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Modeling traumatic brain injury lifetime data: Improved estimators for the Generalized Gamma distribution under small samples

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  • Pedro L Ramos
  • Diego C Nascimento
  • Paulo H Ferreira
  • Karina T Weber
  • Taiza E G Santos
  • Francisco Louzada

Abstract

In this paper, from the practical point of view, we focus on modeling traumatic brain injury data considering different stages of hospitalization, related to patients’ survival rates following traumatic brain injury caused by traffic accidents. From the statistical point of view, the primary objective is related to overcoming the limited number of traumatic brain injury patients available for studying by considering different estimation methods to obtain improved estimators of the model parameters, which can be recommended to be used in the presence of small samples. To have a general methodology, at least in principle, we consider the very flexible Generalized Gamma distribution. We compare various estimation methods using extensive numerical simulations. The results reveal that the penalized maximum likelihood estimators have the smallest mean square errors and biases, proving to be the most efficient method among the investigated ones, mainly to be used in the presence of small samples. The Simulated Annealing technique is used to avoid numerical problems during the optimization process, as well as the need for good initial values. Overall, we considered an amount of three real data sets related to traumatic brain injury caused by traffic accidents to demonstrate that the Generalized Gamma distribution is a simple alternative to be used in this type of applications for different occurrence rates and risks, and in the presence of small samples.

Suggested Citation

  • Pedro L Ramos & Diego C Nascimento & Paulo H Ferreira & Karina T Weber & Taiza E G Santos & Francisco Louzada, 2019. "Modeling traumatic brain injury lifetime data: Improved estimators for the Generalized Gamma distribution under small samples," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-22, August.
    • Handle: RePEc:plo:pone00:0221332
    DOI: 10.1371/journal.pone.0221332
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    References listed on IDEAS

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    1. Angela Noufaily & M. Jones, 2013. "On maximization of the likelihood for the generalized gamma distribution," Computational Statistics, Springer, vol. 28(2), pages 505-517, April.
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    Cited by:

    1. Shyamal Ghosh & Prajamitra Bhuyan & Maxim Finkelstein, 2022. "On a bivariate copula for modeling negative dependence: application to New York air quality data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1329-1353, December.
    2. Muhammad Ahsan-ul-Haq & Mukhtar Ahmed & Javeria Zafar & Pedro Luiz Ramos, 2022. "Modeling of COVID-19 Cases in Pakistan Using Lifetime Probability Distributions," Annals of Data Science, Springer, vol. 9(1), pages 141-152, February.
    3. Combes, Catherine & Ng, Hon Keung Tony, 2022. "On parameter estimation for Amoroso family of distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 191(C), pages 309-327.

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