Spline Regression









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.


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

Author(s): S Durrleman, R Simon
Journal: Statistics in Medicine
Year published: 1989

The question of nonlinearity in the dose-response relation between particulate matter air pollution and mortality

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

Splines for trend analysis and continuous confounder control

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

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

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

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

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


The %lgtphcurv9 SAS Macro
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
Description: R code for fitting a cubic smoothing spline


Description: R code for performing cubic spline interpolation


Code Plea: Introduction to Splines
Website overview: This webpage gives a good overview of splines with helpful graphics.

Spline Curves
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

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