Tumor control probability of nasopharyngeal carcinoma: a comparison of different mathematical models

Purpose: Radiation dose and tumor volume are factors known to affect the local control of a given type of tumor. Local tumor control is a major factor to consider when a treatment plan is evaluated. This article reports the correlation between tumor control probability, dose, and volume in a retrospective study of 142 patients with nasopharyngeal carcinoma (NPC). Methods and Materials: The tumor volume was outlined and calculated from a computed tomographic scan. Patients were categorized according to tumor volume and radiation dose received in treatment. Local control rate was calculated for each category by the Kaplan-Meier method. Mathematical models were fitted to correlate the local control rate, dose, and volume. Both empirical and mechanistic approaches were attempted; the former included logistic models with two and three parameters, and the latter, the formulation from Brenner and Bentzen with a radiobiological basis. Results: Brenner's model estimated α at 0.041 Gy-1 with 95% confidence limits (-0.032, 0.113) Gy-1. The volume dependent constant h was estimated at 0.160 cm-3 with 95% confidence limits (-0.729, 1.048) cm-3. The Pearson correlation coefficient was 0.64. The magnitude and sign of the fitted parameters were reasonable and consistent with reported clinical experience. The other models were fitted with slightly better goodness of fit (r = 0.65 - 0.68), but with less interpretable parameters. Conclusion: Brenner's model is considered appropriate for a description of the dose and volume effect on the local control of the NPC. It could be used in combination with normal tissue complication probability for treatment plan evaluation to optimize treatment results