Generalized Gamma Distribution for Bayesian Profiling of Facility-Level Variation in 30-Day, Risk-Adjusted Costs Following Percutaneous Coronary Intervention (PCI): The VA’s CART Program
*Colin I O'Donnell, MS, University of Colorado School of Public Health
Keywords: Bayesian profiling, generalized gamma model, model selection
The VA CART program evaluated 30-day follow-up costs post-PCI for 32,080 patients across 62 hospitals between 2008-2011. Given the potential for unequal variance, we compared two random effect models to estimate standardized cost ratios (SCR) of hospital level cost and 95% credibility intervals. Using Bayesian profiling methods, we estimated SCRs using a lognormal model and generalized gamma model (GGM) for cost. Generalized gamma contains as submodels gamma, lognormal, and Weibull. Emphasis was on variation in the SCRs with the goal of identifying outlying hospitals, defined as hospitals with credibility intervals that did not cross the system median SCR value of 1. Profiling implemented in JAGS and R consisted of a single chain, no thinning, 2000 burn-in iterations, followed by 10,000 estimation iterations. The GGM identified one more high-cost hospital than the lognormal model (15 vs. 14) and two fewer low-cost hospitals (16 vs. 18). The difference between the 62 paired SCRs was small, with a mean difference of 0.00006 and standard deviation of 0.095. GGM is easily implemented using Bayesian methods and eliminates the need to choose between competing models.