Technical note: Optimal allocation of limited proton therapy resources using model-based patient selection

Purpose We consider the following scenario: A radiotherapy clinic has a limited number of proton therapy slots available each day to treat cancer patients of a given tumor site. The clinic's goal is to minimize the expected number of complications in the cohort of all patients of that tumor site treated at the clinic, and thereby maximize the benefit of its limited proton resources. Methods To address this problem, we extend the normal tissue complication probability (NTCP) model-based approach to proton therapy patient selection to the situation of limited resources at a given institution. We assume that, on each day, a newly diagnosed patient is scheduled for treatment at the clinic with some probability and with some benefit Delta NTCP$\Delta NTCP$ from protons over photons, which is drawn from a probability distribution. When a new patient is scheduled for treatment, a decision for protons or photons must be made, and a patient may wait only for a limited amount of time for a proton slot becoming available. The goal is to determine the Delta NTCP$\Delta NTCP$ thresholds for selecting a patient for proton therapy, which optimally balance the competing goals of making use of all available slots while not blocking slots with patients with low benefit. This problem can be formulated as a Markov decision process (MDP) and the optimal thresholds can be determined via a value-policy iteration method. Results The optimal Delta NTCP$\Delta NTCP$ thresholds depend on the number of available proton slots, the average number of patients under treatment, and the distribution of Delta NTCP$\Delta NTCP$ values. In addition, the optimal thresholds depend on the current utilization of the facility. For example, if one proton slot is available and a second frees up shortly, the optimal Delta NTCP$\Delta NTCP$ threshold is lower compared to a situation where all but one slot remain blocked for longer. Conclusions MDP methodology can be used to augment current NTCP model-based patient selection methods to the situation that, on any given day, the number of proton slots is limited. The optimal Delta NTCP$\Delta NTCP$ threshold then depends on the current utilization of the proton facility. Although, the optimal policy yields only a small nominal benefit over a constant threshold, it is more robust against variations in patient load.

Automated summary

This study addresses the situation where a radiotherapy clinic has a limited number of proton therapy slots available each day. By extending the normal tissue complication probability model, the researchers use Markov decision process methodology to determine the optimal thresholds for selecting patients for proton therapy, maximizing the benefit of limited resources.