Sequential designs for individualized dosing in phase I cancer clinical trials

Abstract

This paper addresses dose finding in clinical trials where individuals exhibit biologic characteristics that alter the toxicity risks of the individuals. In these situations, instead of determining a dose that works for every patient, the trial aims to identify a dosing algorithm that prescribes dose according to the patient's biomarker or pharmacokinetic expression. Specifically, we aim to dose patients around a pre-specified level of area under the curve of irinotecan concentration using the patients' baseline phenotypes that predict drug clearance. We propose least squares recursion procedures to estimate the dosing algorithm sequentially with an aim to treat patients in the trial around the true unknown dosing algorithm, and introduce a novel application of an eigenvalue theory that guarantees convergence to the true dosing algorithms. Our simulation study demonstrates that using an eigenvalue constraint improves the efficiency of the recursion by as large as 40%, while concentrating in-trial patient allocation around the true dosing algorithm. We also provide practical guidance on design calibration, and design future irinotecan studies based on data from our first trial.

Keywords: Adaptive design; Coherence; Eigenvalue constraint; Least squares recursion; Pharmacokinetic variability.; Precision medicine.

Figure 1

Dosing algorithms according to the least square fit (solid) and the equation arm (dashed).

Figure 2

Calibration of LSR-EVC over a grid of δ₁ and δ₂ for κ = 5.

Figure 3

Single simulated trials by LSR, LSR-EVC, BSA and Equation. (a), (c), (e), (f): Each point indicates the baseline z_i and the given dose x_i of a simulated patient. The solid line indicates the true dosing function θ(z), and the dashed line the least squares estimate θ̂_n(z) using the trial outcomes. (b), (d), (f): Eigenvalue ratio sequence ρ_i versus subject number starting at i = 4. (h): Sequence $|M_i^T{M}_i|$ of versus subject number starting at i = 4.

Figure 4

The true dosing functions considered in the simulation study. A dosing function is denoted as θ(z) = a_z + b_zz where a_z = (t₀ − α)/β and b_z = −γ/β for Scenarios 1-5 (with β = 0.68 under the “A” scenarios and β = 0.32 under “B”), and a_z = g⁻¹ (t₀) and b_z = −ϕ for Scenarios 6A-7B.