This paper tests a new way to find the maximum tolerated dose (MTD) in Phase I cancer trials. The MTD is the highest dose with an acceptable chance of serious toxicity. The authors model toxicity as a continuous score and call an observation dose-limiting toxicity (DLT) when it crosses a preset threshold. Their goal is to learn the MTD while keeping patients safe from too much toxicity.

They use two versions of Bayesian additive regression trees (BART). One, called isotonic BART (iBART), fits a flexible curve and then projects each posterior draw onto a nondecreasing function using a standard algorithm (the pool-adjacent-violators algorithm). The other, monotone BART (mBART), forces each tree in the model to be nondecreasing so the fitted curve is monotone by construction. The models also draw a residual variance. Joint draws of the mean curve and variance give a posterior distribution for the MTD. Dose selection uses escalation with overdose control (EWOC), which picks a conservative lower quantile of the MTD posterior so that the chance of giving a dose above the MTD is limited. The trial rules also include practical dose caps and an “Only Escalation” restriction that prevents dose decreases between cohorts.

The authors compared these tree methods to three parametric dose-finding models used in the literature: a one-parameter linear finder (1PLD), a two-parameter linear finder (2PLD, which also estimates residual variance), and a three-parameter nonlinear finder (3PND, which adds a curvature parameter). They ran simulations with 45 planned patients, seven dose--toxicity scenarios, and cohorts of three. They measured total DLT counts, the number of assignments above the true MTD, signed error in the final dose estimate, and relative absolute error (RAE). The tree methods gave the lowest mean RAE on four of the nonlinear scenarios. On four scenarios the trees also jointly minimized mean DLT counts and above-MTD assignments, suggesting better trade-offs between learning and safety when the true dose--toxicity curve was not simple.