Randomization in Clinical Trials With Small Sample Sizes Using Group Sequential Designs
Daniel Bodden, Ralf-Dieter Hilgers, Franz König.
Abstract
Group sequential designs, which allow early stopping for efficacy or futility, may benefit from balanced sample sizes at interim and final analyses. This requirement for balance limits the choice of admissible randomization procedures. We investigate if the choice of randomization procedure, whether balanced or not, impacts the type I error probability and power in small sample clinical trials with group sequential designs.
Introduction
In traditional clinical trial design, patient enrollment continues until a predetermined sample size is reached. Group sequential designs (GSDs) offer an alternative by allowing for interim analyses at predetermined points, for example by time or achieved sample size during the trial. These interim analyses provide the possibility of stopping the trial early, either for efficacy if the treatment shows a significant benefit, or for futility if continuing the trial is unlikely to yield conclusive results.
Materials and Methods:
We structure the Methods section as follows: First, we describe the literature review setup. This is followed by a description of the clinical trial design and RPs. Next, we outline the adjustment for repeated interim analyses followed by how a t-test can be performed for a GSD. We conclude the section with the simulation study setup used to evaluate T1E and power. The results corresponding to each of these subsections are presented separately in the Results section.
Discussion
Our study highlights that the choice of RP in small sample GSDs affects the trials outcome. This effect is noticeable even under ideal conditions, such as when variance is known. Table 7 provides a framework indicating suitable RPs to pair with GSDs for trials with small stage-wise sample sizes. The framework is applied to equally distributed stages, as evaluated in our simulation, but it can be straightforward extended to accommodate varying interim analysis timing.
Acknowledgments
We thank Chris Jennison for contributing code to calculate group sequential boundary properties, which was used for the initial power calculations in this work and gratefully acknowledge the computing time provided to at the NHR Center NHR4CES at RWTH Aachen University (project number p0024408).
Citation: Bodden D, Hilgers R-D, König F (2025) Randomization in clinical trials with small sample sizes using group sequential designs. PLoS One 20(6): e0325333. https://doi.org/10.1371/journal.pone.0325333
Editor: Dhermendra Tiwari, Goa University, INDIA
Received: November 27, 2024; Accepted: May 9, 2025; Published: June 13, 2025.
Copyright: © 2025 Bodden et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: All code related to the simulation study is available in the following repository: Bodden D, Hilgers RD, König F. Simulation code for evaluating randomization procedures in group sequential designs; 2025. DOI: 10.6084/m9.figshare.28732184.v4.
Funding: RDH is coordinator and FK is member of RealiseD supported by the Innovative Health Initiative Joint Undertaking (IHI JU) under grant agreement No 101165912. The JU receives support from the European Union’s Horizon Europe research and innovation programme and COCIR, EFPIA, Europa Bío, MedTech Europe, and Vaccines Europe. Views and opinions expressed are those of the author(s) only. This publication reflects the author’s views. They do not necessarily reflect those of the Innovative Health Initiative Joint Undertaking and its members, who cannot be held responsible for them. RDH received funding from European Rare Disease Research Coordination and Support Action consortium (ERICA) funded by the European Union’s Horizon 2020 research and innovation programme under Grant Agreement. no. 964908. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
