## 2 Materials and Methods
### Inclusion and Exclusion Criteria  
The inclusion criteria were as follows: (1) patients who were diagnosed with a lumbar disease, including lumbar disc herniation, at the National Health Insurance Service Ilsan Hospital from 2 March 2000 to 30 June 2021 and from whom thermographic images of the lower extremity were acquired; (2) those with at least one of the following preoperative radiologic criteria: diagnosed with herniated lumbar disc (HLD) using CT or MRI; and (3) those whose diagnoses were verified by two radiologists. Patients with developmental stages of lumbar radiculopathy ranging from an acute to chronic status were included. The patients were divided into two groups according to their degree of pain on the visual analog scale (VAS): 1-7 points were classified as mild-to-moderate pain, and 8-10 points indicated severe-to-intractable pain, with 10 points indicating the highest severity. Meanwhile, the exclusion criteria were as follows: (1) patients with diseases that can affect the skin temperature of the lower extremities, such as diabetes, peripheral arterial occlusive disease, and other endocrine diseases; (2) those who had undergone previous cervical or lumbosacral surgery; and (3) those who did not report pain in the past. Clinical Data Collection, Labeling, Preprocessing, ML-Based Classification Modeling, and Calibration Algorithm  
Our study center retrospectively collected clinical data, including information on diagnosis, using DITI. Clinical characteristics, such as age, sex, height, weight, duration of pain, location of pain, maximum angle of pain on the straight leg elevation test, and degree of disc herniation, were used as variables. Because variants of convolutional neural networks have been applied to DITI data in previous studies [13], we instead extracted the data using the region of interest on the National Reference Standard Korean Thermal Data Center Research Platform. DITI included lower extremity sequences, such as the anterior and posterior leg and feet. In the DITI images, 10 region-of-interest values were extracted and used for the left and right areas of the anterior thigh, shin, posterior thigh, calf, and pelma (undersurface of the foot). The authors split the DITI dataset into the training algorithm and test dataset in a 7:3 ratio to evaluate the model's performance. The algorithm for classifying pain severity was evaluated, and the isotonic calibration algorithm was applied using Python 3.6. Among the models that can be implemented with python, we compared logistic regression (LR), which is widely used conventionally; decision tree (DT), which is a representative classical tree algorithm; random forest (RF), which is a representative bagging method; and support vector machine (SVM), which has recently been used in general applications [14]. In the RF method proposed by [PERSON], each tree is a standard classification or regression tree that uses the so-called Gini impurity decrement as the splitting criterion and selects the splitting predictor from a randomly selected subset of predictors. Each tree consists of a bootstrap sample extracted with a replacement from the original dataset, and predictions from all trees are finally aggregated by majority vote [15]. The definition of the model evaluation parameters is shown in Table 1. Sensitivity is true positive (TP)/(TP+ false negative [FN]), specificity is true negative (TN)/(TN + false positive [FP]), positive predicted value (precision) is TP/(TP + FP), recall is TP/(TP + FN), and negative predictive value is TN/(TN + FN). The balanced accuracy (BA), the arithmetic mean of sensitivity and specificity, is 1/2 \(\times\) (sensitivity + specificity). The F1 score, a weighted average of precision and recall, is 2 \(\times\) precision \(\times\) recall/(precision + recall). These parameters have advantages when dealing with imbalanced data and performance evaluation [16]. In terms of calibration, we also assessed the Brier score (BS).