Gilbert W. Fellingham and Athanasios Kottas
12/31/2007 09:00 AM
Applied Mathematics & Statistics
We develop Bayesian parametric and nonparametric hierarchical approaches to modeling health insurance claims data. Both prediction methods produce credibility type estimators, which use relevant information from related experience. In the parametric model, the likelihood arises through a mixture of a gamma distribution for the non-zero costs (severity), with a point mass for the zero costs (propensity). In the nonparametric extension, Dirichlet process priors are associated with the propensity parameters as well as the severity parameters. Posterior inference and prediction for both models is based on Markov chain Monte Carlo posterior simulation methods. A simulation study is used to demonstrate the utility of the nonparametric model across different settings. Moreover, we illustrate the methodology using real data from 1994 and 1995 provided by a major medical provider from a block of medium sized groups in the Midwest. The models were fit to the 1994 data, with their performance assessed and compared using the 1995 data.
