Dose-finding design based on level set estimation in phase I cancer clinical trials

TL;DR

Simulation experiments show that the proposed LSE design achieves a higher accuracy in estimating the MTD and involves a lower risk of overdosing allocation compared to existing designs, thereby indicating that it provides an effective methodology for phase I cancer clinical trial design.

Abstract

The primary objective of phase I cancer clinical trials is to evaluate the safety of a new experimental treatment and to find the maximum tolerated dose (MTD). We show that the MTD estimation problem can be regarded as a level set estimation (LSE) problem whose objective is to determine the regions where an unknown function value is above or below a given threshold. Then, we propose a novel dose-finding design in the framework of LSE. The proposed design determines the next dose on the basis of an acquisition function incorporating uncertainty in the posterior distribution of the dose-toxicity curve as well as overdose control. Simulation experiments show that the proposed LSE design achieves a higher accuracy in estimating the MTD and involves a lower risk of overdosing allocation compared to existing designs, thereby indicating that it provides an effective methodology for phase I cancer clinical trial design.

Figures (13)

• Figure 1: Illustration of LSE for dose finding with five candidate doses. The solid curve represents the DLT probability $\pi(x)$, and the dotted horizontal line represents the threshold, i.e., the target DLT probability $\theta$. Under the monotonicity assumption for $\pi(x)$, the dose space is divided into $L$ and $H$ by the dose $x^* = \max_{x\in\mathcal{X}} L$ as the boundary.
• Figure 2: (left) Initial guess in each case of $\nu$ under $J = 5, ~\theta=0.3, ~\delta_1 = 0.05, ~\tilde{\sigma}_f = 1.35, ~q_1 = q_J = 0.1$. (right) Prior dose-toxicity relationship when $\nu = 3$. The solid blue line represents the median, which is equal to the initial guess. The dashed blue lines represent the 80% and 95% equal-tailed credible intervals. The horizontal line represents the proper dosing interval $[\theta-\delta_1, \theta + \delta_1]$.
• Figure 3: Illustrative example of the proposed design. The upper panel shows the dose allocation path. The white circles represent patients with no DLT and the black circles represent patients with DLT. The lower panel shows the posterior distribution of $\pi(x)$ after the 4th, 7th, and 12th cohorts, with its median (bold line) and 20 random samples from them (red lines), and the value of the acquisition function $\alpha(x)$ at each dose, respectively. The shaded part of the posterior distribution of $\pi(x)$ represents the 95% credible interval and the shaded part of the acquisition function represents the admissible dose set.
• Figure 4: Comparison of accuracy for identifying and allocating the MTD for each design, with PCS (A) and PCA (B) obtained from 2000 simulations. Higher values for both PCS and PCA indicate better performance.
• Figure 5: Comparison of the risk of overdosing for each design with POS (A) and POA (B) obtained from 2000 simulations. Lower values for both POS and POA indicate better performance.

Theorems & Definitions (11)

• Lemma 1: Lemma 1 in Bogunovic et al. bogunovic2020corruption
• Corollary 1
• Definition 1
• Theorem 1
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof