BESS: A Bayesian Estimator of Sample Size

TL;DR

BESS introduces a Bayesian estimator for clinical trial sample size that directly ties the required n to observed data via the posterior probability of a positive decision (POS). By coupling three elements—evidence (e), confidence (POS threshold c), and sample size (n)—BESS delivers interpretable, data-driven sample-size statements and supports interim re-estimation. The framework accommodates binary, continuous (known variance), and count data through conjugate hierarchical models and yields e-Coherence and n-Coherence properties, ensuring monotone relationships between evidence, n, and POS. Simulation studies show BESS produces sample sizes comparable to oracle Frequentist SSE when error rates are matched and offers potential reductions in required subjects via informative priors. The dose-optimization case demonstrates BESS’s practical utility for adaptive design and interim analyses, highlighting its flexibility and potential for broader Bayesian-integrated trial planning in oncology and beyond.

Abstract

We consider a Bayesian framework for estimating the sample size of a clinical trial. The new approach, called BESS, is built upon three pillars: Sample size of the trial, Evidence from the observed data, and Confidence of the final decision in the posterior inference. It uses a simple logic of "given the evidence from data, a specific sample size can achieve a degree of confidence in trial success." The key distinction between BESS and standard sample size estimation (SSE) is that SSE, typically based on Frequentist inference, specifies the true parameters values in its calculation to achieve properties under repeated sampling while BESS assumes possible outcome from the observed data to achieve high posterior probabilities of trial success. As a result, the calibration of the sample size is directly based on the probability of making a correct decision rather than type I or type II error rates. We demonstrate that BESS leads to a more interpretable statement for investigators, and can easily accommodates prior information as well as sample size re-estimation. We explore its performance in comparison to the standard SSE and demonstrate its usage through a case study of oncology optimization trial. An R tool is available at https://ccte.uchicago.edu/BESS.

Figures (3)

• Figure 1: Combined Error Rates (CER) and Combined False Rates (CFR) across various sample sizes for the four designs under comparison. Different $k$ values are used to illustrate the importance of type I error rate over the type II error rate in CER or FDR over FOR in CFR.
• Figure A.1: Illustration of the contour defined by $\mathcal{B}_2(n,\theta_1,\theta_0) = 0$: (a) Tangent line $\theta_1 = \theta_0 + \theta_n^*$ touching the contour at the tangent point. (b) Region of interest $\{(\theta_1,\theta_0);\theta_1 - \theta_0 \leq \theta_n^*, \theta_1 \in (0,1), \theta_0 \in (0,1)\}$, shown as the blue dashed area; the blue shaded region denotes $\mathcal{B}_2(n,\theta_1,\theta_0) < 0$. (c) Shrinkage of the contour as $n$ increases, with the tangent line $\theta_1 = \theta_0 + \theta_{n+1}^*$ (dashed light red line) "succeeding" the previous tangent line $\theta_1 = \theta_0 + \theta_{n}^*$ (solid red line), where $\theta_{n+1}^* > \theta_n^*$. (d) Radius $y_n$ (purple dashed line) with angle $\varphi_n$. In all panels, the black contour is the contour and red lines are tangent lines.
• Figure A.2: Flowchart of simulation process to compare sample sizes estimated under BESS and that of the frequentist method.

Theorems & Definitions (14)

• Theorem 1
• Remark 1
• Remark 2
• Proposition 1
• Proposition 2
• Theorem 2
• Theorem 3
• Proposition 3
• Theorem 4
• Lemma 1