Exploring the predictive power of interaction terms in a sophisticated risk equalization model using regression trees

This study explores the predictive power of interaction terms between the risk adjusters in the Dutch risk equalization (RE) model of 2014. Due to the sophistication of this RE-model and the complexity of the associations in the dataset (N = ~16.7 million), there are theoretically more than a million interaction terms. We used regression tree modelling, which has been applied rarely within the field of RE, to identify interaction terms that statistically significantly explain variation in observed expenses that is not already explained by the risk adjusters in this RE-model. The interaction terms identified were used as additional risk adjusters in the RE-model. We found evidence that interaction terms can improve the prediction of expenses overall and for specific groups in the population. However, the prediction of expenses for some other selective groups may deteriorate. Thus, interactions can reduce financial incentives for risk selection for some groups but may increase them for others. Furthermore, because regression trees are not robust, additional criteria are needed to decide which interaction terms should be used in practice. These criteria could be the right incentive structure for risk selection and efficiency or the opinion of medical experts.