A Bayesian mixture model relating dose to critical organs and functional complication in 3D conformal radiation therapy

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Abstract
A goal of cancer radiation therapy is to deliver maximum dose to the target tumor while minimizing complications due to irradiation of critical organs. Technological advances in 3D conformal radiation therapy has allowed great strides in realizing this goal; however, complications may still arise. Critical organs may be adjacent to tumors or in the path of the radiation beam. Several mathematical models have been proposed that describe the relationship between dose and observed functional complication; however, only a few published studies have successfully fit these models to data using modern statistical methods which make efficient use of the data. One complication following radiation therapy of head and neck cancers is the patient's inability to produce saliva. Xerostomia (dry mouth) leads to high susceptibility to oral infection and dental caries and is, in general, unpleasant and an annoyance. We present a dose–damage–injury model that subsumes any of the various mathematical models relating dose to damage. The model is a nonlinear, longitudinal mixed effects model where the outcome (saliva flow rate) is modeled as a mixture of a Dirac measure at zero and a gamma distribution whose mean is a function of time and dose. Bayesian methods are used to estimate the relationship between dose delivered to the parotid glands and the observational outcome—saliva flow rate. A summary measure of the dose–damage relationship is modeled and assessed by a Bayesian χ2 test for goodness-of-fit.