Bayesian profiling for cost with zeros to decompose total cost into probability of cost and mean nonzero cost

Cost of health care can vary substantially across hospitals, centers, or providers. Data from electronic health records provide information for studying patterns of cost variation and identifying high or low cost centers. Cost data often include zero values when patients receive no care, and joint two-part models have been developed for clustered cost data with zeros. Standard methods for center comparisons, sometimes called profiling, can use these methods to incorporate zero values into total cost. However, zero costs also provide opportunities to further examine sources of cost variation and outliers. For example, a hospital may have high (or low) cost due to frequency of nonzero cost, amount of nonzero cost, or a combination of those. We give methods for decomposing hospital differences in total cost with zeros into components for probability of use (i.e., of nonzero cost) and for cost of use (mean of nonzero cost). The components multiply to total cost and quantify components on the same easily interpreted multiplicative scales. The methods are based on Bayesian hierarchical models and counterfactual arguments, with Markov chain Monte Carlo estimation. We used simulated data to illustrate use, interpretation, and visualization of the methods in diverse situations, and applied the methods to 30,024 patients at 57 US Veterans Administration hospitals to characterize outlier hospitals in one year cost of inpatient care following a cardiac procedure. Twenty eight percent of patients had zero cost. These methods are useful in providing insight into cost variation and outliers for planning future studies or interventions.