A utility approach to individualized optimal dose selection using biomarkers

Abstract

In many settings, including oncology, increasing the dose of treatment results in both increased efficacy and toxicity. With the increasing availability of validated biomarkers and prediction models, there is the potential for individualized dosing based on patient specific factors. We consider the setting where there is an existing dataset of patients treated with heterogenous doses and including binary efficacy and toxicity outcomes and patient factors such as clinical features and biomarkers. The goal is to analyze the data to estimate an optimal dose for each (future) patient based on their clinical features and biomarkers. We propose an optimal individualized dose finding rule by maximizing utility functions for individual patients while limiting the rate of toxicity. The utility is defined as a weighted combination of efficacy and toxicity probabilities. This approach maximizes overall efficacy at a prespecified constraint on overall toxicity. We model the binary efficacy and toxicity outcomes using logistic regression with dose, biomarkers and dose-biomarker interactions. To incorporate the large number of potential parameters, we use the LASSO method. We additionally constrain the dose effect to be non-negative for both efficacy and toxicity for all patients. Simulation studies show that the utility approach combined with any of the modeling methods can improve efficacy without increasing toxicity relative to fixed dosing. The proposed methods are illustrated using a dataset of patients with lung cancer treated with radiation therapy.

Keywords: constrained LASSO; efficacy toxicity trade-off; optimal treatment regime; personalized medicine; utility.

Figure 1

Top: Individual level E-T plot with choice of dose with theoretical β_E, β_T for three subjects. The utility curve uses θ = 1. Bottom: Individual level optimal dose as a function of θ for the same three subjects.

Figure 2

Left: Population level E-T plot with choice of θ with theoretical β_E, β_T, Right: Population level E-T trade-off at different toxicity tolerance levels.

Figure 3

Simulation results for scenario 0. Boxplot of average efficacy with same toxicity for 1000 simulation trials. The compared methods are theory with true coefficients; FS: Forward Selection; LASSO; cLASSO: constrained LASSO; FD: Fixed Dosing. All methods are constrainted at P(T)=0.20. Means are 0.599, 0.528, 0.528, 0.539, 0.452, respectively.