Spline Regression
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
Dose-response and trend analysis in epidemiology: alternatives to categorical analysis(link is external and opens in a new window)
Author(s): S GreenlandJournal: Epidemiology
Year published: 1995
Author(s): K Steenland, JA Deddens
Journal: Epidemiology
Year published: 2004
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 Durrleman, R Simon
Journal: Statistics in Medicine
Year published: 1989
Author(s): S Roberts, MA Martin
Journal: American Journal of Epidemiology
Year published: 2006
Author(s): CJ Howe, SR Cole, DJ Westreich, S Greenland, S Napravnik, JJ Eron Jr.
Journal: Epidemiology
Year published: 2011
Application Articles
Author(s): BH Strand, D Kuh, I Shah, J Guralnik, R Hardy
Journal: Journal of Epidemiology and Community Health
Year published: 2012
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
Author(s): JL Hankinson, JR Odencrantz, KB Fedan
Journal: American Journal of Respiratory and Critical Care Medicine
Year published: 1999
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
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.
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