Personalized dose selection in radiation therapy using statistical models for toxicity and efficacy with dose and biomarkers as covariates

Selection of dose for cancer patients treated with radiation therapy (RT) must balance the increased efficacy with the increased toxicity associated with higher dose. Historically, a single dose has been selected for a population of patients (e.g., all stage III non-small cell lung cancer). However, the availability of new biologic markers for toxicity and efficacy allows the possibility of selecting a more personalized dose. We consider the use of statistical models for toxicity and efficacy as a function of RT dose and biomarkers to select an optimal dose for an individual patient, defined as the dose that maximizes the probability of efficacy minus the sum of weighted toxicity probabilities. This function can be shown to be equal to the expected value of the utility derived from a particular family of bivariate outcome utility matrices. We show that if dose is linearly related to the probability of toxicity and efficacy, then any marker that only acts additively with dose cannot improve efficacy, without also increasing toxicity. Using a dataset of lung cancer patients treated with RT, we illustrate this approach and compare it to non-marker-based dose selection. Because typical metrics used in evaluating new markers (e.g., area under the ROC curve) do not directly address the ability of a marker to improve efficacy at a fixed probability of toxicity, we utilize a simulation study to assess the effects of marker-based dose selection on toxicity and efficacy outcomes.