Traditionally, linear regression has been the technique of choice for predicting medical risk. This paper presents a new approach to modeling the second part of two-part models utilizing extensions of the generalized linear model. The primary method of estimation for this model is maximum likelihood. This method as well as the generalizations quasi-likelihood and extended quasi-likelihood are discussed. An example using medical expense data from Washington State employees is used to illustrate the methods. The model includes demographic variables as well as an Ambulatory. Care Group variable to account for prior health status.