Fitting Heavy-Tailed Distributions to Health Care Data by Parametric and Bayesian Methods

Abstract

We consider fitting parametric distributions to health care data that often exhibit heavy tails. The three-parameter generalized gamma distribution and its special cases, the lognormal, Weibull, and gamma, are examined. Continuous gamma mixing of the Weibull distribution leads to the Burr distribution and its special cases, the log-logistic and Pareto distributions. For finite mixtures we consider Coxian-phase type distributions and mixtures of exponentials. Both maximum likelihood and Bayesian methods are presented with prescriptions for fitting these models using recent enhancements to SAS software. Comparisons between competing models are made using probability–probability plots, formal likelihood ratio tests for nested models, and Vuong test for strictly nonnested models. We provide a demonstration of these methods with two empirical data sets, one with completely observed hospital length of stays, and the other with censored follow-up times of patients who received a bone marrow transplant.

AMS Subject Classification:

• 62F02
• 62F15
• 62N01

Keywords:

• Bayesian methods
• Coxian phase-type model
• Length of stay
• Mixture distributions
• SAS software

Acknowledgment

We thank the associate editor and two anonymous referees for their careful reading of our article, and for incisive comments and suggestions for improvement.