Table 1 Methods to approximate true non-linear effects

Categorization

The confounder is grouped (e.g. on pre-specified percentile values such as quartiles) and subsequently the outcome is regressed on the exposure and the now categorical confounding variable

Easy to apply

Homogeneity of the effects is assumed within groups, resulting in severe loss of information and possibly residual confounding

Non-linear terms

The outcome is regressed on the confounder and the non-linear term of that same confounder, e.g., a quadratic term

Easy to apply

Adding non-linear order terms increases the flexibility of the model

Coefficients are difficult to interpret^*

Linear spline regression

First, the confounding variable is categorized and subsequently a first power function is fitted for each category separately. After fitting the spline functions these are added to the regression model

Good approximation of the true effect

Coefficients are easy to interpret

Restricted cubic spline regression

Same as linear spline regression, but instead a more flexible third power function is fitted for each category separately. To avoid instability in the tails where there’s not much data, restricted cubic splines are often used where at the tails a line is fitted rather than a curve.

Good approximation of the true effect

Adding splines increases the flexibility of the model

Coefficients are difficult to interpret^*