# Prediction of Post-Intubation Tachycardia Using Machine-Learning Models
### Feature Selection  
Our purpose was to predict a post-intubation tachycardia, for which the input feature was obtained from the \"input area\" in Figure 3, and the output was 1 (or true) if the tachycardia occurred in the \"output area\"; otherwise it was 0 (or false). In this paper, tachycardia is defined as a HR greater than 100 bpm for more than 1 min. The input feature is defined using two types of data (e.g., EMR and vital signs). First, a 24-dimensional feature vector \(f_{\mathbf{EMR}}\) was obtained from EMR, including age, sex, BMI, and so forth; details of the 24-dimensional feature can be found in the first two rows of Table A1 in the Appendix. For example, if the patient was female and had a cardiovascular disease (e.g., hypertension), then \(f_{\mathbf{EMR}}\) was \([\dots,f_{sex}=1,\dots,f_{hypertension}=1,\dots]\). Second, a 129-dimensional feature vector \(f_{\mathbf{vital}}\) was obtained from the vital signs. The \(f_{\mathbf{vital}}\) contains mainly min, max, mean, and standard deviation (sd) of each vital sign; details can be found in Table A1 of the Appendix. For example, if systolic blood pressure (SBP) of the baseline was 130 and the minimum value of respiratory rate (RR) was 4.9, then \(f_{\mathbf{vital}}\) was \([\dots,f_{baseSBP}=130,\dots,f_{minRR}=4.9,\dots]\). The two feature vectors \(f_{\mathbf{EMR}}\) and \(f_{\mathbf{vital}}\) were merged into a 153-dimensional feature vector \(f_{\mathbf{input}}\). Every numerical element of the \(f_{\mathbf{input}}\) was normalized between 0 and 1. Feature selection finds a promising set of features that has a potential to contribute performance improvement. Feature selection is known to shorten training time, reduce overfitting, and improve accuracy [15]. It has produced useful results for ventricular tachycardia and arrhythmia in previous studies [12; 13]. We compared feature selection with three different measurements: recursive feature elimination (RFE), Gini index (GI), and a univariate statistical test (UST) using mutual information. The RFE and GI-based feature selection were performed with a random forest (RF) classifier using scikit-learn [16]. By grid searching, RFE, GI, and UST-based feature selection resulted in 10, 15, and 15 promising feature sets, respectively. Details of the selected features are listed in Table 2.  
In addition to feature selection with the three measurements, we also prepared two additional feature sets: a \(p\)-value based feature set and a manually designed feature set. In Table 2, the \"\(P\)-based\" and \"Hand-crafted\" feature sets indicate the two feature sets, respectively. The \(P\)-based feature set was defined by statistical clues; we conducted a t-test or Wilcox test for continuous variables (e.g., height, tidal volume), and chi-squared or Fisher tests for categorical variables (e.g., sex, ephedrine). We observed significant statistical differences in baseline heart rate, noninvasive heart rate, and remifentanil values, as shown in Table 3. However, the hand-crafted feature set was carefully designed through an exploratory data analysis process. That is, by manually examining a group of patients, we picked eight promising features, including sex, HR_mean, remifentanil_CE_max, remifentanil_CP_max, remifentanil_VOL_max, remifentanil_VOL_mean, BIS_min, and MV_max.