Modeling tumor control probability for spatially inhomogeneous risk of failure based on clinical outcome data

Objectives of this work are (1) to derive a general clinically relevant approach to model tumor control probability (TCP) for spatially variable risk of failure and (2) to demonstrate its applicability by estimating TCP for patients planned for photon and proton irradiation.

The approach divides the target volume into sub-volumes according to retrospectively observed spatial failure patterns. The product of all sub-volume TCP_i values reproduces the observed TCP for the total tumor. The derived formalism provides for each target sub-volume i the tumor control dose (D_50,i) and slope (γ_50,i) parameters at 50% TCP_i. For a simultaneous integrated boost (SIB) prescription for 45 advanced head and neck cancer patients, TCP values for photon and proton irradiation were calculated and compared. The target volume was divided into gross tumor volume (GTV), surrounding clinical target volume (CTV), and elective CTV (CTVE). The risk of a local failure in each of these sub-volumes was taken from the literature.

Convenient expressions for D_50,i and γ_50,i were provided for the Poisson and the logistic model. Comparable TCP estimates were obtained for photon and proton plans of the 45 patients using the sub-volume model, despite notably higher dose levels (on average +4.9%) in the low-risk CTVE for photon irradiation. In contrast, assuming a homogeneous dose response in the entire target volume resulted in TCP estimates contradicting clinical experience (the highest failure rate in the low-risk CTVE) and differing substantially between photon and proton irradiation.

The presented method is of practical value for three reasons: It (a) is based on empirical clinical outcome data; (b) can be applied to non-uniform dose prescriptions as well as different tumor entities and dose-response models; and (c) is provided in a convenient compact form. The approach may be utilized to target spatial patterns of local failures observed in patient cohorts by prescribing different doses to different target regions. Its predictive power depends on the uncertainty of the employed established TCP parameters D₅₀ and γ₅₀ and to a smaller extent on that of the clinically observed pattern of failure risk.