Using Generalized Additive Models to Detect and Estimate Threshold Associations

Benedetti Andrea, Abrahamowicz Michal, Leffondré Karen, Goldberg Mark S. and Tamblyn Robyn
Additional contact information
Benedetti Andrea: McGill University
Abrahamowicz Michal: McGill University
Leffondré Karen: Université de Bordeaux 2
Goldberg Mark S.: McGill University
Tamblyn Robyn: McGill University

The International Journal of Biostatistics, 2009, vol. 5, issue 1, 27

Abstract: In a variety of research settings, investigators may wish to detect and estimate a threshold in the association between continuous variables. A threshold model implies a non-linear relationship, with the slope changing at an unknown location. Generalized additive models (GAMs) (Hastie and Tibshirani, 1990) estimate the shape of the non-linear relationship directly from the data and, thus, may be useful in this endeavour.We propose a method based on GAMs to detect and estimate thresholds in the association between a continuous covariate and a continuous dependent variable. Using simulations, we compare it with the maximum likelihood estimation procedure proposed by Hudson (1966).We search for potential thresholds in a neighbourhood of points whose mean numerical second derivative (a measure of local curvature) of the estimated GAM curve was more than one standard deviation away from 0 across the entire range of the predictor values. A threshold association is declared if an F-test indicates that the threshold model fit significantly better than the linear model.For each method, type I error for testing the existence of a threshold against the null hypothesis of a linear association was estimated. We also investigated the impact of the position of the true threshold on power, and precision and bias of the estimated threshold.Finally, we illustrate the methods by considering whether a threshold exists in the association between systolic blood pressure (SBP) and body mass index (BMI) in two data sets.

Keywords: generalized additive models; GAMs; threshold; simulation; linear regression; F-test (search for similar items in EconPapers)
Date: 2009
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.2202/1557-4679.1172 (text/html)
For access to full text, subscription to the journal or payment for the individual article is required.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bpj:ijbist:v:5:y:2009:i:1:n:26

Ordering information: This journal article can be ordered from
https://www.degruyter.com/journal/key/ijb/html

DOI: 10.2202/1557-4679.1172

Access Statistics for this article

The International Journal of Biostatistics is currently edited by Antoine Chambaz, Alan E. Hubbard and Mark J. van der Laan

More articles in The International Journal of Biostatistics from De Gruyter
Bibliographic data for series maintained by Peter Golla ().