Modelling bivariate ordinal responses smoothly with examples from ophthalmology and genetics

Research output: Contribution to journalJournal articleResearchpeer-review

  • R Bustami
  • E Lesaffre
  • G Molenberghs
  • Loos, Ruth
  • M Danckaerts
  • R Vlietinck

A non-parametric implementation of the bivariate Dale model (BDM) is presented as an extension of the generalized additive model (GAM) of Hastie and Tibshirani. The original BDM is an example of a bivariate generalized linear model. In this paper smoothing is introduced on the marginal as well as on the association level. Our non-parametric procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in the linear BDM, hence it also provides a kind of goodness-of-fit test for a bivariate generalized linear model. Cubic smoothing spline functions for the covariates are estimated by maximizing a penalized version of the log-likelihood. The method is applied to two studies. The first study is the classical Wisconsin Epidemiologic Study of Diabetic Retinopathy. The second study is a twin study, where the association between the elements of twin pairs is of primary interest. The results show that smoothing on the association level can give a significant improvement to the model fit.

Original languageEnglish
JournalStatistics in Medicine
Volume20
Issue number12
Pages (from-to)1825-42
Number of pages18
ISSN0277-6715
DOIs
Publication statusPublished - 30 Jun 2001
Externally publishedYes

    Research areas

  • Adolescent, Child, Child Behavior/physiology, Diabetic Retinopathy/epidemiology, Female, Humans, Likelihood Functions, Logistic Models, Male, Models, Biological, Models, Genetic, Models, Statistical, Risk Factors, Statistics, Nonparametric, Twin Studies as Topic

ID: 258040802