Restricted Cubic Spline Modeling: An Extensive Primer

• Activity Number: 417
• Type: Contributed
• Date/Time: Wednesday, August 6, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Teaching of Statistics in the Health Sciences
• Author(s): Ralph G. O'Brien*+ and Matt Karafa and John Castelloe
• Companies: Cleveland Clinic Foundation and Cleveland Clinic Foundation and SAS Institute, Inc.
• Keywords: spline regression ; natural splines ; statistical modeling ; sample-size planning ; power analysis ; nonlinear regression

Abstract

The restricted cubic spline technique is simple, direct, and very useful, but it is not yet familiar to most analysts, even experts in statistical modeling. This tutorial shows how to use standard linear least squares, logistic, Cox survival, Poisson, or other common regression methods to fit and test smooth functions, Y = f(X), where X is continuous, and f(X) is potentially nonlinear. Also called "natural" splines, the approach offers advantages over standard polynomial models (including with splines), monotonic regression (PAVA), and "free-form" fittings (LOESS, generalized additive models). While the algebra defining f(X) is perplexing, its graphical depictions are straightforward and investigators find them intuitive and realistic. In that common regression methods are the analytical engines, the statistician merely applies all of the familiar tools for computing estimates and confidence/prediction intervals, testing hypotheses, running diagnostics, and performing sample-size analyses. Additional predictors may also be included in the model, as usual. All of this is illustrated by using common software to carry out sample-size planning and data analyses for a realistic study.