Continuous Variables: to Categorize or to Model?

Continuous variables are often encountered in life. We measure age, blood pressure and many other things. In medicine, such measurements are often used to assess risk or prognosis or to select a therapy. However, the question of how best to use information from continuous variables is relevant in many areas. To relate an outcome variable to a single continuous variable, a suitable regression model is required. A simple and popular approach is to assume a linear effect, but the linearity assumption may be violated. Alternatively, researchers typically apply cutpoints to categorize the variable, implying regression models with step functions. We illustrate problems caused by categorization and introduce fractional polynomials (FP) as a useful extension of polynomial regression. Investigating the effect of age as a prognostic factor for breast cancer, we show how conclusions depend critically on how the continuous variable is analyzed.