A Flexible Two-Part Random Effects Model for Correlated Medical Costs
Mark Cowen, Quality Institute, St. Joseph Mercy Health System  *Lei Liu, University of Virginia  Robert Strawderman, Cornell University 

Keywords: Generalized linear mixed model; Gaussian quadrature; Health economics; Generalized Gamma distribution

We use the two part random effects model (Olsen and Schafer 2001, Tooze et al. 2002) to analyze correlated medical costs, with a large portion of zero costs and right skewness and heteroscedasticity for positive costs. We use two GLMMs for the odds of cost being positive (part I) and the amount of positive cost (part II), connected by correlated random effects to account for the cross-equation correlation. In addition, we assume that in part II: (1) positive medical costs follow a flexible generalized Gamma distribution which includes lognormal, Gamma, and Weibull distribution as special cases; (2) heteroscedasticity is present in that the scale depends on covariates. The estimation is proceeded by Gaussian quadrature technique in SAS Proc NLMIXED. Our model is applied to pharmacy costs of 56245 adult patients clustered within 239 physicians in a Midwestern managed care organization.

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