TY - JOUR
T1 - Birnbaum–Saunders frailty regression models
T2 - Diagnostics and application to medical data
AU - Leão, Jeremias
AU - Leiva, Víctor
AU - Saulo, Helton
AU - Tomazella, Vera
N1 - Funding Information:
The authors thank the Editors and reviewers for their constructive comments on an earlier version of this manuscript that resulted in this improved version. This research work was partially supported by FAPESP, CNPq, and CAPES grants, Brazil, and by FONDECYT 1160868 grant, Chile.
Publisher Copyright:
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2017/3/1
Y1 - 2017/3/1
N2 - In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum–Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.
AB - In survival models, some covariates affecting the lifetime could not be observed or measured. These covariates may correspond to environmental or genetic factors and be considered as a random effect related to a frailty of the individuals explaining their survival times. We propose a methodology based on a Birnbaum–Saunders frailty regression model, which can be applied to censored or uncensored data. Maximum-likelihood methods are used to estimate the model parameters and to derive local influence techniques. Diagnostic tools are important in regression to detect anomalies, as departures from error assumptions and presence of outliers and influential cases. Normal curvatures for local influence under different perturbations are computed and two types of residuals are introduced. Two examples with uncensored and censored real-world data illustrate the proposed methodology. Comparison with classical frailty models is carried out in these examples, which shows the superiority of the proposed model.
KW - Birnbaum–Saunders distribution
KW - Censored data
KW - Global and local influence
KW - Maximum-likelihood method
KW - Residual analysis
UR - http://www.scopus.com/inward/record.url?scp=85008222795&partnerID=8YFLogxK
U2 - 10.1002/bimj.201600008
DO - 10.1002/bimj.201600008
M3 - Article
C2 - 28054373
AN - SCOPUS:85008222795
VL - 59
SP - 291
EP - 314
JO - Biometrical Journal
JF - Biometrical Journal
SN - 0323-3847
IS - 2
ER -