title: Joint modelling of longitudinal and multi-state processes: application to clinical progressions in prostate cancer.
abstract: 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.
authors.affiliation: INSERM U1219, ISPED, Université de Bordeaux, Bordeaux, France.
authors.forename: Loïc
authors.initials: L
authors.lastname: Ferrer
authors.affiliation: INSERM U1219, ISPED, Université de Bordeaux, Bordeaux, France.
authors.forename: Virginie
authors.initials: V
authors.lastname: Rondeau
authors.affiliation: Department of Public Health Sciences, University of Chicago and NRG Oncology, Chicago, IL, U.S.A.
authors.forename: James
authors.initials: J
authors.lastname: Dignam
authors.affiliation: Department of Radiation Oncology, University of British Columbia, Vancouver, Canada.
authors.forename: Tom
authors.initials: T
authors.lastname: Pickles
authors.affiliation: INSERM U1219, ISPED, Université de Bordeaux, Bordeaux, France.
authors.forename: Hélène
authors.initials: H
authors.lastname: Jacqmin-Gadda
authors.affiliation: INSERM U1219, ISPED, Université de Bordeaux, Bordeaux, France.
authors.forename: Cécile
authors.initials: C
authors.lastname: Proust-Lima
mesh_terms: D018450:Disease Progression; D006801:Humans; D008137:Longitudinal Studies; D008297:Male; D015233:Models, Statistical; D009364:Neoplasm Recurrence, Local; D011336:Probability; D016016:Proportional Hazards Models; D017430:Prostate-Specific Antigen; D011471:Prostatic Neoplasms / Q000628:therapy*
chemical_list: D017430:Prostate-Specific Antigen
keywords: R; joint modelling; longitudinal process; multi-state process; prostate cancer; shared random effects