A test of the claim that plan rankings are determined by relative complication and tumor-control probabilities

Abstract

Purpose: This study tests an accepted claim regarding tumor control (TCP) and normal tissue complication (NTCP) probability functions. The claim is that treatment plans can be ranked using relative probabilities, even when the absolute probabilities are unknown. The assumption supports the use of probability models for plan optimization and the comparison of treatment techniques.

Methods: The claim was tested using a hypothetical model consisting of two tissues, and illustrated with clinical data. Plans were scored using the probability of uncomplicated tumor control. The scores of different plans were compared by fixing their relative risks for an individual tissue complication, but adjusting the absolute probability levels up or down. The tested claim is that the plan rankings should not change.

Results: In the two-tissue model, the rankings of competing plans were reversed by doubling all the probabilities. The preference ordering of lung cancer plans changed after the risk of pulmonary complication was reduced by 3-fold. In another site, the ranking of plans by overall complication-free probability was disturbed by errors that preserved the ordering of plans with respect to any individual complication. An adjustment of +/- 2.5% in the initial NTCP values for two tissues changed the direction in which a plan score moved in response to a fixed tradeoff in complication risk in an optimization search.

Conclusions: Contrary to claims, plan rankings are not determined by the relative probabilities of adverse events. The effect on plan scores of trading one complication for another depends on the absolute levels of risk. Absolute errors in NTCP and TCP functions result in the wrong ranking of plans, even when relative probabilities are correct. An optimization routine based on TCP and NTCP calculations may be forced in the wrong direction by small errors in the probability estimates.