Normal tissue complications are a common side effect of radiation therapy. They are the consequence of the dose of radiation received by the normal tissue surrounding the tumor site. It is not known what function of the dose distribution to the normal tissue drives the presence and severity of the complications. Regarding the density of the dose distribution as a curve, a summary measure is obtained by integrating a weighting function of dose (w(d)) over the dose density. For biological reasons the weight function should be monotonic. We propose to study the dose effect on a clinical outcome using a nonparametric method by estimating this weight function smoothly and subject to the monotonicity constraint. In our approach w(d) is written as a integral of a smooth positive function of d. 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.
Schipper, Matthew; Taylor, Jeremy; and Lin, Xihong, "Generalized Monotonic Functional Mixed Models with Application to Modeling Normal Tissue Complications " (August 2006). The University of Michigan Department of Biostatistics Working Paper Series. Working Paper 61.