Assessing the uncertainty in a normal tissue complication probability difference (∆NTCP): radiation-induced liver disease (RILD) in liver tumour patients treated with proton vs X-ray therapy

Modern radiotherapy technologies such as proton beam therapy (PBT) permit dose escalation to the tumour and minimize unnecessary doses to normal tissues. To achieve appropriate patient selection for PBT, a normal tissue complication probability (NTCP) model can be applied to estimate the risk of treatment-related toxicity relative to X-ray therapy (XRT). A methodology for estimating the difference in NTCP (∆NTCP), including its uncertainty as a function of dose to normal tissue, is described in this study using the Delta method, a statistical method for evaluating the variance of functions, considering the variance-covariance matrix. We used a virtual individual patient dataset of radiation-induced liver disease (RILD) in liver tumour patients who were treated with XRT as a study model. As an alternative option for individual patient data, dose-bin data, which consists of the number of patients who developed toxicity in each dose level/bin and the total number of patients in that dose level/bin, are useful for multi-institutional data sharing. It provides comparable accuracy with individual patient data when using the Delta method. With reliable NTCP models, the ∆NTCP with uncertainty might potentially guide the use of PBT; however, clinical validation and a cost-effectiveness study are needed to determine the appropriate ∆NTCP threshold.