Spline Regression

Overview

Software

Description

Websites

Readings

Courses

 

Overview

In regression modeling when we include a continuous predictor variable in our model, either as the main exposure of interest or as a confounder, we are making the assumption that the relationship between the predictor variable and the outcome is linear. In other words, a one unit increase in the predictor variable is associated with a fixed difference in the outcome. Thus, we make no distinction between a one unit increase in the predictor variable near the minimum value and a one unit increase in the predictor variable near the maximum value. This assumption of linearity may not always be true, and may lead to an incorrect conclusion about the relationship between the exposure and outcome, or in the case of a confounder that violates the linearity assumption, may lead to residual confounding. Spline regression is one method for testing non-linearity in the predictor variables and for modeling non-linear functions.

Readings

Methodological Articles

Author(s): AM Strasak, N Umlauf, RM Pfeiffer, S Lang
Journal: Computational Statistics and Data Analysis
Year published: 2011

Flexible regression models with cubic splines(link is external and opens in a new window)

Author(s): S Roberts, MA Martin
Journal: American Journal of Epidemiology
Year published: 2006

Splines for trend analysis and continuous confounder control(link is external and opens in a new window)

Author(s): CJ Howe, SR Cole, DJ Westreich, S Greenland, S Napravnik, JJ Eron Jr.
Journal: Epidemiology
Year published: 2011

Application Articles

Childhood, adolescent and early adult body mass index in relation to adult mortality: results from the British 1946 birth cohort(link is external and opens in a new window)

Author(s): BH Strand, D Kuh, I Shah, J Guralnik, R Hardy
Journal: Journal of Epidemiology and Community Health
Year published: 2012

Psychosocial factors and coronary calcium in adults without clinical cardiovascular disease(link is external and opens in a new window)

Author(s): AV Diez Roux, N Ranjit, L Powell, S Jackson, TT Lewis, S Shea, C Wu
Journal: Annals of Internal Medicine
Year published: 2006

Spirometric reference values from a sample of the general U.S. population(link is external and opens in a new window)

Author(s): JL Hankinson, JR Odencrantz, KB Fedan
Journal: American Journal of Respiratory and Critical Care Medicine
Year published: 1999

Amount of leisure-time physical activity and risk of nonfatal myocardial infarction(link is external and opens in a new window)

Author(s): GS Lovasi, RN Lemaitre, DS Siscovick, S Dublin, JC Bis, T Lumley, SR Heckbert, NL Smith, BM Psaty
Journal: Annals of Epidemiology
Year published: 2007

Software


The %lgtphcurv9 SAS Macro(link is external and opens in a new window)
Description: This webpage provides a link to a SAS Macro, as well as documentation, for implementing restricted cubic splines in SAS.

Fit a Smoothing Spline(link is external and opens in a new window)
Description: R code for fitting a cubic smoothing spline

SplineFun(link is external and opens in a new window)

Description: R code for performing cubic spline interpolation

Websites


Code Plea: Introduction to Splines(link is external and opens in a new window)
Website overview: This webpage gives a good overview of splines with helpful graphics.

Spline Curves(link is external and opens in a new window)
Website overview: A book chapter written by Dr. Donald House from Clemson University that gives a very good background on splines.

A Primer on Regression Splines(link is external and opens in a new window)

Website overview: An online PDF by Jeffrey S. Racine giving an overview of regression splines and includes sample R code.

Join the Conversation

Have a question about methods? Join us on Facebook

JOIN(link is external and opens in a new window)