Synergy effects between grafting and subdivision in Re-RX with J48graft for the diagnosis of thyroid disease

Highlights

• Elucidate synergy effects between grafting and subdivision in Re-RX with J48graft.

• Provide the theoretical explanation underlying the excellent synergy effects.

• demonstrate how grafting and subdivision can highly extract accurate and concise rules.

• Re-RX with J48graft extracts highly accurate and concise rules from the thyroid dataset.

Abstract

Numerous methods for diagnosing thyroid disease have been developed, but the majority of these are black-box models. By contrast, the Recursive-Rule Extraction algorithm with J48graft is a white-box model that can provide highly accurate and concise classification rules. However, the potential capabilities of Re-RX with J48graft in terms of rule extraction remain unknown. Therefore, the aim of the present study was to elucidate the synergy effects between grafting and subdivision in Re-RX with J48graft, which work effectively in combination to extract highly accurate and concise classification rules for the diagnosis of thyroid disease. In the present study, I demonstrate how grafting and subdivision can extract highly accurate and concise classification rules from the Thyroid dataset, which is a large and highly imbalanced dataset consisting of 7200 medical records classified as normally functioning thyroid, hypothyroidism, or hyperthyroidism. I also provide the theoretical explanation underlying the excellent synergy effects between the two processes. Re-RX with J48graft not only achieved the most accurate classification rules, but also extracted simple and concrete concise classification rules for majority class samples. In addition, compared with previous methods, Re-RX with J48graft extracted rules with fewer antecedents. The maximum accuracy of the extracted rules was very high, at 97.02%. These findings suggest that Re-RX with J48graft can extract highly accurate and concise rules, which could assist healthcare professionals in the diagnosis of thyroid disease and help improve the level of care.

Introduction

Thyroid diseases affect about 200 million people worldwide, which accounts for nearly 15% of the adult population. In the United States, about 27 million people are affected by thyroid diseases, half of whom remain undiagnosed. The most common thyroid diseases lead to thyroid dysfunction, with 80% of cases being diagnosed as hypothyroidism, a condition in which the thyroid gland, a small, butterfly-shaped gland in the lower part of the neck, is underactive and incapable of producing adequate levels of thyroid hormone, and 20% of cases are diagnosed as hyperthyroidism, a condition in which the thyroid gland is overactive and produces an excess of thyroid hormone. The thyroid gland produces two active hormones—triiodothyronine (T₃) and levothyroxine (LT₄)—that play a variety of important roles in the human body and are vital in the production of proteins and the regulation of body temperature. Because thyroid function affects every major organ in the body, thyroid disorders should be taken very seriously. The thyroid gland is susceptible to a number of very distinct problems, some of which are extremely common. Under production of thyroid hormone can lead to hypothyroidism, whereas overproduction can result in hyperthyroidism. Both of these disorders are relatively common among the general population [1]. To help cells convert oxygen and nutrients into energy, T₃ and LT₄ production must fall within normal ranges; these ranges are usually based on the concentration of thyroid hormone in the blood. In the present study, normal ranges were calculated for the following: T₃, LT₄, thyroid stimulating hormone (TSH), thyroxine (T₄) utilization rate, and free thyroxine index (FTI) [2]. Symptoms related to thyroid diseases can be easily confused with those for other conditions, making thyroid diseases difficult to diagnose. Fortunately, a TSH test can identify thyroid disorders even before symptom onset [3].

Thyroid function diagnosis is a three-class classification problem. Numerous supervised methods for diagnosing thyroid disease have been successfully applied to the classification of different tissues. These methods include the following: extreme learning machines (ELMs) [1]; support vector machines (SVMs) [4], [5], [6]; neural networks (NNs) [7], [8], [9], [10], [11], [12]; decision trees (DTs) [7]; k-nearest neighbor (kNN) classifiers [13]; fuzzy classifiers (FCs) [14], [15]; hybrid case-based reasoning [16]; mixture-of-expert models [17]; immune algorithms [18]; immune recognition systems [19]; neuro-fuzzy expert systems [20]; differential evolution [21]; classification [22], [23]; and discriminant analysis [24].

However, the majority of methods currently used to diagnose thyroid disease are black-box models that are unable to satisfactory reveal information hidden in the data. For example, even if a method allows instances to be accurately assigned to groups, no information is provided to users regarding the reasoning underlying that assignment. Therefore, systems and/or algorithms that can provide insight into these underlying rationales are highly desirable. Among supervised methods, rule extraction studies are becoming increasingly popular due to their capability of providing such explanations. However, extracted rules must have a high level of accuracy, particularly in the medical setting, and yet still be simple and easy to understand.

Some researchers have experimented with extracting Boolean rules from NNs [25], [26], [27], which has led to encouraging results that exhibit good performance, a reduced number of rules, relevant input variables, and increased interpretability. However, because these methods use Boolean rules, they do not extract continuous rules.

The Recursive-Rule Extraction algorithm with J48graft (Re-RX with J48graft) was first proposed in 2015 [28], and its considerable effectiveness for use in financial [29] and medical datasets [30], [31] has since been confirmed. Re-RX with J48graft is based on the Re-RX algorithm [32]. In the Re-RX algorithm, a C4.5 DT [33] is frequently employed in a recursive manner, while multi-layer perceptrons (MLPs) are trained using backpropagation NNs (BPNNs); this allows pruning [34] and therefore generates more efficient MLPs for highly accurate rule extraction. The Re-RX algorithm cascade repeats the BPNN, the pruning, and C4.5.

Re-RX with J48graft, a white-box model, can provide highly accurate and concise classification and be easily explained and interpreted in accordance with the concise extracted rules associated with IF-THEN forms. Due to the ease of understanding this type of model allows, it is often preferred by physicians and clinicians.

Recently, I proposed using both discrete and continuous attributes to generate a DT in the Re-RX algorithm framework (hereafter Continuous Re-RX [35]). Although this seems to be counterintuitive with the design concept of the Re-RX algorithm in that it results in the generation of a more complex DT, the use of both types of attributes is done to enhance accuracy [35].

Typically, the accuracy of each extracted classification rule is assessed by the number of correctly classified test samples, while the interpretability is assessed by the number of extracted rules and the average number of antecedents in the extracted rules; however, for extracted classification rules, both accuracy and interpretability should be considered.

Results regarding the extraction of classification rules for the diagnosis of thyroid disease have been reported in a number of studies [5], [11], [14], [15]. Among these, Duch et al. [11] reported highly accuracy classification for the Thyroid dataset and provided two types of relatively simple and concrete classification rule sets.

The present study, aimed to elucidate the synergy effects of grafting in J48graft and subdivision in Re-RX with J48graft, which work effectively in combination to extract highly accurate and concise classification rules for the diagnosis of thyroid disease. This paper demonstrates the reason why highly accurate and concise classification rules can be extracted by grafting and subdivision, respectively, and provide a theoretical explanation of the synergy effects. A concrete comparison is also given of the accuracy and characteristics of these rules for the Thyroid dataset in the form of IF-THEN rules with those extracted by Continuous Re-RX [35] and both types of rule extraction algorithms proposed by Duch et al. [11].

The Thyroid dataset is a multi-class and highly imbalanced medical dataset that comprises both discrete and continuous, i.e., mixed, attributes. It was obtained from the University of California Irvine (UCI) Machine Learning Repository [36]. Two versions of the Thyroid dataset have been used for benchmarking in previous studies. One version comprises 7200 samples [11], [14], [15], [17], while the other comprises 215 samples [1], [3], [5], [6], [16], [17], [18], [19], [20], [21].