title: Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data.
abstract: 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.
authors.affiliation: Department of Statistics, Universidade Federal do Amazonas, Manaus, Brazil.|Department of Statistics, Universidade Federal de São Carlos, São Carlos, Brazil.
authors.forename: Jeremias
authors.initials: J
authors.lastname: Leão
authors.affiliation: Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Viña del Mar, Chile.|School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile.
authors.forename: Víctor
authors.initials: V
authors.lastname: Leiva
authors.affiliation: Institute of Mathematics and Statistics, Universidade Federal de Goiás, Goiânia, Brazil.|Department of Statistics, Universidade de Brasília, Brasília, Brazil.
authors.forename: Helton
authors.initials: H
authors.lastname: Saulo
authors.affiliation: Department of Statistics, Universidade Federal de São Carlos, São Carlos, Brazil.
authors.forename: Vera
authors.initials: V
authors.lastname: Tomazella
mesh_terms: D001699:Biometry / Q000379:methods*; D019937:Diagnostic Techniques and Procedures; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016019:Survival Analysis
keywords: Birnbaum-Saunders distribution; Censored data; Global and local influence; Maximum-likelihood method; Residual analysis