A novel approach to learning through categorical variables applicable to the classification of solitary pulmonary nodule malignancy

Abstract

Background: One of the main drawbacks in constructing a classification model is that some or all of the covariates are categorical variables. Classical methods either assign labels to each output of a categorical variable or are summarised measures (frequencies and percentages), which can be interpreted as probabilities. Methods: We adopted a novel mathematical procedure to construct a classification model from categorical variables based on a non-classical probability approach. More specifically, we codified the variables following the categorical data representation from the Discriminant Correspondence Analysis before constructing a non-classical probability matrix system that represents an entangled system of dependent-independent variables. We then developed a disentangled procedure to obtain an empirical density function for each representative class (minimum of two classes). Finally, we constructed our classification model using the density functions. Results: We applied the proposed procedure to build a classification model of the malignancy of Solitary Pulmonary Nodule (SPN) after five years of follow up using routine clinical data. First, with 2/3 (270) of the sample of 404 patients with SPN, we constructed the classification model, and then validated it with the remaining 1/3(134) we validated it. We tested the procedure’s stability by repeating the analysis randomly 1000 times. We obtained a model accuracy of 0.74, an F1 score of 0.58, a Cohen’s Kappa value of 0.41 and a Matthews Correlation Coefficient of 0.45. Finally, the area under the ROC curve was 0.86. Conclusion: The proposed procedure provides a machine learning classification model with an acceptable performance of a classification model of solitary pulmonary nodule malignancy constructed from routine clinical data and mainly composed of categorical variables. It provides an acceptable performance, which could be used by clinicians as a tool to classify SPN malignancy in routine clinical practice.