Stochastic optimal control to guide adaptive cancer therapy

Abstract

Although adaptive cancer therapy shows promise in integrating evolutionary dynamics into treatment scheduling, the stochastic nature of cancer evolution has seldom been taken into account. Various sources of random perturbations can impact the evolution of heterogeneous tumors, making performance metrics of any treatment policy random as well. In this paper, we propose an efficient method for selecting optimal adaptive treatment policies under randomly evolving tumor dynamics. The goal is to improve the cumulative "cost" of treatment, a combination of the total amount of drugs used and the total treatment time. As this cost also becomes random in any stochastic setting, we maximize the probability of reaching the treatment goals (tumor stabilization or eradication) without exceeding a pre-specified threshold (or a "budget"). We use a novel Stochastic Optimal Control formulation and Dynamic Programming to find such "threshold-aware" optimal treatment policies. Our approach enables an efficient algorithm to compute these policies for a range of threshold values simultaneously. Compared to treatment plans shown to be optimal in a deterministic setting, the new "threshold-aware" policies significantly improve the chances of the therapy succeeding under the budget, which is correlated with a lower general drug usage. We illustrate this method using two specific examples, but our approach is far more general and provides a new tool for optimizing adaptive therapies based on a broad range of stochastic cancer models. Author SummaryTumor heterogeneities provide an opportunity to improve therapies by leveraging complex (often competitive) interactions of different types of cancer cells. These interactions are usually stochastic due to both individual cell differences and random events affecting the patient as a whole. The new generation of cancer models strive to account for this inherent stochasticity, and adaptive treatment plans need to reflect it as well. In optimizing such treatment, the most common approach is to maximize the probability of eventually stabilizing or eradicating the tumor. In this paper, we consider a more nuanced version of success, maximizing the probability of reaching these therapy goals before the cumulative burden from the disease and treatment exceed a chosen threshold. Importantly, our method allows computing such optimal treatment plans efficiently and for a range of thresholds at once. If used on a high-fidelity personalized model, our general approach could potentially be used by clinicians to choose the most suitable threshold after a detailed discussion of a specific patients goals (e.g., to include the trade-offs between toxicity and quality of life).