Non-linear regression modelling for medical professionals; making curved paths straightforward

Abstract

Regression models provide information on complex relationships between patient factors, investigations, diagnoses, treatments, and outcomes. These inferences underpin evidence-based medicine. However, by default regression models assume straight-line relationships, and the common approach of splitting continuous variables into groups has several disadvantages. We discuss pitfalls with these common approaches, and provide an interactive regression model playground, which acts as a point-and-click showcase of these concepts. More flexible regression modelling techniques are available, which allow non-linear relationships between predictors and outcome to be captured. However, they have been shown to be underused in medical research. We feel a major contributor to this is that more flexible non-linear models are typically explained for a statistical audience, creating a barrier for medical professionals. In this article, we introduce non-linear regression for medical researchers. Specifically, we focus on restricted cubic splines (RCS), which allow curved relationships to be fit, within the context of regression models. This has the benefit that the overall structure of the regression model and its outputs, which are familiar to medical researchers, stays the same, with the simple addition of non-linear modelling of specific variables. We implement RCS in a case study, with accompanying example R scripts (available on GitHub). We also launch an R package (“rmsMD”) which aims to make this technique approachable to medical researchers, as well as creating publication-ready tables and plots. Overall, this article equips medical researchers with an intuitive understanding of non-linear modelling, which can then be applied with the easy-to-use tools provided.