Based on the manuscript: Generalized 3+3 (G3): An Effective Rule-Based Dose-Finding Design, Yuan Ji, Yunxuan Zhang, Andrew Ji Department of, Public Health Sciences, The University of Chicago, IL. The University of Chicago Laboratory Schools, IL. Link: 2024.08.18.24312178v1.full.pdf

BACKGROUND: For over three decades, the choice of phase I dose-finding trial designs has been under scrutiny  (Kurzrock et al.,2021), particularly concerning whether model-based statistical designs are superior to the 3+3 design (Storer, 1989), a model-free design. Despite its lackluster performance in computer simulations, the 3+3 design remains the gold standard in the clinical community. Its enduring popularity is largely attributed to its simplicity and proven practical values. However, the 3+3 design only provides dosing decisions for 3 or 6 participants treated with a dose, while more recent designs can decide for any number of participants. In addition, the inability to assign more than 6 participants to a dose leads to inferior performance in computer simulations for the 3+3 design (Ji & Wang, 2013).

We propose the Generalized 3+3 (G3) design to demonstrate that statistical designs for phase I dose-finding trials can be effective without a probability model. The G3 design aims to achieve two key objectives: (1) to preserve all decision rules of the traditional 3+3 design while extending it to accommodate cohort sizes beyond 3 or 6 participants, and (2) to improve performance in computer simulations, matching the efficiency of more advanced designs.

METHOD: During a phase I trial, the dose being tested at any given time is called the 'current dose.' A group of participants is treated with this dose, and some may experience dose-limiting toxicity (DLT). The ratio of the participant number with DLTs to the total number treated at the current dose is the observed toxicity rate (OTR). For example, if 3 participants are treated and 1 experiences DLT, the OTR is 1/3. Based on OTR, the G3 design follows a simple decision rule to decide the dose for the next cohort of participants:

Step 1 [Dose Escalation] For 3 or 6 participants at the current dose, apply the decisions of the 3+3 design. For other numbers, if the OTR is less than 0.2, E (escalate to the next higher dose); if the OTR is greater than 0.29, D (De-escalate to the next lower dose); otherwise, S (stay at the current dose).

Step 2 [Safety Rules] If the number of participants with DLTs exceeds the boundary in Figure 1b, remove the current dose and all the higher doses from the trial.

Step 3 [Stopping and MTD Selection Rules] A trial is stopped either when a prespecified sample size is reached or when no dose is left. In the former case, use rules in Figure 1c to select a dose as MTD. In the latter case, no dose is selected.

RESULTS: Following Step 1, a decision table can be easily generated to guide the dose assignment throughout the trial. The G3 decisions are highly similar to advanced designs like BOIN (Liu and Ying, 2015) and i3+3 (Liu et al., 2020), differing only in two places. More importantly, only G3 can replicate the decisions of the 3+3 design. Computer simulations confirm the favorable operating characteristics of the G3 design, a major improvement over the 3+3 design.

CONCLUSION: The G3 design extends the 3+3 design by producing desirable decisions for any participants treated with the current dose. Implementation of G3 requires no software. The supplementary material provides a standard protocol language for G3 and additional simulation results. For the first time, a model-free design like G3 can show competitive performance to advanced model-based designs, solidifying its feasibility and application for phase I dose-finding trials.