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All Journal Asian Journal of Science, Technology, Engineering, and Art Mikailalsys Journal of Mathematics and Statistics
Nyam, Peter Weng
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Arts Computer Science & IT Engineering Mathematics Mechanical Engineering Social Sciences

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Applications of the Bayesian Methods in Clinical Trials with Large Sample Size Amani, D. J; Bishir, A.; Usman, M. A.; Amos, S.; Yelwa, A.; Nyam, Peter Weng
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i1.7483

Abstract

Bayesian methods have gained prominence as robust alternatives to traditional frequentist approaches in the design and analysis of clinical trials, particularly those involving large sample sizes. While frequentist methods rely on fixed hypotheses and long-run probability interpretations, Bayesian frameworks incorporate prior knowledge and allow for iterative updating of evidence as data accrue. This adaptability facilitates the implementation of innovative trial structures such as adaptive designs and platform trials, while also supporting real-time decision-making. The integration of historical or external data within Bayesian analyses further enhances trial efficiency, especially in interim monitoring and interpretation of treatment effects. Despite these advantages, the broader adoption of Bayesian methods in confirmatory Phase III trials remains constrained by computational demands, challenges in the elicitation and justification of prior distributions, and varying degrees of regulatory acceptance. Nevertheless, advancements in high-performance computing, the emergence of hybrid Bayesian–frequentist methodologies, and growing regulatory engagement underscore a progressive shift toward broader implementation. This paper critically examines the evolution, methodological underpinnings, and practical applications of Bayesian approaches in large-sample clinical trials, offering a comparative assessment with frequentist methods. It also outlines key benefits, prevailing limitations, and potential trajectories for future research and regulatory alignment. These insights contribute to ongoing discourse on optimizing trial design for enhanced scientific rigor, ethical standards, and decision-making in evidence-based medicine.
A Bayesian Decision-Theoretic Framework for Optimally Managing Asymmetric Error Costs in Hypothesis Testing Daniel, John Abisi A; Bishir, A.; Ibrahim, Abdulhalim Isah; ZabiZabi, Zainab Muhammad; Gabchiya, Abubakar; Nyam, Peter Weng
Asian Journal of Science, Technology, Engineering, and Art Vol 3 No 6 (2025): Asian Journal of Science, Technology, Engineering, and Art
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ajstea.v3i6.7714

Abstract

The classical Neyman–Pearson paradigm of hypothesis testing mandates control of the Type I error rate (α) while maximizing power (1 − β), but this foundational approach has been widely criticized for its rigidity, reliance on arbitrary significance thresholds, and inability to formally incorporate the relative costs of different errors. This paper presents a Bayesian decision-theoretic framework as a principled alternative for optimizing the trade-off between Type I and Type II errors. By combining prior information with observed data to form a posterior distribution and minimizing a loss function that explicitly quantifies the consequences of decisions, the optimal decision rule emerges naturally and balances posterior evidence against asymmetric error costs. A detailed case study in medical diagnostics illustrates the practical advantages of this approach, demonstrating how optimal decisions change when the severity of errors is explicitly taken into account. The paper argues that the Bayesian framework provides a more coherent, flexible, and context-sensitive methodology for statistical decision-making, moving beyond the limitations imposed by a fixed α.
Co-Authors Amani, D. J Amos, S. Bishir, A. Daniel, John Abisi A Gabchiya, Abubakar Ibrahim, Abdulhalim Isah Usman, M. A. Yelwa, A. ZabiZabi, Zainab Muhammad