Incorporating self-reported health measures in risk equalization through constrained regression

Abstract

Most health insurance markets with premium-rate restrictions include a risk equalization system to compensate insurers for predictable variation in spending. Recent research has shown, however, that even the most sophisticated risk equalization systems tend to undercompensate (overcompensate) groups of people with poor (good) self-reported health, confronting insurers with incentives for risk selection. Self-reported health measures are generally considered infeasible for use as an explicit 'risk adjuster' in risk equalization models. This study examines an alternative way to exploit this information, namely through 'constrained regression' (CR). To do so, we use administrative data (N = 17 m) and health survey information (N = 380 k) from the Netherlands. We estimate five CR models and compare these models with the actual Dutch risk equalization model of 2016 which was estimated by ordinary least squares (OLS). In the CR models, the estimated coefficients are restricted, such that the under-/overcompensation for groups based on self-reported general health is reduced by 20, 40, 60, 80, or 100%. Our results show that CR can improve outcomes for groups that are not explicitly flagged by risk adjuster variables, but worsens outcomes for groups that are explicitly flagged by risk adjuster variables. Using a new standardized metric that summarizes under-/overcompensation for both types of groups, we find that the lighter constraints can lead to better outcomes than OLS.

How to deal with persistently low/high spenders in health plan payment systems?

“…Guided by the aforementioned study of Withagen‐Koster et al. ( 2020 ), we specify the constraint such that the overcompensation of people with multiple‐year low spending is reduced by 50% compared to the base model.…”

“…Another strategy to exploit the predictiveness of spending persistence is “constrained regression.” This method allows for indirect use of predictive information by implementing a (set of) constraints on the coefficients of the existing risk adjustors (Layton et al., 2018 ; van Kleef et al., 2017 , 2020 ; Withagen‐Koster et al., 2020 ). In the context of this paper a constraint could mean that “mean predicted spending” for a group in Table 1 equals “mean actual spending” for that group.…”

“…Compared to an unconstrained model, a constrained RA model programmed to reduce under/overcompensation for groups of interest tends to shift RA payments from people “flagged” as “healthy” by risk adjustor variables (e.g., no DCG) to those flagged as “unhealthy” (e.g., at least one DCG). Previous empirical simulations have shown that constrained regression can improve payment fit for some groups, but worsen it for others (van Kleef et al., 2017 ; Withagen‐Koster et al., 2020 ). Given a certain choice of “relevant” groups, however, well‐specified constraints can improve the performance of RA models.…”

“…For example, Withagen‐Koster et al. ( 2020 ) find that for a cross tabulation of yes/no morbidity flag (according to morbidity indicators included in the Dutch RA model) and yes/no (very) poor or moderate self‐reported health (as used by the researchers to define constraints in their alternative RA model), the absolute weighted mean under/overcompensation on the four combinations is lowest for constraints that reduce the undercompensation on the group of people with (very) poor or moderate self‐reported health by 20%–80%. The optimal percentage reduction, however, is not a universal constant, but depends on the specification of the RA model, the characteristics of subgroups used for evaluation, and the weighting of under/overcompensations for subgroups of interest.…”

The pattern of health insurance economic resilience in the Covid 19 pandemic shock

“…Health insurance is based on people's significant risks in receiving health services that they cannot afford alone. One of the goals of health insurance is to distribute income in favor of people who cannot cope with these risks [8,9].…”