Bayesian generalized monotonic functional mixed models for the effects of radiation dose histograms on normal tissue complications.

When treating cancer patients with radiation therapy, the normal tissue in an organ close to the tumour usually receives some dose of radiation. The dose is not of the same intensity throughout the organ. This radiation can cause normal tissue complications, so for treatment planning purposes, it is important to understand the relationship between the distribution of dose intensities in the organ and the occurrence of complications. One general summary measure of the dose effect is obtained by integrating a weighting function (w(d)) over the dose distribution. The weighting function w(d) should be monotone for biological reasons. Because the true shape of w(d) is not known, we estimate it non-parametrically subject to the monotonicity constraint. In our approach w(d) is written as a weighted sum of monotone basis functions. The weights in this sum are formulated as a mixture of point mass at zero and a Gamma random variable. A key feature of our method is that it allows for flat regions through the use of this mixture prior. The model is estimated using a Markov Chain Monte Carlo algorithm. We illustrate our method with data from a head and neck cancer study in which the irradiation of the parotid gland results in loss of saliva flow.