Logistic regression when covariates are random effects from a non-linear mixed model

Rolando De la Cruz, Guillermo Marshall, Fernando A. Quintana

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Pages (from-to)735-749
Number of pages15
JournalBiometrical Journal
Issue number5
StatePublished - Sep 2011


  • Best linear unbiased predictor (BLUP) and two-stage estimator
  • Gaussian quadrature methods
  • Laplace approximation
  • Logistic regression model
  • Non-linear mixed-effects models


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