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.

Risk sharing between competing health plans and sponsors.

In many countries, competing health plans receive capitation payments from a sponsor, whether government or a private employer. All capitation payment methods are far from perfect and have raised concerns about risk selection. Paying health plans partly on the basis of capitation and partly on the basis of actual costs ("risk sharing") reduces plans' incentives for selection but sacrifices some incentives for efficiency. This paper summarizes our empirical research on Dutch health plans with respect to various forms of risk sharing. All sponsors can improve their payment systems by either implementing or changing their form of risk sharing.

Costs in the last year of life in The Netherlands.

The costs of health care in the last year of life are a subject of debate and myth. Expensive interventions at the end of life often are blamed for the rapid increase in health care spending, but evidence about the existence of such exceptionally high expenditures at the end of life is rare and faulty. This investigation examines the development and composition of health care costs at the end of life for all age groups in The Netherlands. In contrast with earlier studies, this research analyzes both acute care (cure) and long-term care (care) costs. As an alternative for the frequently used concept of calendar years, we employed the concept of life years for calculating the costs at the end of life. We found that when life approaches its end, health care expenditures indeed rise sharply, especially in the last months. However, when we compared total cure costs in the last year of life to the total cure costs for the entire population, we concluded that the end-of-life share was only about 10%. Results of this study show that interventions to reduce costs in the last year of life will have only a modest impact compared to the total health care budget.

Risk sharing as a supplement to imperfect capitation: a tradeoff between selection and efficiency.

This paper describes forms of risk sharing between insurers and the regulator in a competitive individual health insurance market with imperfectly risk-adjusted capitation payments. Risk sharing implies a reduction of an insurer's incentives for selection as well as for efficiency. In a theoretical analysis, we show how the optimal extent of risk sharing may depend on the weights the regulator assigns to these effects. Some countries employ outlier or proportional risk sharing as a supplement to demographic capitation payments. Our empirical results strongly suggest that other forms of risk sharing yield better tradeoffs between selection and efficiency.

Access to coverage for high-risks in a competitive individual health insurance market: via premium rate restrictions or risk-adjusted premium subsidies?

A competitive market for individual health insurance tends to risk-adjusted premiums. Premium rate restrictions are often considered a tool to increase access to coverage for high-risk individuals in such a market. However, such regulation induces selection which may have several adverse effects. As an alternative approach we consider risk-adjusted premium subsidies. Empirical results of simulated premium models and subsidy formulae are presented. It is shown that sufficiently adjusted subsidies eliminate the need for premium rate restrictions and consequently avoid their adverse effects. Therefore, the subsidy approach is the preferred strategy to increase access to coverage for high-risk individuals.

Deductibles in health insurance: can the actuarially fair premium reduction exceed the deductible?

The actuarially fair premium reduction in case of a deductible relative to full insurance is affected by: (1) out-of-pocket payments, (2) moral hazard, (3) administrative costs, and, in case of a voluntary deductible, (4) adverse selection. Both the partial effects and the total effect of these factors are analyzed. Moral hazard and adverse selection appear to have a substantial effect on the expected health care costs above a deductible but a small effect on the expected out-of-pocket expenditure. A premium model indicates that for a broad range of deductible amounts the actuarially fair premium reduction exceeds the deductible.

Ignoring small predictable profits and losses: a new approach for measuring incentives for cream skimming.

Under inadequate capitation formulae competing health insurers have an incentive for cream skimming, i.e., the selection of enrollees whom the insurer expects to be profitable. When evaluating different capitation formulae, previous studies used various indicators of incentives for cream skimming. These conventional indicators are based on all actual profits and losses or on all predictable profits and losses. For the latter type of indicators, this paper proposes, as a new approach, to ignore the small predictable profits and losses. We assume that this new approach provides a better indication of the size of the cream skimming problem than the conventional one, because an insurer has to take into account its costs of cream skimming and the (statistical) uncertainties about the net benefits of cream skimming. Both approaches are applied in theoretical and empirical analyses. The results show that, if our assumption is right, the problem of cream skimming is overestimated by the conventional ways of measuring incentives for cream skimming, especially in the case of relatively good capitation formulae.

The high costs of death: should health plans get higher payments when members die?

OBJECTIVES: Since 1993, major reforms have been implemented in the Dutch social health insurance system. The competing sickness funds receive risk-adjusted capitation payments based on age, gender, region, and a disability indicator. As these very crude health indicators do not reflect expected costs accurately, an extensive ex post equalization between sickness funds takes place. Mortality has been suggested as an additional risk adjuster, mainly because of high health care expenditures before death. The authors investigated whether capitation payments could be improved by using mortality as a risk adjuster. METHODS: Using data sets that cover a general population and contain individual-level information on demographic characteristics, health care costs, hospitalizations, and year of death (when applicable), expenditures in a period of up to 7 years before death and the consequences for capitation payments if mortality-related costs are taken into account, were analyzed. RESULTS: For a general population, costs per person-year in the last calendar year of life were estimated at 15.3 times average. For those younger than 65 years, this number was 27.3 times average, and for the elderly, it was 4.7 times average. Most of these excess costs were unpredictable. Even with the most comprehensive regression model, actual costs of decedents were still 250% higher than predicted costs. Mortality would improve capitation payments marginally, at best. CONCLUSION: The empirical findings, added to theoretical and practical problems of using mortality in this context, suggest that mortality should not be used as a risk adjuster. Further research should be directed at other, more promising risk adjusters.

Mandatory pooling as a supplement to risk-adjusted capitation payments in a competitive health insurance market.

Risk-adjusted capitation payments (RACPs) to competing health insurers are an essential element of market-oriented health care reforms in many countries. RACPs based on demographic variables only are insufficient, because they leave ample room for cream skimming. However, the implementation of improved RACPs does not appear to be straightforward. A solution might be to supplement imperfect RACPs with a form of mandatory pooling that reduces the incentives for cream skimming. In a previous paper it was concluded that high-risk pooling (HRP), is a promising supplement to RACPs. The purpose of this paper is to compare HRP with two other main variants of mandatory pooling. These variants are called excess-of-loss (EOL) and proportional pooling (PP). Each variant includes ex post compensations to insurers for some members which depend to various degrees on actually incurred costs. Therefore, these pooling variants reduce the incentives for cream skimming which are inherent in imperfect RACPs, but they also reduce the incentives for efficiency and cost containment. As a rough measure of the latter incentives we use the percentage of total costs for which an insurer is at risk. This paper analyzes which of the three main pooling variants yields the greatest reduction of incentives for cream skimming given such a percentage. The results show that HRP is the most effective of the three pooling variants.

Risk-adjusted capitation payments for catastrophic risks based on multi-year prior costs.

In many countries regulated competition among health insurance companies has recently been proposed or implemented. A crucial issue is whether or not the benefits package offered by competing insurers should also cover catastrophic risks (like several forms of expensive long-term care) in addition to non-catastrophic risks (like hospital care and physician services). In 1988 the Dutch government proposed compulsory national health insurance based on regulated competition among insurer as well as among providers of care. The competing insurers should offer a benefits package covering both non-catastrophic risks and catastrophic risks. The insurers would be largely financed via risk-adjusted capitation payments. The government intended to use a capitation formula that is, besides some demographic variables, based on multi-year prior costs. This paper presents the results of an explorative empirical analysis of the possible consequences of such a capitation formula for catastrophic risks. The main conclusion is that this formula would be inadequate because it would leave ample room for cream skimming.

Multiyear diagnostic information from prior hospitalization as a risk-adjuster for capitation payments.

As part of a move toward a more market-oriented health-care system, major changes have been implemented in the Dutch social health insurance system. The competing sickness funds now receive risk-adjusted capitation payments, currently based on the age-sex distribution of the insurance portfolios. These very crude health indicators do not reflect expected costs accurately. The authors examine whether the incorporation of inpatient diagnostic information over a multiyear period can increase the accuracy of the capitation model. Using a panel data set (n approximately 50,000) comprising annual costs and diagnostic information for 5 successive years, the authors compare demographic and diagnostic models in their ability to predict future health care costs. The predictive accuracy of an age-sex-based capitation formula improves substantially when diagnostic information from an individual's prior hospitalizations is used as an additional risk-adjuster. The longer the period over which diagnostic information is available, the better is the predictive accuracy. The expected loss in 1992 for insured persons with the highest costs in 1988 decreases from 88% (demographic model) to 62% (1-year diagnostic model) and to 43% (3-year diagnostic model). The use of diagnostic information from prior hospitalizations is a promising option for improving the capitation formulae. The authors' results are relevant not only for situations where competing insurers are capitated, as in the Netherlands, but also when providers (United Kingdom) or health maintenance organizations (United States) are capitated.

Mandatory high-risk pooling: an approach to reducing incentives for cream skimming.

Risk-adjusted capitation payments (RACPs) to competing health insurers are an essential element of market-oriented health care reforms in The Netherlands. Crude RACPs are inadequate, especially because they encourage insurers to select against people expected to be unprofitable--a practice called cream skimming. However, implementing improved RACPs does not appear to be straightforward. This paper analyzes an approach that, given a system of crude RACPs, reduces insurers' incentives for cream skimming in the market for individual health insurance, while preserving incentives for efficiency and cost containment. Under the proposed system of Mandatory High-Risk Pooling (MHRP), each insurer would be allowed to periodically predetermine a small fraction of its members whose costs would be (partially) pooled. The pool would be financed with mandatory, flat-rate contributions. The results suggest that MHRP is a promising supplement to RACPs.