Benchmarking proton RBE models.

To biologically optimise proton therapy, models which can accurately predict variations in
proton RBE are essential. Current phenomenological models show large disagreements in RBE
predictions, due to different model assumptions and differences in the data to which they were fit. In
this work, thirteen RBE models were benchmarked against a comprehensive proton RBE dataset to
evaluate predictions when all models are fit using the same data and fitting techniques, and to assess
the statistical robustness of the models.
Approach: Model performance was initially evaluated by fitting to the full dataset, and then a cross-
validation approach was applied to assess model generalisability and robustness. The impact of
weighting the fit and the choice of biological endpoint (either single or multiple survival levels) was
also evaluated.
Results: Fitting the models to a common dataset reduced differences between their predictions,
however significant disagreements remained due to different underlying assumptions. All models
performed poorly under cross-validation in the weighted fits, suggesting that some uncertainties on
the experimental data were significantly underestimated, resulting in over-fitting and poor
performance on unseen data. The simplest model, which depends linearly on the LET but has no tissue
or dose dependence, performed best for a single survival level. However, when fitting to multiple
survival levels simultaneously, more complex models with tissue dependence performed better. All
models had significant residual uncertainty in their predictions compared to experimental data.
Significance: This analysis highlights that poor quality of error estimation on the dose response
parameters introduces substantial uncertainty in model fitting. The significant residual error present
in all approaches illustrates the challenges inherent in fitting to large, heterogeneous datasets and the
importance of robust statistical validation of RBE models.

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