  Citation: Saxena, A.; Rubens, M.; Ramamoorthy,V.; Zhang, Z.; Ahmed, M.A.; McGranaghan, P.; Das, S.; Veledar, E. A Brief Overview of Adaptive Designs for Phase I Cancer Trials. Cancers 2022, 14, 1566. https://doi.org/10.3390/ cancers14061566 Academic Editors: Luciano Cascione, Francesco Denti and Antonietta Mira Received: 17 February 2022 Accepted: 17 March 2022 Published: 18 March 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Review A Brief Overview of Adaptive Designs for Phase I Cancer Trials Anshul Saxena 1,2, * , Muni Rubens 3 , Venkataraghavan Ramamoorthy 1 , Zhenwei Zhang 1 , Md Ashfaq Ahmed 1 , Peter McGranaghan 3,4, * , Sankalp Das 5 and Emir Veledar 1,2 1 Center for Advanced Analytics, Baptist Health South Florida, Miami, FL 33176, USA; drvenky37@gmail.com (V.R.); Zhenwei.Zhang@baptisthealth.net (Z.Z.); MdAshfaq.Ahmed@baptisthealth.net (M.A.A.); EmirV@baptisthealth.net (E.V.) 2 Robert Stempel College of Public Health & Social Work, Florida International University, Miami, FL 33199, USA 3 Miami Cancer Institute, Baptist Health South Florida, Miami, FL 33176, USA; mrube001@fiu.edu 4 Department of Internal Medicine and Cardiology, Charité—Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin and Humboldt Universität zu Berlin, 10117 Berlin, Germany 5 Wellness and Employee Health, Baptist Health South Florida, Miami, FL 33176, USA; SankalpD@baptisthealth.net * Correspondence: AnshulS@baptisthealth.net (A.S.); peter.mcgranaghan@charite.de (P.M.) Simple Summary: Phase I cancer trials are important for new drug developments to test the safety and optimal dosage of cancer drugs which are usually toxic. Understanding biostatistical methodolo- gies of these designs is important for developing phase I studies that are both safe for the participants and which use optimal dosages for better outcomes. Currently there are several phase I designs that are being refined and modified for better outcomes and newer designs are being continuously developed. In this review article, we described several important phase I study designs to provide a brief overview of existing methods. Our review could be helpful to the research community who intent to have a better and yet a concise summary of existing methods. Abstract: Phase I studies are used to estimate the dose-toxicity profile of the drugs and to select appropriate doses for successive studies. However, literature on statistical methods used for phase I studies are extensive. The objective of this review is to provide a concise summary of existing and emerging techniques for selecting dosages that are appropriate for phase I cancer trials. Many advanced statistical studies have proposed novel and robust methods for adaptive designs that have shown significant advantages over conventional dose finding methods. An increasing number of phase I cancer trials use adaptive designs, particularly during the early phases of the study. In this review, we described nonparametric and algorithm-based designs such as traditional 3 + 3, accelerated titration, Bayesian algorithm-based design, up-and-down design, and isotonic design. In addition, we also described parametric model-based designs such as continual reassessment method, escalation with overdose control, and Bayesian decision theoretic and optimal design. Ongoing studies have been continuously focusing on improving and refining the existing models as well as developing newer methods. This study would help readers to assimilate core concepts and compare different phase I statistical methods under one banner. Nevertheless, other evolving methods require future reviews. Keywords: phase I trial; cancer clinical trial; adaptive design; maximum tolerated dose; dose-limiting toxicity; nonparametric designs; algorithm-based designs; parametric model-based designs 1. Introduction The phase I clinical trials, also known as first-in-human studies, evaluate the phar- macokinetic and pharmacodynamic properties of clinical drugs as well as their safety and tolerability. Phase I clinical trials are usually done among healthy volunteers who do not Cancers 2022, 14, 1566. https://doi.org/10.3390/cancers14061566 https://www.mdpi.com/journal/cancers