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

Authors

  • Rolando De la Cruz,

    Corresponding author
    1. Departamento de Salud Páblica, Escuela de Medicina, Pontificia Universidad Católica de Chile, Marcoleta 434, Casilla 114D, Santiago, Chile
    2. Departamento de Estadstica, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
    • Phone: +56-2-354-8034, Fax: +56-2-633-1840
    Search for more papers by this author
  • Guillermo Marshall,

    1. Departamento de Estadstica, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
    Search for more papers by this author
  • Fernando A. Quintana

    1. Departamento de Estadstica, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Casilla 306, Santiago 22, Chile
    Search for more papers by this author

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.

Ancillary