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.

A method to simulate incentives for cost containment under various cost sharing designs: an application to a first-euro deductible and a doughnut hole.

Many health insurance schemes include deductibles to provide consumers with cost containment incentives (CCI) and to counteract moral hazard. Policymakers are faced with choices on the implementation of a specific cost sharing design. One of the guiding principles in this decision process could be which design leads to the strongest CCI. Despite the vast amount of literature on the effects of cost sharing, the relative effects of specific cost sharing designs-e.g., a traditional deductible versus a doughnut hole-will mostly be absent for a certain context. This papers aims at developing a simulation model to approximate the relative effects of different deductible modalities on the CCI. We argue that the CCI depends on the probability that healthcare expenses end up in the deductible range and the expected healthcare expenses given that they end up in the deductible range. Our empirical application shows that different deductible modalities result in different CCIs and that the CCI under a certain modality differs across risk-groups.

Overpaying morbidity adjusters in risk equalization models.

Most competitive social health insurance markets include risk equalization to compensate insurers for predictable variation in healthcare expenses. Empirical literature shows that even the most sophisticated risk equalization models-with advanced morbidity adjusters-substantially undercompensate insurers for selected groups of high-risk individuals. In the presence of premium regulation, these undercompensations confront consumers and insurers with incentives for risk selection. An important reason for the undercompensations is that not all information with predictive value regarding healthcare expenses is appropriate for use as a morbidity adjuster. To reduce incentives for selection regarding specific groups we propose overpaying morbidity adjusters that are already included in the risk equalization model. This paper illustrates the idea of overpaying by merging data on morbidity adjusters and healthcare expenses with health survey information, and derives three preconditions for meaningful application. Given these preconditions, we think overpaying may be particularly useful for pharmacy-based cost groups.

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.

Diagnoses-based cost groups in the Dutch risk-equalization model: the effects of including outpatient diagnoses.

BACKGROUND: The Dutch basic health-insurance scheme for curative care includes a risk equalization model (RE-model) to compensate competing health insurers for the predictable high costs of people in poor health. Since 2004, this RE-model includes the so-called Diagnoses-based Cost Groups (DCGs) as a risk adjuster. Until 2013, these DCGs have been mainly based on diagnoses from inpatient hospital treatment. OBJECTIVES: This paper examines (1) to what extent the Dutch RE-model can be improved by extending the inpatient DCGs with diagnoses from outpatient hospital treatment and (2) how to treat outpatient diagnoses relative to their corresponding inpatient diagnoses. METHOD: Based on individual-level administrative costs we estimate the Dutch RE-model with three different DCG modalities. Using individual-level survey information from a prior year we examine the outcomes of these modalities for different groups of people in poor health. CONCLUSIONS: We find that extending DCGs with outpatient diagnoses has hardly any effect on the R-squared of the RE-model, but reduces the undercompensation for people with a chronic condition by about 8%. With respect to incentives, it may be preferable to make no distinction between corresponding inpatient and outpatient diagnoses in the DCG-classification, although this will be at the expense of the predictive accuracy of the RE-model.

Shifted deductibles for high risks: more effective in reducing moral hazard than traditional deductibles.

In health insurance, a traditional deductible (i.e. with a deductible range [0,d]) is in theory not effective in reducing moral hazard for individuals who know (ex-ante) that their expenditures will exceed the deductible amount d, e.g. those with a chronic disease. To increase the effectiveness, this paper proposes to shift the deductible range to [s(i),s(i)+d], with starting point s(i) depending on relevant risk characteristics of individual i. In an empirical illustration we assume the optimal shift to be such that the variance in out-of-pocket expenditures is maximized. Results indicate that for the 10-percent highest risks in our data the optimal starting point of a euro1000-deductible is to be found (far) beyond euro1200, which corresponds with a deductible range of [1200,2200] or further. We conclude that, compared to traditional deductibles, shifted deductibles with a risk-adjusted starting point lower out-of-pocket expenditures and may further reduce moral hazard.

Risk equalization and voluntary deductibles: a complex interaction.

The presence of voluntary deductibles in the Swiss and Dutch mandatory health insurance has important implications for the respective risk equalization systems. In a theoretical analysis, we discuss the consequences of equalizing three types of expenditures: the net claims that are reimbursed by the insurer, the out-of-pocket expenditures and the expenditure savings due to moral hazard reduction. Equalizing only the net claims, as done in Switzerland, creates incentives for cream skimming and prevents insurers from incorporating out-of-pocket expenditures and moral hazard reductions into their premium structure. In an empirical analysis, we examine the effect of self-selection and conclude that the Swiss and Dutch risk equalization systems do not fully adjust for differences in health status between those who choose a deductible and those who do not. We discuss how this may lead to incentives for cream skimming and to a reduction of cross-subsidies from healthy to unhealthy individuals compared to a situation without voluntary deductibles.

Does risk equalization reduce the viability of voluntary deductibles?

Theoretically, a risk avers consumer takes a deductible if the premium rebate (far) exceeds his/her expected out-of-pocket expenditures. In the absence of risk equalization, insurers are able to offer high rebates because those who select into a deductible plan have below-average expenses. This paper shows that, for high deductibles, such rebates cannot be offered if risk equalization would "perfectly" adjust for the effect of self selection. Since the main goal of user charges is to reduce moral hazard, some effect of self selection on the premium rebate can be justified to increase the viability of voluntary deductibles.

Health-based risk adjustment Improving the pharmacy-based cost group model to reduce gaming possibilities.

The pharmacy-based cost group (PCG) model uses medication prescribed to individuals in a base-year as marker for chronic conditions which are employed to adjust capitation payments to their health plans in the subsequent year. Although the PCG model enhances predictive performance, possibilities for gaming may arise as it is based on prior utilization. This study investigates several strategies to mitigate this problem. The best strategies appear to be: use a (high) number of prescribed daily doses to assign persons to PCGs, do not allow for comorbidity, and remove PCGs with low future costs. This PCG model accounts for almost twice as much variance as do demographic models. In 2002 the Dutch government implemented this model in the sickness fund sector (two-thirds of the population).