Predictive modeling of right-skewed health insurance costs using copula regression and ensemble learning

Abstract

This study compares four predictive models in the context of a response variable characterized by a right-skewed, non-symmetric distribution, specifically health cost insurance data. The modeling approaches employed include copula-based models (copula regression with logarithmic transformation and standard copula regression) and ensemble learning methods (Random Forest/RF and Extreme Gradient Boosting/XGBoost). The health cost data was partitioned into 80% for training and 20% for testing. Model fitting was conducted using the training data, while model evaluation was performed using the testing data. The performance of each model was assessed based on several evaluation metrics: Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE), and Median Absolute Deviation (MAD). Additionally, this study includes an analysis of outlier prediction, where the constructed models were utilized to predict outliers within the health cost data. The results of the study indicate that the copula regression model with logarithmic transformation is more suitable for response variables exhibiting non-symmetric, right-skewed distributions, such as health expenditure data. This is evidenced by the low values of the MAD and MAPE metrics. Another key finding is that the copula regression and XGBoost models demonstrate superior performance in predicting outliers compared to the other two models evaluated in this study.