Estimating and presenting non-linear associations with restricted cubic splines

Most of the regression models commonly used in epidemiology-including logistic regression and methods for time-to-event outcomes such as Cox regression-define the relationship between a set of covariates and the outcome of interest using linear functions, thus making implicit assumptions of linearity for continuous covariates. Categorizing continuous covariates, which represents a common option to address non-linearities, introduces additional assumptions and has recognized limitations in terms of results interpretation. Restricted cubic splines (RCS) offer a flexible alternative tool that can improve the model fit in the presence of non-linear associations, overcoming many of the limitations of categorical approaches and providing information on the shape of the exposure-outcome relationship. Including RCS transformations in regression models, however, is not straightforward analytically and presents challenges in terms of interpretation and graphical presentation of the exposure-outcome association. In this paper, we provide an introduction to the application of RCS in regression modeling for assessing non-linear exposure-outcome associations in epidemiological studies. We present RCS as a flexible extension of categorization and describe the two key steps of integrating RCS in regression: model fitting and graphical presentation. We detail key considerations that can guide the choice of RCS transformations, the interpretation of regression output, and the translation of regression results into graphical displays of the exposure-outcome association. To accompany this presentation, we also provide a set of functions and examples in R, Stata, and SAS, thereby providing a comprehensive set of tools for flexibly and robustly incorporating continuous covariates into regression modeling.