Use of generalised additive models to categorise continuous variables in clinical prediction

Abstract

Background: In medical practice many, essentially continuous, clinical parameters tend to be categorised by physicians for ease of decision-making. Indeed, categorisation is a common practice both in medical research and in the development of clinical prediction rules, particularly where the ensuing models are to be applied in daily clinical practice to support clinicians in the decision-making process. Since the number of categories into which a continuous predictor must be categorised depends partly on the relationship between the predictor and the outcome, the need for more than two categories must be borne in mind.

Methods: We propose a categorisation methodology for clinical-prediction models, using Generalised Additive Models (GAMs) with P-spline smoothers to determine the relationship between the continuous predictor and the outcome. The proposed method consists of creating at least one average-risk category along with high- and low-risk categories based on the GAM smooth function. We applied this methodology to a prospective cohort of patients with exacerbated chronic obstructive pulmonary disease. The predictors selected were respiratory rate and partial pressure of carbon dioxide in the blood (PCO2), and the response variable was poor evolution. An additive logistic regression model was used to show the relationship between the covariates and the dichotomous response variable. The proposed categorisation was compared to the continuous predictor as the best option, using the AIC and AUC evaluation parameters. The sample was divided into a derivation (60%) and validation (40%) samples. The first was used to obtain the cut points while the second was used to validate the proposed methodology.

Results: The three-category proposal for the respiratory rate was ≤ 20;(20,24];> 24, for which the following values were obtained: AIC=314.5 and AUC=0.638. The respective values for the continuous predictor were AIC=317.1 and AUC=0.634, with no statistically significant differences being found between the two AUCs (p =0.079). The four-category proposal for PCO2 was ≤ 43;(43,52];(52,65];> 65, for which the following values were obtained: AIC=258.1 and AUC=0.81. No statistically significant differences were found between the AUC of the four-category option and that of the continuous predictor, which yielded an AIC of 250.3 and an AUC of 0.825 (p =0.115).

Conclusions: Our proposed method provides clinicians with the number and location of cut points for categorising variables, and performs as successfully as the original continuous predictor when it comes to developing clinical prediction rules.

Figures

Figure 1

Graphical representation of two hypothetical shapes between the predictor and outcome using generalised additive models. (a) Linear relationship (b) Non-linear relationship.

Figure 2

Graphical representation of the cut points obtained for the respiratory rate. Cut points obtained, based on the relationship between respiratory rate and poor evolution.

Figure 3

Graphical representation of the cut points obtained for PCO2. Cut points obtained, based on the relationship between PCO2 and poor evolution.

Figure 4

Graphical representation of the average-risk category width and location for PCO2 based on sample size.