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

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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.

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Authors and Affiliations

  1. Department of Epidemiology and Biostatistics, Michigan State University, B 629 West Fee, 909 Fee Road, East Lansing, Michigan, 48824-1315, USA

    Joseph C. Gardiner & Zhehui Luo

  2. Center for Health Research, Geisinger Health System, Danville, Pennsylvania, USA

    Xiaoqin Tang

  3. Department of Statistics and Probability, Michigan State University, East Lansing, Michigan, USA

    R. V. Ramamoorthi

Authors
  1. Joseph C. Gardiner
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  2. Zhehui Luo
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  3. Xiaoqin Tang
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  4. R. V. Ramamoorthi
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Correspondence to Joseph C. Gardiner.

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Gardiner, J.C., Luo, Z., Tang, X. et al. Fitting Heavy-Tailed Distributions to Health Care Data by Parametric and Bayesian Methods. J Stat Theory Pract 8, 619–652 (2014). https://doi.org/10.1080/15598608.2013.824823

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  • DOI: https://doi.org/10.1080/15598608.2013.824823

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