Spurious interaction as a result of categorization

It is common in applied epidemiological and clinical research to convert continuous variables into categorical variables by grouping values into categories. Such categorized variables are then often used as exposure variables in some regression model. There are numerous statistical arguments why this practice should be avoided, and in this paper we present yet another such argument.

We show that categorization may lead to spurious interaction in multiple regression models. We give precise analytical expressions for when this may happen in the linear regression model with normally distributed exposure variables, and we show by simulations that the analytical results are valid also for other distributions. Further, we give an interpretation of the results in terms of a measurement error problem.

We show that, in the case of a linear model with two normally distributed exposure variables, both categorized at the same cut point, a spurious interaction will be induced unless the two variables are categorized at the median or they are uncorrelated. In simulations with exposure variables following other distributions, we confirm this general effect of categorization, but we also show that the effect of the choice of cut point varies over different distributions.

Categorization of continuous exposure variables leads to a number of problems, among them spurious interaction effects. Hence, this practice should be avoided and other methods should be considered.