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Generalized monotonic functional mixed models with application to modelling normal tissue complications

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  • Matthew Schipper
  • Jeremy M. G. Taylor
  • Xihong Lin

Abstract

Summary. Normal tissue complications are a common side effect of radiation therapy. They are the consequence of the dose of radiation that is received by the normal tissue surrounding the site of the tumour. Within a specified organ each voxel receives a certain dose of radiation, leading to a distribution of doses over the organ. It is often not known what aspect of the dose distribution drives the presence and severity of the complications. A summary measure of the dose distribution can be obtained by integrating a weighting function of dose (w(d)) over the density of dose. For biological reasons the weight function should be monotonic. We propose a generalized monotonic functional mixed model to study the dose effect on a clinical outcome by estimating this weight function non‐parametrically by using splines and subject to the monotonicity constraint, while allowing for overdispersion and correlation of multiple obervations within the same subject. 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.

Suggested Citation

  • Matthew Schipper & Jeremy M. G. Taylor & Xihong Lin, 2008. "Generalized monotonic functional mixed models with application to modelling normal tissue complications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(2), pages 149-163, April.
    • Handle: RePEc:bla:jorssc:v:57:y:2008:i:2:p:149-163
    DOI: 10.1111/j.1467-9876.2007.00606.x
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    Cited by:

    1. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    2. Liebl, Dominik & Walders, Fabian, 2019. "Parameter regimes in partial functional panel regression," Econometrics and Statistics, Elsevier, vol. 11(C), pages 105-115.
    3. Eduardo L. Montoya, 2020. "On the Number of Independent Pieces of Information in a Functional Linear Model with a Scalar Response," Stats, MDPI, vol. 3(4), pages 1-16, November.

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