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.

Is there one measure-of-fit that fits all? A taxonomy and review of measures-of-fit for risk-equalization models.

This study provides a taxonomy of measures-of-fit that have been used for evaluating risk-equalization models since 2000 and discusses important properties of these measures, including variations in analytic method. It is important to consider the properties of measures-of-fit and variations in analytic method, because they influence the outcomes of evaluations that eventually serve as a basis for policymaking. Analysis of 81 eligible studies resulted in the identification of 71 unique measures that were divided into 3 categories based on treatment of the prediction error: measured based on squared errors, untransformed errors, and absolute errors. We conclude that no single measure-of-fit is best across situations. The choice of a measure depends on preferences about the treatment of the prediction error and the analytic method. If the objective is measuring financial incentives for risk selection, the only adequate evaluation method is to assess the predictive performance for non-random groups.

Improving the prediction model used in risk equalization: cost and diagnostic information from multiple prior years.

Currently-used risk-equalization models do not adequately compensate insurers for predictable differences in individuals' health care expenses. Consequently, insurers face incentives for risk rating and risk selection, both of which jeopardize affordability of coverage, accessibility to health care, and quality of care. This study explores to what extent the predictive performance of the prediction model used in risk equalization can be improved by using additional administrative information on costs and diagnoses from three prior years. We analyze data from 13.8 million individuals in the Netherlands in the period 2006-2009. First, we show that there is potential for improving models' predictive performance at both the population and subgroup level by extending them with risk adjusters based on cost and/or diagnostic information from multiple prior years. Second, we show that even these extended models do not adequately compensate insurers. By using these extended models incentives for risk rating and risk selection can be reduced substantially but not removed completely. The extent to which risk-equalization models can be improved in practice may differ across countries, depending on the availability of data, the method chosen to calculate risk-adjusted payments, the value judgment by the regulator about risk factors for which the model should and should not compensate insurers, and the trade-off between risk selection and efficiency.