Proposal of a general framework to categorize continuous predictor variables

The use of discretized variables in the development of prediction models is a common practice, in part because the decision-making process is more natural when it is based on rules created from segmented models. Although this practice is perhaps more common in medicine, it is extensible to any area of knowledge where a predictive model helps in decision-making. Therefore, providing researchers with a useful and valid categorization method could be a relevant issue when developing prediction models. In this paper, we propose a new general methodology that can be applied to categorize a predictor variable in any regression model where the response variable belongs to the exponential family distribution. Furthermore, it can be applied in any multivariate context, allowing to categorize more than one continuous covariate simultaneously. In addition, a computationally very efficient method is proposed to obtain the optimal number of categories, based on a pseudo-BIC proposal. Several simulation studies have been conducted in which the efficiency of the method with respect to both the location and the number of estimated cut-off points is shown. Finally, the categorization proposal has been applied to a real data set of 543 patients with chronic obstructive pulmonary disease from Galdakao Hospital's five outpatient respiratory clinics, who were followed up for 10 years. We applied the proposed methodology to jointly categorize the continuous variables six-minute walking test and forced expiratory volume in one second in a multiple Poisson generalized additive model for the response variable rate of the number of hospital admissions by years of follow-up. The location and number of cut-off points obtained were clinically validated as being in line with the categorizations used in the literature.