title: Logistic regression when covariates are random effects from a non-linear mixed model.
abstract: In many studies, the association of longitudinal measurements of a continuous response and a binary outcome are often of interest. A convenient framework for this type of problems is the joint model, which is formulated to investigate the association between a binary outcome and features of longitudinal measurements through a common set of latent random effects. The joint model, which is the focus of this article, is a logistic regression model with covariates defined as the individual-specific random effects in a non-linear mixed-effects model (NLMEM) for the longitudinal measurements. We discuss different estimation procedures, which include two-stage, best linear unbiased predictors, and various numerical integration techniques. The proposed methods are illustrated using a real data set where the objective is to study the association between longitudinal hormone levels and the pregnancy outcome in a group of young women. The numerical performance of the estimating methods is also evaluated by means of simulation.
authors.affiliation: Departamento de Salud Páblica, Escuela de Medicina, Pontificia Universidad Católica de Chile, Marcoleta 434, Casilla 114D, Santiago, Chile. rolando@med.puc.cl
authors.forename: Rolando
authors.initials: R
authors.lastname: De la Cruz
authors.forename: Guillermo
authors.initials: G
authors.lastname: Marshall
authors.forename: Fernando A
authors.initials: FA
authors.lastname: Quintana
mesh_terms: D000704:Analysis of Variance; D018997:Chorionic Gonadotropin, beta Subunit, Human / Q000494:pharmacology; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D008137:Longitudinal Studies; D017711:Nonlinear Dynamics; D011247:Pregnancy; D012372:ROC Curve; D013269:Stochastic Processes
chemical_list: D018997:Chorionic Gonadotropin, beta Subunit, Human