# Describe two assumptions or limitations of modelling NTCP

Question 1. There are a large number of fractionation schedules being considered for stereotactic lung cancer treatments (Kestin et al 2014 ‘Dose-response relationship with clinical outcome for lung steteotactic body radiotherapy (SBRT) delivered via online image guidance’ Radiotherapy and Oncology; 110: 499-504). Two schedules considered are the following:

18 Gy x 3 fractions 7.5 Gy x 8 fractions
The alpha/beta value for lung tumours has been considered to range between 4 and 8 Gy (Van Leeuwen, C. M., A. L. Oei, J. Crezee, A. Bel, N. A. P. Franken, L. J. A. Stalpers and H. P. Kok (2018). “The alfa and beta of tumours: a review of parameters of the linear-quadratic model, derived from clinical radiotherapy studies.” Radiation Oncology 13(1).). An estimated alpha/beta value of 4Gy could be used for normal tissue lung.

You can assume that 50% of the normal lung volume receives 60% of the target dose and 50% of the normal lung volume receives 10% of the target dose

a. How would you compare these different prescription doses to establish if they are equivalent or not?

b. Using the methodology you have suggested in question 1 calculate equivalent dose values for all of these schedules. Which of these schedules is likely to result in the greatest impact to the tumour?

c. What assumptions have you made in your calculations? How do these assumptions impact on your results?

d. What impact would a change in alpha/beta value for the lung tumour between 4 and 8 Gy have on your results?

e. Dose within the target volume may vary between 95% and 107% of the prescribed dose. What impact does this have on your results I If the delivered dose is actually 95% of the prescribed dose what impact does this have on your conclusions?

Ii If the delivered dose is actually 107% of the prescribed what impact does this have on your conclusions?

Question 2.
Current understanding and recommended modelling techniques for radiation pneumonitis has been presented in the lung QUANTEC report (Marks, L. B., S. M. Bentzen, J. O. Deasy, F. M. Kong, J. D. Bradley, I. S. Vogelius, I. El Naqa, J. L. Hubbs, J. V. Lebesque, R. D. Timmerman, M. K. Martel and A. Jackson (2010). “Radiation dose-volume effects in the lung.” Int J Radiat Oncol Biol Phys 76(3 Suppl): S70-76.). This report suggests that the Lyman Kutcher Burman (a probit) model and a logit model could both be considered in modelling risk estimates and presents possible different parameters for each.

Some possible parameters for the risk of radiation penumonitis extracted from this paper include the following: a / b = 4 GyFor a logit fit: TD50 = 30.8 Gy and g50=0.97 For the Lyman Kutcher Burman model: TD50=31.4 Gy, m=0.45 and n=1.03
a) Determine the risk of radiation pneumonitis (lung damage) for the logit models for the fractionation schedules presented in question 1.

b) Describe two assumptions or limitations of modelling NTCP.