Restricted Cubic Spline Regression: A Brief Introduction

Sometimes, the relationship between an outcome (dependent) variable and the explanatory (independent) variable(s) is not linear. Restricted cubic splines are a way of testing the hypothesis that the relationship is not linear or summarizing a relationship that is too non-linear to be usefully summarized by a linear relationship. Restricted cubic splines are just a transformation of an independent variable. Thus, they can be used not only in ordinary least squares regression, but also in logistic regression, survival analysis, and so on. The range of values of the independent variable is split up, with “knots” defining the end of one segment and the start of the next. Separate curves are fit to each segment. Overall, the splines are defined so that the resulting fitted curve is smooth and continuous. This presentation describes when splines might be used, how the splines are defined, choice of knots, and interpretation of the regression results.