## 1 Introduction  
The negative consequences of students' dropping out of school are significant for both the individual and society. The educational deficiencies of dropout students could severely limit economic and social well-being in their later lives [1]. The society also suffers losses because the nation's productive capacity could be undermined by the shortage of the skilled workforce, and also the dropout students are more likely to be frequent recipients of welfare and unemployment subsidies [2]. Because of those negative consequences, students' dropouts have long been considered as a serious educational problem by educators, researchers, and policymakers. A dropout early warning system can help schools to preemptively identify students who are at risk of dropping out of school and to promptly react to them [3]. The students at risk are likely to drop out without carefully considering the negative consequences of their decisions or without having an opportunity to consult with experts. The early intervention informed by the dropout early warning system can redirect potential dropout students onto the path to graduation and lead them to a better future [4]. Because of the great potential, many governments have developed dropout early warning systems. For example, the department of education and early childhood development in the state of Victoria in Australia developed the Student Mapping Tool (SMT) to help schools to identify students at risk of disengagement and dropout [5], and the state of Wisconsin in the United States developed the Dropout Early Warning System (DEWS) to predict students' dropouts [6]. In the United States, about half of public high schools implemented the dropout early warning systems during 2014-2015 [7]. Machine learning is a promising tool for building a predictive model for a dropout early warning system. However, the class-imbalance could be one of the potential difficulties in implementing a dropout early warning system using machine learning. In the binary outcome representing students' dropouts, the proportions of the two classes (i.e., dropouts and non-dropouts) tend to be imbalanced (e.g., 1.4 percent of dropouts vs. 98.6 percent of non-dropouts in Korean high school in 2016). In general, machine learning classifiers trained on datasets with imbalanced classes tend to show a very poor performance in predicting the minor class because the classifiers ignore the minor class as a noise [8; 9]. Because the class of interest in dropout prediction is a minor class (i.e., dropouts), the class-imbalance issue could severely degrade the sensitivity of the early warning system in predicting potential dropout students. Another key issue in the presence of class imbalance is to use performance metrics that are sensitive to performance differences. Traditionally, the area under the curve (AUC) in the receiver operating characteristic (ROC) curve has been widely used in machine learning literature. However, in the presence of class imbalance, the ROC curve analysis may not be sensitive enough to differentiate the performances of classifiers, and the precision-recall (PR) curve may perform better [10]. In the literature, [PERSON] et al. [11] predicted student failure at school using genetic programming and different machine learning approaches by addressing the class imbalance issue using the synthetic minority oversampling techniques (SMOTE), and identified the best model based on the true positive (TP) rate, true negative (TN) rate, and accuracy. [PERSON] [6] used machine learning to build a predictive model of student dropout risk, and identified the best statistical model using the ROC curve. [PERSON] et al. [12] used various machine learning algorithms for early dropout prediction, and used the TP rate, TN rate, accuracy, and AUC. However, in the previous literature, the class-imbalance issue and the advantage of using the PR curve have not been fully discussed yet.