Calculation of the uncertainty in complication probability for various dose-response models, applied to the parotid gland.
OBJECTIVE
Usually, models that predict normal tissue complication probability (NTCP) are fitted to clinical data with the maximum likelihood (ML) method. This method inevitably causes a loss of information contained in the data. In this study, an alternative method is investigated that calculates the parameter probability distribution (PD), and, thus, conserves all information. The PD method also allows the calculation of the uncertainty in the NTCP, which is an (often-neglected) prerequisite for the intercomparison of both treatment plans and NTCP models. The PD and ML methods are applied to parotid gland data, and the results are compared.


METHODS
The drop in salivary flow due to radiotherapy was measured in 25 parotid glands of 15 patients. Together with the parotid gland dose-volume histograms (DVH), this enabled the calculation of the parameter PDs for three different NTCP models (Lyman, relative seriality, and critical volume). From these PDs, the NTCP and its uncertainty could be calculated for arbitrary parotid gland DVHs. ML parameters and resulting NTCP values were calculated also.


RESULTS
All models fitted equally well. The parameter PDs turned out to have nonnormal shapes and long tails. The NTCP predictions of the ML and PD method usually differed considerably, depending on the NTCP model and the nature of irradiation. NTCP curves and ML parameters suggested a highly parallel organization of the parotid gland.


CONCLUSIONS
Considering the substantial differences between the NTCP predictions of the ML and PD method, the use of the PD method is preferred, because this is the only method that takes all information contained in the clinical data into account. Furthermore, PD method gives a true measure of the uncertainty in the NTCP.
Schilstra
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Department of Radiation Oncology, Groningen University Hospital, Hanzeplein 1, PO Box 30.001, 9700 RB Groningen, The Netherlands.
Meertens
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D016001:Confidence Intervals; D004307:Dose-Response Relationship, Radiation; D006258:Head and Neck Neoplasms / Q000532:radiotherapy; D006801:Humans; D016013:Likelihood Functions; D008954:Models, Biological; D010306:Parotid Gland / Q000187:drug effects / Q000502:physiology / Q000528:radiation effects*; D010862:Pilocarpine / Q000494:pharmacology; D010865:Pilot Projects; D011336:Probability; D011836:Radiation Tolerance; D011837:Radiation-Protective Agents / Q000494:pharmacology
D011837:Radiation-Protective Agents; D010862:Pilocarpine