A shared frailty model for multivariate longitudinal data on adverse event of radiation therapy

Oral mucositis is an inflammatory adverse event when treating head and neck cancer patients with radiation therapy (RT). The severity of its occurrence is believed to mainly depend on its site and the distribution of a cumulative radiation dose in the mouth area. The motivating study investigating differences in radiosensitivities (mucositis progression) at distinct sites where the severity of mucositis is assessed regularly at eight distinct sites on an ordinal scale results in multivariate longitudinal data and thus poses certain challenges. To deal with the multivariate longitudinal data in this particular setting, we take a time-to-event approach focusing on the first occurrence of severe mucositis at the distinct sites using the fact that the site-specific cumulative radiation dose thought to be the main driver of oral mucositis develops over time. Thereby, we may address multivariate longitudinal processes in a simpler and more compact fashion. In this article, to find out differences in mucositis progression at eight distinct sites we propose a shared frailty model for multivariate parallel processes within individuals. The shared frailty model directly incorporating 'process indicators' as covariates turns out to adequately explain the differences in the parallel processes (here, mucositis progressions at distinct sites) while taking individual effects into account. The parallel result with the one from the previous analysis based on the same data but conducted with an alternative statistical methodology shows adequacy of the proposed approach.