arXiv subjects

Riko Kelter

Publications and source records attributed to Riko Kelter.

10 recordsLinked to original sources

arXiv2026

Simulation-Free Bayesian Power and Sample Size Calculations for Bayes Factors in Single-Arm Phase II Trials with Binary Endpoints

Bayes factors provide a coherent Bayesian measure of evidence for competing hypotheses and have recently been used as the basis for single-arm phase II trial designs with binary endpoints. In contrast to classical power analyses based on test statistics and p-values, Bayes-factor based sample size calculations target high probabilities of obtaining compelling evidence either for a relevant treatment effect or for the null hypothesis, given pre-specified Bayes-factor thresholds. This paper explains how to design single-arm phase II binomial trials using Bayes factors with a focus on simulation-free calibration of Bayesian and frequentist power, type-I-error, and the probability of compelling evidence for the null. Two oncology-motivated examples illustrate the approach and are implemented in the bfbin2arm R package, with code provided in an appendix. The methodology fits naturally into current efforts to innovate and modernize clinical trial design through Bayesian and adaptive methods.

stat.ME↗

arXiv2026

Optimal sequential two-stage Bayes Factor Design for two-arm clinical Phase II Trials with binary Endpoints

Two-arm phase II clinical trials often benefit from an interim analysis that allows early stopping for futility, but Bayesian calibration of such designs is usually based on computationally intensive Monte Carlo simulation. In this work, a simulation-free methodology is developed to obtain Bayesian optimal two-stage designs in two-arm phase II trials with binary endpoints using Bayes factors as the primary measure of evidence. Building on recent matrix-search methods for fixed-sample two-arm Bayes factor designs and earlier correction formulas for one-arm two-stage designs, the proposed approach derives exact expressions for the operating characteristics of a two-stage two-arm design with a single futility interim. Bayesian power and type-I error are obtained by correcting the corresponding fixed-sample quantities for trajectories that would have been removed by early stopping, yielding a fully numerical calibration procedure that avoids Monte Carlo error entirely. The resulting method searches over admissible interim and final sample sizes to identify the optimal design that satisfies target constraints on Bayesian power, type-I error, and the probability of compelling evidence in favour of the null hypothesis, while minimizing the expected sample size under the null hypothesis. The methodology is illustrated in realistic phase II settings, including a detailed re-analysis of the riociguat trial in systemic sclerosis. Overall, the approach extends simulation-free Bayes factor design methodology to the practically important setting of two-arm two-stage phase II trials and provides a transparent basis for Bayesian design calibration and sensitivity analysis.

stat.ME↗

arXiv2026

Power and Sample Size Calculations for Bayes Factors in two-arm clinical Phase II Trials with binary Endpoints

Bayesian sample size calculations in clinical trials usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power often lack closed-form or approximate numerical solutions. In this paper, we focus on power and sample size calculations for Bayes factors in the two-arm binomial setting of phase II trials. We cover point-null versus composite and directional hypothesis tests, derive the corresponding Bayes factors, and discuss relevant aspects to consider when pursuing Bayesian design of experiments with the introduced approach. Based on these Bayes factors, we propose a numerical approach which allows to determine the necessary sample size to obtain prespecified bounds of Bayesian power and type-I-error rate in a computationally efficient way. Our method does not rely on Monte Carlo simulations and instead solely relies on standard numerical methods. Real-world examples of phase II trials from oncology and autoimmune diseases illustrate the advantage of the proposed calibration method. In summary, our approach allows for a Bayes-frequentist compromise by providing a Bayesian analogue to a frequentist power analysis for various Bayes factors in the two-arm binomial setting of a phase II clinical trial. The methods are implemented in our R package bfbin2arm.

stat.ME↗

arXiv2025

The Bayesian optimal two-stage design for clinical phase II trials based on Bayes factors

Sequential trial design is an important statistical approach to increase the efficiency of clinical trials. Bayesian sequential trial design relies primarily on conducting a Monte Carlo simulation under the hypotheses of interest and investigating the resulting design characteristics via Monte Carlo estimates. This approach has several drawbacks, namely that replicating the calibration of a Bayesian design requires repeating a possibly complex Monte Carlo simulation. Furthermore, Monte Carlo standard errors are required to judge the reliability of the simulation. All of this is due to a lack of closed-form or numerical approaches to calibrate a Bayesian design which uses Bayes factors. In this paper, we propose the Bayesian optimal two-stage design for clinical phase II trials based on Bayes factors. The optimal two-stage Bayes factor design is a sequential clinical trial design that is built on the idea of trinomial tree branching, a method we propose to correct the resulting design characteristics for introducing a single interim analysis. We build upon this idea to invent a calibration algorithm which yields the optimal Bayesian design that minimizes the expected sample size under the null hypothesis. Examples show that our design recovers Simon's two-stage optimal design as a special case, improves upon non-sequential Bayesian design based on Bayes factors, and can be calibrated quickly, as it makes use only of standard numerical techniques instead of time-consuming Monte Carlo simulations. Furthermore, the design allows to ensure a minimum probability on compelling evidence in favour of the null hypothesis, which is not possible with other designs. As the idea of trinomial tree branching is neither dependent on the endpoint, nor on the use of Bayes factors, the design can therefore be generalized to other settings, too.

stat.ME↗

arXiv2025

Bayesian Power and Sample Size Calculations for Bayes Factors in the Binomial Setting

Bayesian design of experiments and sample size calculations usually rely on complex Monte Carlo simulations in practice. Obtaining bounds on Bayesian notions of the false-positive rate and power therefore often lack closed-form or approximate numerical solutions. In this paper, we focus on the sample size calculation in the binomial setting via Bayes factors, the predictive updating factor from prior to posterior odds. We discuss the drawbacks of sample size calculations via Monte Carlo simulations and propose a numerical root-finding approach which allows to determine the necessary sample size to obtain prespecified bounds of Bayesian power and type-I-error rate almost instantaneously. Real-world examples and applications in clinical trials illustrate the advantage of the proposed method. We focus on point-null versus composite and directional hypothesis tests, derive the corresponding Bayes factors, and discuss relevant aspects to consider when pursuing Bayesian design of experiments with the introduced approach. In summary, our approach allows for a Bayes-frequentist compromise by providing a Bayesian analogue to a frequentist power analysis for the Bayes factor in binomial settings. A case study from a Phase II trial illustrates the utility of our approach. The methods are implemented in our R package bfpwr.

stat.ME↗

arXiv2020

fbst: An R package for the Full Bayesian Significance Test for testing a sharp null hypothesis against its alternative via the e-value

Hypothesis testing is a central statistical method in psychology and the cognitive sciences. However, the problems of null hypothesis significance testing (NHST) and p-values have been debated widely, but few attractive alternatives exist. This article introduces the fbst R package, which implements the Full Bayesian Significance Test (FBST) to test a sharp null hypothesis against its alternative via the e-value. The statistical theory of the FBST has been introduced by Pereira et al. (1999) more than two decades ago and since then, the FBST has shown to be a Bayesian alternative to NHST and p-values with both theoretical and practical highly appealing properties. The algorithm provided in the fbst package is applicable to any Bayesian model as long as the posterior distribution can be obtained at least numerically. The core function of the package provides the Bayesian evidence against the null hypothesis, the e-value. Additionally, p-values based on asymptotic arguments can be computed and rich visualisations for communication and interpretation of the results can be produced. Three examples of frequently used statistical procedures in the cognitive sciences are given in this paper which demonstrate how to apply the FBST in practice using the fbst package. Based on the success of the FBST in statistical science, the fbst package should be of interest to a broad range of researchers in psychology and the cognitive sciences and hopefully will encourage researchers to consider the FBST as a possible alternative when conducting hypothesis tests of a sharp null hypothesis.

stat.ME↗

arXiv2020

The Full Bayesian Significance Test and the e-value -- Foundations, theory and application in the cognitive sciences

Hypothesis testing is a central statistical method in psychological research and the cognitive sciences. While the problems of null hypothesis significance testing (NHST) have been debated widely, few attractive alternatives exist. In this paper, we provide a tutorial on the Full Bayesian Significance Test (FBST) and the e-value, which is a fully Bayesian alternative to traditional significance tests which rely on p-values. The FBST is an advanced methodological procedure which can be applied to several areas. In this tutorial, we showcase with two examples of widely used statistical methods in psychological research how the FBST can be used in practice, provide researchers with explicit guidelines on how to conduct it and make available R-code to reproduce all results. The FBST is an innovative method which has clearly demonstrated to perform better than frequentist significance testing. However, to our best knowledge, it has not been used so far in the psychological sciences and should be of wide interest to a broad range of researchers in psychology and the cognitive sciences.

stat.ME↗

arXiv2020

How to choose between different Bayesian posterior indices for hypothesis testing in practice

Hypothesis testing is an essential statistical method in psychology and the cognitive sciences. The problems of traditional null hypothesis significance testing (NHST) have been discussed widely, and among the proposed solutions to the replication problems caused by the inappropriate use of significance tests and $p$-values is a shift towards Bayesian data analysis. However, Bayesian hypothesis testing is concerned with various posterior indices for significance and the size of an effect. This complicates Bayesian hypothesis testing in practice, as the availability of multiple Bayesian alternatives to the traditional $p$-value causes confusion which one to select and why. In this paper, we compare various Bayesian posterior indices which have been proposed in the literature and discuss their benefits and limitations. Our comparison shows that conceptually not all proposed Bayesian alternatives to NHST and $p$-values are beneficial, and the usefulness of some indices strongly depends on the study design and research goal. However, our comparison also reveals that there exist at least two candidates among the available Bayesian posterior indices which have appealing theoretical properties and are, to our best knowledge, widely underused among psychologists.

stat.ME↗

arXiv2020

Bayesian model selection in the $\mathcal{M}$-open setting -- Approximate posterior inference and probability-proportional-to-size subsampling for efficient large-scale leave-one-out cross-validation

Comparison of competing statistical models is an essential part of psychological research. From a Bayesian perspective, various approaches to model comparison and selection have been proposed in the literature. However, the applicability of these approaches strongly depends on the assumptions about the model space $\mathcal{M}$, the so-called model view. Furthermore, traditional methods like leave-one-out cross-validation (LOO-CV) estimate the expected log predictive density (ELPD) of a model to investigate how the model generalises out-of-sample, which quickly becomes computationally inefficient when sample size becomes large. Here, we provide a tutorial on approximate Pareto-smoothed importance sampling leave-one-out cross-validation (PSIS-LOO), a computationally efficient method for Bayesian model comparison. First, we discuss several model views and the available Bayesian model comparison methods in each. We then use Bayesian logistic regression as a running example how to apply the method in practice, and show that it outperforms other methods like LOO-CV or information criteria in terms of computational effort while providing similarly accurate ELPD estimates. In a second step, we show how even large-scale models can be compared efficiently by using posterior approximations in combination with probability-proportional-to-size subsampling. We show how to compare competing models based on the ELPD estimates provided, and how to conduct posterior predictive checks to safeguard against overconfidence in one of the models under consideration. We conclude that the method is attractive for mathematical psychologists who aim at comparing several competing statistical models, which are possibly high-dimensional and in the big-data regime.

stat.AP↗

arXiv2020

A new Bayesian two-sample t-test for effect size estimation under uncertainty based on a two-component Gaussian mixture with known allocations and the region of practical equivalence

Testing differences between a treatment and control group is common practice in biomedical research like randomized controlled trials (RCT). The standard two-sample t-test relies on null hypothesis significance testing (NHST) via p-values, which has several drawbacks. Bayesian alternatives were recently introduced using the Bayes factor, which has its own limitations. This paper introduces an alternative to current Bayesian two-sample t-tests by interpreting the underlying model as a two-component Gaussian mixture in which the effect size is the quantity of interest, which is most relevant in clinical research. Unlike p-values or the Bayes factor, the proposed method focusses on estimation under uncertainty instead of explicit hypothesis testing. Therefore, via a Gibbs sampler the posterior of the effect size is produced, which is used subsequently for either estimation under uncertainty or explicit hypothesis testing based on the region of practical equivalence (ROPE). An illustrative example, theoretical results and a simulation study show the usefulness of the proposed method, and the test is made available in the R package bayest.

stat.ME↗