Modeling heavy-tailed distributions in healthcare utilization by parametric and Bayesian methods

Distributions of healthcare utilization such as hospital length of stay and inpatient cost are generally right skewed. The extremes represent legitimate observations on patients who, because of the severity of their illness and need for medical intervention, have long in-stays and incur large costs. In this context we demonstrate the application of several parametric models for fitting heavy tailed data. Both maximum likelihood and Bayesian methods are used for estimation in certain Coxian phase-type models, mixtures of exponential distributions, and for comparison, the lognormal, loglogistic, Weibull, generalized gamma and generalized Pareto —including the standard Pareto and Burr distributions. We focus on the mean and percentiles of the response, and illustrate our methods with an empirical example on fitting models to hospital stays for acute myocardial infarction in the Nationwide Inpatient Sample of the Healthcare Utilization Project. A suite of SAS procedures is used in all computations, specifically the procedures GENMOD, LIFEREG, MCMC, NLMIXED, FMM and SEVERITY.