Bayesian Phase I/II Biomarker-based Dose Finding for Precision Medicine with Molecularly Targeted Agents

Abstract

The optimal dose for treating patients with a molecularly targeted agent may differ according to the patient's individual characteristics, such as biomarker status. In this article, we propose a Bayesian phase I/II dose-finding design to find the optimal dose that is personalized for each patient according to his/her biomarker status. To overcome the curse of dimensionality caused by the relatively large number of biomarkers and their interactions with the dose, we employ canonical partial least squares (CPLS) to extract a small number of components from the covariate matrix containing the dose, biomarkers, and dose-by-biomarker interactions. Using these components as the covariates, we model the ordinal toxicity and efficacy using the latent-variable approach. Our model accounts for important features of molecularly targeted agents. We quantify the desirability of the dose using a utility function and propose a two-stage dose-finding algorithm to find the personalized optimal dose according to each patient's individual biomarker profile. Simulation studies show that our proposed design has good operating characteristics, with a high probability of identifying the personalized optimal dose.

Keywords: Bayesian adaptive design; dose finding; partial least squares; personalized dose finding; personalized medicine.

Figure 1:

Scree plots of the root mean squared error of prediction (RMSEP) versus the number of CPLS components for efficacy and toxicity.

Figure 2:

Main effects and interaction effects on efficacy probabilities for the eight scenarios. The radius of a circle is proportional to the absolute value of the coefficient. Red and black circles respectively represent positive and negative coefficients.

Figure 3:

Main effects and interaction effects on toxicity probabilities for the eight scenarios. The radius of a circle is proportional to the absolute value of the coefficient. Red and black circles respectively represent positive and negative coefficients.

Figure 4:

Utility of the five doses for 16 biomarker patterns under the eight scenarios. Each graph shows the utility for one biomarker pattern. The symbols “+” and “−” above each graph indicate the status for the 5 biomarkers. The eight curves within each sub-group represent the utilities for the eight scenarios.