Reserving in the Age of Obesity

Motivation: There is increasing evidence that obesity contributes to the cost of medical care in workers compensation, and that this contribution is significant in magnitude. For instance, a recent study of workers compensation claims of Duke University employees shows that, for the morbidly obese, the medical costs per 100 full-time equivalent employees are nearly seven times as high as for employees of recommended weight. In the following study, the evidence of the contribution of obesity to the medical costs of workers compensation is generalized to a set of claims that comprises 36 U.S. States and nine injury years. Further, it is shown how the cost difference between “obese claims” and comparable “non-obese claims” develops as claims mature—this evidence of the difference in development offers important guidance for both reserving and ratemaking. The study is confined to the effect of obesity on severity—the effect of obesity on claim frequency is beyond the scope of this analysis.

Method: The study makes use of a matched-pairs research framework. Every obese claim in the data set is matched with a non-obese claim. Exact matching applies to all claim characteristics, except age at injury, where proximity matching is employed. The set of matched pairs is then analyzed using a semiparametric Bayesian multilevel model, the nonparametric component of which accounts for the possible nonlinear influence of age. Aside from age, the covariates comprise the injury year, the nature of injury, the U.S. state, and the industry— these four covariates enter the model as random effects. Further, the gender of the claimant and cross-state differences in the legislative environment, as they manifest themselves in mandatory utilization review and mandatory bill review, are accounted for using indicator variables. The model is estimated by means of MCMC (Markov Chain Monte Carlo simulation). The reversible jump concept of Bayesian modeling averaging is used in determining the functional form of the nonparametric component that captures the influence of age.

Results: The study shows that, in the aggregate, obese claims are 2.8 times more expensive than non-obese claims at the 12-month maturity, but this cost difference climbs to a factor of 4.5 at the three-year maturity and to 5.3 at the five-year maturity. Further, the cost difference (at the five-year maturity) is less for females than for males. Mandatory utilization review and, in particular, mandatory bill review significantly reduce the cost difference between obese and non-obese claims.

Availability: The semiparametric multilevel model was estimated using JAGS with R. JAGS (Just Another Gibbs Sampler, http://www-ice.iarc.fr/~martyn/software/jags/) is an open-source platform for Gibbs sampling, developed by Martyn Plummer at the International Agency for Research on Cancer of the World Health Organization in Lyon, France. The reversible jump routine was written as a C++ JAGS module. R is an open-source statistical modeling platform (http://www.r-project.org/), which is administered by the Technical University of Vienna.

Keywords: Obesity, Multilevel Model, Partial Linear Model, Reversible Jump MCMC, Semiparametric Model, Workers Compensation