A flexible two-part random effects model for correlated medical costs

Abstract

In this paper, we propose a flexible “two-part” random effects model ( Olsen and Schafer, 2001; Tooze et al., 2002) for correlated medical cost data. Typically, medical cost data are right-skewed, involve a substantial proportion of zero values, and may exhibit heteroscedasticity. In many cases, such data are also obtained in hierarchical form, e.g., on patients served by the same physician. The proposed model specification therefore consists of two generalized linear mixed models (GLMM), linked together by correlated random effects. Respectively, and conditionally on the random effects and covariates, we model the odds of cost being positive (Part I) using a GLMM with a logistic link and the mean cost (Part II) given that costs were actually incurred using a generalized gamma regression model with random effects and a scale parameter that is allowed to depend on covariates (cf., Manning et al., 2005). The class of generalized gamma distributions is very flexible and includes the lognormal, gamma, inverse gamma and Weibull distributions as special cases. We demonstrate how to carry out estimation using the Gaussian quadrature techniques conveniently implemented in SAS Proc NLMIXED. The proposed model is used to analyze pharmacy cost data on 56,245 adult patients clustered within 239 physicians in a mid-western U.S. managed care organization.