering of categorical data, and can implement variable selection and semi-supervised outcome guiding if desired. Incorporates an option to perform model averaging over multiple initialisations to reduce the effects of local optima and improve the automatic estimation of the true number of clusters. For further details, see the paper by Rao and Kirk (2024) .

Hierarchical Modeling and Frequency Method Checking on Overdispersed Gaussian, Poisson, and Binomial Data

We utilize approximate Bayesian machinery to fit two-level conjugate hierarchical models on overdispersed Gaussian, Poisson, and Binomial data and evaluates whether the resulting approximate Bayesian interval estimates for random effects meet the nominal confidence levels via frequency coverage evaluation. The data that Rgbp assumes comprise observed sufficient statistic for each random effect, such as an average or a proportion of each group, without population-level data. The approximate Bayesian tool equipped with the adjustment for density maximization produces approximate point and interval estimates for model parameters including second-level variance component, regression coefficients, and random effect. For the Binomial data, the package provides an option to produce posterior samples of all the model parameters via the acceptance-rejection method. The package provides a quick way to evaluate coverage rates of the resultant Bayesian interval estimates for random effects via a parametric bootstrapping, which we call frequency method checking.

Simulate, Evaluate, and Analyze Dose Finding Trials with Bayesian MCPMod

Bayesian MCPMod (Fleischer et al. (2022) ) is an innovative method that improves the traditional MCPMod by systematically incorporating historical data, such as previous placebo group data. This package offers functions for simulating, analyzing, and evaluating Bayesian MCPMod trials with normally and binary distributed endpoints. It enables the assessment of trial designs incorporating historical data across various true dose-response relationships and sample sizes. Robust mixture prior distributions, such as those derived with the Meta-Analytic-Predictive approach (Schmidli et al. (2014) ), can be specified for each dose group. Resulting mixture posterior distributions are used in the Bayesian Multiple Comparison Procedure and modeling steps. The modeling step also includes a weighted model averaging approach (Pinheiro et al. (2014) ). Estimated dose-response relationships can be bootstrapped and visualized.

A Shiny Application for End-to-End Bayesian Decision Network Analysis and Web-Deployment

A Shiny application for learning Bayesian Decision Networks from data. This package can be used for probabilistic reasoning (in the observational setting), causal inference (in the presence of interventions) and learning policy decisions (in Decision Network setting). Functionalities include end-to-end implementations for data-preprocessing, structure-learning, exact inference, approximate inference, extending the learned structure to Decision Networks and policy optimization using statistically rigorous methods such as bootstraps, resampling, ensemble-averaging and cross-validation. In addition to Bayesian Decision Networks, it also features correlation networks, community-detection, graph visualizations, graph exports and web-deployment of the learned models as Shiny dashboards.

Neural AutoRegressive Fractionally Integrated Moving Average Model

Methods and tools for forecasting univariate time series using the NARFIMA (Neural AutoRegressive Fractionally Integrated Moving Average) model. It combines neural networks with fractional differencing to capture both nonlinear patterns and long-term dependencies. The NARFIMA model supports seasonal adjustment, Box-Cox transformations, optional exogenous variables, and the computation of prediction intervals. In addition to the NARFIMA model, this package provides alternative forecasting models including NARIMA (Neural ARIMA), NBSTS (Neural Bayesian Structural Time Series), and NNaive (Neural Naive) for performance comparison across different modeling approaches. The methods are based on algorithms introduced by Chakraborty et al. (2025) .

Variance Estimation of FMT Method (Fully Moderated T-Statistic)

The FMT method computes posterior residual variances to be used in the denominator of a moderated t-statistic from a linear model analysis of gene expression data. It is an extension of the moderated t-statistic originally proposed by Smyth (2004) . LOESS local regression and empirical Bayesian method are used to estimate gene specific prior degrees of freedom and prior variance based on average gene intensity levels. The posterior residual variance in the denominator is a weighted average of prior and residual variance and the weights are prior degrees of freedom and residual variance degrees of freedom. The degrees of freedom of the moderated t-statistic is simply the sum of prior and residual variance degrees of freedom.