Response-adaptive randomization in clinical trials: from myths to practical considerations David S. Robertson 1 , Kim May Lee 1 , Boryana C. L´ opez-Kolkovska 1 , and Sof´ ıa S. Villar *1 1 MRC Biostatistics Unit, University of Cambridge, Cambridge, UK Abstract Response-Adaptive Randomization (RAR) is part of a wider class of data-dependent sampling algorithms, for which clinical trials are typically used as a motivating application. In that context, patient allocation to treatments is determined by randomization probabilities that change based on the accrued response data in order to achieve experimental goals. RAR has received abundant theoretical attention from the biostatistical literature since the 1930’s and has been the subject of numerous debates. In the last decade, it has received renewed consideration from the applied and methodological communities, driven by well-known practical examples and its widespread use in machine learning. Papers on the subject present different views on its usefulness, and these are not easy to reconcile. This work aims to address this gap by providing a unified, broad and fresh review of methodological and practical issues to consider when debating the use of RAR in clinical trials. Keywords: Ethics; patient allocation; power; sample size imbalance, time trends, type I error control. 1 Introduction Randomization to allocate patients to treatments is a defining element of a well-conducted study, ensuring comparability of treatment groups, mitigating selection bias, and providing the basis for statistical inference (Rosenberger and Lachin, 2016). In clinical trials, a randomization scheme which remains unchanged with patient responses is still the most frequently used patient allocation proce- dure. Alternatively, randomization probabilities can be adapted during the trial based on the accrued responses, with the aim of achieving experimental objectives. Objectives that can be targeted with a * Address correspondence to Sof´ ıa S. Villar, MRC Biostatistics Unit, University of Cambridge, East Forvie Site, Robinson Way, Cambridge CB2 0SR, UK; E-mail: sofia.villar@mrc-bsu.cam.ac.uk 1 arXiv:2005.00564v4 [stat.ME] 7 Jun 2022