Using Quantile and Asymmetric Least Squares Regression for Optimal Risk Adjustment

Abstract

In this paper, we analyze optimal risk adjustment for direct risk selection (DRS). Integrating insurers' activities for risk selection into a discrete choice model of individuals' health insurance choice shows that DRS has the structure of a contest. For the contest success function (csf) used in most of the contest literature (the Tullock-csf), optimal transfers for a risk adjustment scheme have to be determined by means of a restricted quantile regression, irrespective of whether insurers are primarily engaged in positive DRS (attracting low risks) or negative DRS (repelling high risks). This is at odds with the common practice of determining transfers by means of a least squares regression. However, this common practice can be rationalized for a new csf, but only if positive and negative DRSs are equally important; if they are not, optimal transfers have to be calculated by means of a restricted asymmetric least squares regression. Using data from German and Swiss health insurers, we find considerable differences between the three types of regressions. Optimal transfers therefore critically depend on which csf represents insurers' incentives for DRS and, if it is not the Tullock-csf, whether insurers are primarily engaged in positive or negative DRS. Copyright © 2016 John Wiley & Sons, Ltd.

Impact of abiraterone acetate with and without prior docetaxel chemotherapy on the survival of patients with metastatic castration-resistant prostate cancer: a population-based study

“…The duration of abiraterone treatment in our study, which was slightly shorter in the postchemotherapy group than in the exception patient group, supports this notion. The median survival in our postchemotherapy group (12.0 [95% CI 11.0-19.0] mo) was slightly less than that observed in the COU-AA-301 trial 3 .0] mo), whereas the latter is similar to the survival in our exception patient group (14.0 [95% CI [11][12][13][14][15][16][17][18][19][20] mo). However, our patients were older than those in the COU-AA-301 trial , and the trial patients may have had a different comorbidity or disease profile, which we were unable to assess.…”

“…We performed quantile regression to assess the impact of prior docetaxel exposure on the median days of prostate-cancerrelated hospital stay, adjusted for several covariates. 16,17 Survival since initiation of abiraterone therapy was evaluated with the use of Kaplan-Meier analysis 18 and differences between abiraterone groups with the use of the logrank test. We used the Cox proportional hazards model to estimate the hazard ratio of prior docetaxel exposure, adjusted for several covariates, which respected the proportional hazards assumption.…”

Introducing risk adjustment and free health plan choice in employer-based health insurance: Evidence from Germany

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Improving Risk Equalization with Constrained Regression

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