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.

Joint modelling of longitudinal and multi-state processes: application to clinical progressions in prostate cancer.

Joint modelling of longitudinal and survival data is increasingly used in clinical trials on cancer. In prostate cancer for example, these models permit to account for the link between longitudinal measures of prostate-specific antigen (PSA) and time of clinical recurrence when studying the risk of relapse. In practice, multiple types of relapse may occur successively. Distinguishing these transitions between health states would allow to evaluate, for example, how PSA trajectory and classical covariates impact the risk of dying after a distant recurrence post-radiotherapy, or to predict the risk of one specific type of clinical recurrence post-radiotherapy, from the PSA history. In this context, we present a joint model for a longitudinal process and a multi-state process, which is divided into two sub-models: a linear mixed sub-model for longitudinal data and a multi-state sub-model with proportional hazards for transition times, both linked by a function of shared random effects. Parameters of this joint multi-state model are estimated within the maximum likelihood framework using an EM algorithm coupled with a quasi-Newton algorithm in case of slow convergence. It is implemented under R, by combining and extending mstate and JM packages. The estimation program is validated by simulations and applied on pooled data from two cohorts of men with localized prostate cancer. Thanks to the classical covariates available at baseline and the repeated PSA measurements, we are able to assess the biomarker's trajectory, define the risks of transitions between health states and quantify the impact of the PSA dynamics on each transition intensity. Copyright © 2016 John Wiley & Sons, Ltd.