The 3 + 3 design in dose-finding studies with small sample sizes: Pitfalls and possible remedies

Abstract

In the last few years, numerous novel designs have been proposed to improve the efficiency and accuracy of phase I trials to identify the maximum-tolerated dose (MTD) or the optimal biological dose (OBD) for noncytotoxic agents. However, the conventional 3+3 approach, known for its and poor performance, continues to be an attractive choice for many trials despite these alternative suggestions. The article seeks to underscore the importance of moving beyond the 3+3 design by highlighting a different key element in trial design: the estimation of sample size and its crucial role in predicting toxicity and determining the MTD. We use simulation studies to compare the performance of the most used phase I approaches: 3+3, Continual Reassessment Method (CRM), Keyboard and Bayesian Optimal Interval (BOIN) designs regarding three key operating characteristics: the percentage of correct selection of the true MTD, the average number of patients allocated per dose level, and the average total sample size. The simulation results consistently show that the 3+3 algorithm underperforms in comparison to model-based and model-assisted designs across all scenarios and metrics. The 3+3 method yields significantly lower (up to three times) probabilities in identifying the correct MTD, often selecting doses one or even two levels below the actual MTD. The 3+3 design allocates significantly fewer patients at the true MTD, assigns higher numbers to lower dose levels, and rarely explores doses above the target dose-limiting toxicity (DLT) rate. The overall performance of the 3+3 method is suboptimal, with a high level of unexplained uncertainty and significant implications for accurately determining the MTD. While the primary focus of the article is to demonstrate the limitations of the 3+3 algorithm, the question remains about the preferred alternative approach. The intention is not to definitively recommend one model-based or model-assisted method over others, as their performance can vary based on parameters and model specifications. However, the presented results indicate that the CRM, Keyboard, and BOIN designs consistently outperform the 3+3 and offer improved efficiency and precision in determining the MTD, which is crucial in early-phase clinical trials.