Comparing Credibility Estimates of Health Insurance Claims Costs

We fit a linear mixed model and a Bayesian hierarchical model to data provided by an insurance company located in the Midwest. We used models fit to the 1994 data to predict health insurance claims costs for 1995. We implemented the linear mixed model in SAS and used two different prediction methods to predict 1995 costs. In the linear mixed model we assumed a normal likelihood. In the hierarchical Bayes model, we used Markov chain Monte Carlo methods to obtain posterior distributions of the parameters, as well as predictive distributions of the next year’s costs. We assumed the likelihood for this model to be a mixture of a gamma distribution for the nonzero costs, with a point mass for the zero costs. All prediction methods use credibility-type estimators that use relevant information from related experience. The linear mixed model was heavily influenced by the skewed nature of the data. The assumed gamma likelihood of the full Bayesian analysis appeared to underestimate the tails of the distributions. All prediction models underestimated costs for 1995.