title: A multivariate random-effects model with restricted parameters: application to assessing radiation therapy for brain tumours.
abstract: In clinical studies, multiple endpoints are often measured for each patient longitudinally. The multivariate random-effects or random coefficient model has been a useful method for analysis. However, medical research problems may impose restrictions on the model parameters of interests. For example, in a paediatric brain tumour study on radiation therapy, there is a natural ordering in the white matter relaxation time of brain tissues among different regions surrounding the primary tumour, i.e. the closer a specific region of brain tissues is to the centre of primary tumour, the shorter is the relaxation time. Such parameter constraints should be accounted for in the analysis. This article proposes a class of multivariate random coefficient models with restricted parameters and derives its maximum likelihood estimates (MLE). We propose a modified EM algorithm for the quadratic optimalization with linear inequality constraints necessary in deriving the MLE. The method is applied to analysing the paediatric brain tumour study.
authors.affiliation: Division of Biostatistics, University of Maryland Greenebaum Cancer Center, 22 South Greene Street, Baltimore, MD 21201, USA. hfang@umm.edu
authors.forename: Hong-Bin
authors.initials: HB
authors.lastname: Fang
authors.forename: Guo-Liang
authors.initials: GL
authors.lastname: Tian
authors.forename: Xiaoping
authors.initials: X
authors.lastname: Xiong
authors.forename: Ming
authors.initials: M
authors.lastname: Tan
mesh_terms: D000293:Adolescent; D000465:Algorithms; D001932:Brain Neoplasms / Q000532:radiotherapy*; D002648:Child; D002675:Child, Preschool; D006801:Humans; D008137:Longitudinal Studies; D008279:Magnetic Resonance Imaging; D008954:Models, Biological; D015233:Models, Statistical; D015999:Multivariate Analysis; D011878:Radiotherapy