Polychotomization of continuous variables in regression models based on the overall C index

When developing multivariable regression models for diagnosis or prognosis, continuous independent variables can be categorized to make a prediction table instead of a prediction formula. Although many methods have been proposed to dichotomize prognostic variables, to date there has been no integrated method for polychotomization. The latter is necessary when dichotomization results in too much loss of information or when central values refer to normal states and more dispersed values refer to less preferable states, a situation that is not unusual in medical settings (e.g. body temperature, blood pressure). The goal of our study was to develop a theoretical and practical method for polychotomization.

We used the overall discrimination index C, introduced by Harrel, as a measure of the predictive ability of an independent regressor variable and derived a method for polychotomization mathematically. Since the naïve application of our method, like some existing methods, gives rise to positive bias, we developed a parametric method that minimizes this bias and assessed its performance by the use of Monte Carlo simulation.

The overall C is closely related to the area under the ROC curve and the produced di(poly)chotomized variable's predictive performance is comparable to the original continuous variable. The simulation shows that the parametric method is essentially unbiased for both the estimates of performance and the cutoff points. Application of our method to the predictor variables of a previous study on rhabdomyolysis shows that it can be used to make probability profile tables that are applicable to the diagnosis or prognosis of individual patient status.

We propose a polychotomization (including dichotomization) method for independent continuous variables in regression models based on the overall discrimination index C and clarified its meaning mathematically. To avoid positive bias in application, we have proposed and evaluated a parametric method. The proposed method for polychotomizing continuous regressor variables performed well and can be used to create probability profile tables.