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

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

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.

Más información

Título según WOS: ID WOS:000485062200018 Not found in local WOS DB
Título de la Revista: PLOS ONE
Volumen: 14
Número: 8
Editorial: PUBLIC LIBRARY SCIENCE
Fecha de publicación: 2019
DOI:

10.1371/journal.pone.0221332

Notas: ISI