Premium
Maximum likelihood estimation in the joint analysis of time‐to‐event and multiple longitudinal variables
Author(s) -
Lin Haiqun,
McCulloch Charles E.,
Mayne Susan T.
Publication year - 2002
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1179
Subject(s) - covariate , categorical variable , event (particle physics) , longitudinal study , statistics , variable (mathematics) , econometrics , random effects model , longitudinal data , variables , event data , computer science , mathematics , data mining , medicine , meta analysis , quantum mechanics , mathematical analysis , physics
Joint modelling of longitudinal and survival data has received much attention in recent years. Most have concentrated on a single longitudinal variable. This paper considers joint modelling in the presence of multiple longitudinal variables. We explore direct association of time‐to‐event and multiple longitudinal processes through a frailty model and use a mixed effects model for each of the longitudinal variables. Correlations among the longitudinal variables are induced through correlated random effects. We allow effects of categorical and continuous covariates on both longitudinal and time‐to‐event responses and explore interactions between the longtudinal variables and other covariates on time‐to‐event. Estimates of the parameters are obtained by maximizing the joint likelihood for the longitudinal variable processes and the event process. We use a one‐step‐late EM algorithm to handle the direct dependence of the event process on the modelled longitudinal variables along with the presence of other fixed covariates in both processes. We argue that such a joint analysis with multiple longitudinal variables is advantageous to one with only a single longitudinal variable in revealing interplay among multiple longitudinal variables and the time‐to‐event. Copyright © 2002 John Wiley & Sons, Ltd.