1
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Gallardo DI, Brandão M, Leão J, Bourguignon M, Calsavara V. A New Mixture Model With Cure Rate Applied to Breast Cancer Data. Biom J 2024; 66:e202300257. [PMID: 39104134 DOI: 10.1002/bimj.202300257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/16/2023] [Revised: 03/13/2024] [Accepted: 03/18/2024] [Indexed: 08/07/2024]
Abstract
We introduce a new modelling for long-term survival models, assuming that the number of competing causes follows a mixture of Poisson and the Birnbaum-Saunders distribution. In this context, we present some statistical properties of our model and demonstrate that the promotion time model emerges as a limiting case. We delve into detailed discussions of specific models within this class. Notably, we examine the expected number of competing causes, which depends on covariates. This allows for direct modeling of the cure rate as a function of covariates. We present an Expectation-Maximization (EM) algorithm for parameter estimation, to discuss the estimation via maximum likelihood (ML) and provide insights into parameter inference for this model. Additionally, we outline sufficient conditions for ensuring the consistency and asymptotic normal distribution of ML estimators. To evaluate the performance of our estimation method, we conduct a Monte Carlo simulation to provide asymptotic properties and a power study of LR test by contrasting our methodology against the promotion time model. To demonstrate the practical applicability of our model, we apply it to a real medical dataset from a population-based study of incidence of breast cancer in São Paulo, Brazil. Our results illustrate that the proposed model can outperform traditional approaches in terms of model fitting, highlighting its potential utility in real-world scenarios.
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Affiliation(s)
- Diego I Gallardo
- Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción, Chile
| | - Márcia Brandão
- Departamento de Estatística, Universidade Federal do Amazonas, Manaus, Brazil
| | - Jeremias Leão
- Departamento de Estatística, Universidade Federal do Amazonas, Manaus, Brazil
| | - Marcelo Bourguignon
- Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal, Brazil
| | - Vinicius Calsavara
- Department of Computational Biomedicine, Cedars-Sinai Medical Center, Los Angeles, California, USA
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2
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Vilca F, Vila R, Saulo H, Sánchez L, Leão J. Theoretical results and modeling under the discrete Birnbaum-Saunders distribution. COMMUN STAT-THEOR M 2022. [DOI: 10.1080/03610926.2022.2110843] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Filidor Vilca
- Department of Statistics, Universidade Estadual de Campinas, Campinas, Brazil
| | - Roberto Vila
- Department of Statistics, Universidade de Brasília, Brasília, Brazil
| | - Helton Saulo
- Department of Statistics, Universidade de Brasília, Brasília, Brazil
| | - Luis Sánchez
- Institute of Statistics, Universidad Austral de Chile, Valdivia, Chile
| | - Jeremias Leão
- Department of Statistics, Universidade Federal do Amazonas, Manaus, Brazil
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Martínez-Flórez G, Olmos NM, Venegas O. Unit-bimodal Birnbaum-Saunders distribution with applications. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2069260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Guillermo Martínez-Flórez
- Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba, Colombia
| | - Neveka M. Olmos
- Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile
| | - Osvaldo Venegas
- Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco, Chile
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4
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Saulo H, Souza R, Vila R, Leiva V, Aykroyd RG. Modeling Mortality Based on Pollution and Temperature Using a New Birnbaum-Saunders Autoregressive Moving Average Structure with Regressors and Related-Sensors Data. SENSORS 2021; 21:s21196518. [PMID: 34640834 PMCID: PMC8512640 DOI: 10.3390/s21196518] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Revised: 09/22/2021] [Accepted: 09/25/2021] [Indexed: 12/18/2022]
Abstract
Environmental agencies are interested in relating mortality to pollutants and possible environmental contributors such as temperature. The Gaussianity assumption is often violated when modeling this relationship due to asymmetry and then other regression models should be considered. The class of Birnbaum–Saunders models, especially their regression formulations, has received considerable attention in the statistical literature. These models have been applied successfully in different areas with an emphasis on engineering, environment, and medicine. A common simplification of these models is that statistical dependence is often not considered. In this paper, we propose and derive a time-dependent model based on a reparameterized Birnbaum–Saunders (RBS) asymmetric distribution that allows us to analyze data in terms of a time-varying conditional mean. In particular, it is a dynamic class of autoregressive moving average (ARMA) models with regressors and a conditional RBS distribution (RBSARMAX). By means of a Monte Carlo simulation study, the statistical performance of the new methodology is assessed, showing good results. The asymmetric RBSARMAX structure is applied to the modeling of mortality as a function of pollution and temperature over time with sensor-related data. This modeling provides strong evidence that the new ARMA formulation is a good alternative for dealing with temporal data, particularly related to mortality with regressors of environmental temperature and pollution.
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Affiliation(s)
- Helton Saulo
- Department of Statistics, Universidade de Brasília, Brasília 70910-90, Brazil; (H.S.); (R.S.); (R.V.)
| | - Rubens Souza
- Department of Statistics, Universidade de Brasília, Brasília 70910-90, Brazil; (H.S.); (R.S.); (R.V.)
| | - Roberto Vila
- Department of Statistics, Universidade de Brasília, Brasília 70910-90, Brazil; (H.S.); (R.S.); (R.V.)
| | - Víctor Leiva
- School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile
- Correspondence: or
| | - Robert G. Aykroyd
- Department of Statistics, University of Leeds, Leeds, West Yorkshire LS2 9JT, UK;
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Predicting PM2.5 and PM10 Levels during Critical Episodes Management in Santiago, Chile, with a Bivariate Birnbaum-Saunders Log-Linear Model. MATHEMATICS 2021. [DOI: 10.3390/math9060645] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Improving air quality is an important environmental challenge of our time. Chile currently has one of the most stable and emerging economies in Latin America, where human impact on natural resources and air quality does not go unperceived. Santiago, the capital of Chile, is one of the cities in which particulate matter (PM) levels exceed national and international limits. Its location and climate cause critical conditions for human health when interaction with anthropogenic emissions is present. In this paper, we propose a predictive model based on bivariate regression to estimate PM levels, related to PM2.5 and PM10, simultaneously. Birnbaum-Saunders distributions are used in the joint modeling of real-world PM2.5 and PM10 data by considering as covariates some relevant meteorological variables employed in similar studies. The Mahalanobis distance is utilized to assess bivariate outliers and to detect suitability of the distributional assumption. In addition, we use the local influence technique for analyzing the impact of a perturbation on the overall estimation of model parameters. In the predictions, we check the categorization for the observed and predicted cases of the model according to the primary air quality regulations for PM.
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Saulo H, Leão J, Leiva V, Vila R, Tomazella V. A bivariate fatigue-life regression model and its application to fracture of metallic tools. BRAZ J PROBAB STAT 2021. [DOI: 10.1214/20-bjps490] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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7
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Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections. MATHEMATICS 2020. [DOI: 10.3390/math9010044] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Sign, Wilcoxon and Mann-Whitney tests are nonparametric methods in one or two-sample problems. The nonparametric methods are alternatives used for testing hypothesis when the standard methods based on the Gaussianity assumption are not suitable to be applied. Recently, the functional data analysis (FDA) has gained relevance in statistical modeling. In FDA, each observation is a curve or function which usually is a realization of a stochastic process. In the literature of FDA, several methods have been proposed for testing hypothesis with samples coming from Gaussian processes. However, when this assumption is not realistic, it is necessary to utilize other approaches. Clustering and regression methods, among others, for non-Gaussian functional data have been proposed recently. In this paper, we propose extensions of the sign, Wilcoxon and Mann-Whitney tests to the functional data context as methods for testing hypothesis when we have one or two samples of non-Gaussian functional data. We use random projections to transform the functional problem into a scalar one, and then we proceed as in the standard case. Based on a simulation study, we show that the proposed tests have a good performance. We illustrate the methodology by applying it to a real data set.
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Vila R, Leão J, Saulo H, Shahzad MN, Santos-Neto M. On a bimodal Birnbaum–Saunders distribution with applications to lifetime data. BRAZ J PROBAB STAT 2020. [DOI: 10.1214/19-bjps448] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Leão J, Leiva V, Saulo H, Tomazella V. A survival model with Birnbaum–Saunders frailty for uncensored and censored cancer data. BRAZ J PROBAB STAT 2018. [DOI: 10.1214/17-bjps360] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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11
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Affiliation(s)
- Rodney V. Fonseca
- Departamento de Estatística, Universidade Estadual de Campinas, Campinas/SP, Brazil
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12
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Desousa MF, Saulo H, Leiva V, Scalco P. On a tobit–Birnbaum–Saunders model with an application to medical data. J Appl Stat 2017. [DOI: 10.1080/02664763.2017.1322559] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Mário F. Desousa
- Faculty of Management, Accounting and Economics, Universidade Federal de Goiás, Goiania, Brazil
- Department of Statistics, Universidade Estadual de Campinas, São Paulo, Brazil
| | - Helton Saulo
- Department of Statistics, Universidade de Brasília, Brasília, Brazil
| | - Víctor Leiva
- School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile
| | - Paulo Scalco
- Faculty of Management, Accounting and Economics, Universidade Federal de Goiás, Goiania, Brazil
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14
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Saulo H, Leão J, Leiva V, Aykroyd RG. Birnbaum–Saunders autoregressive conditional duration models applied to high-frequency financial data. Stat Pap (Berl) 2017. [DOI: 10.1007/s00362-017-0888-6] [Citation(s) in RCA: 37] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Leão J, Leiva V, Saulo H, Tomazella V. Birnbaum-Saunders frailty regression models: Diagnostics and application to medical data. Biom J 2017; 59:291-314. [DOI: 10.1002/bimj.201600008] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2016] [Revised: 10/09/2016] [Accepted: 10/21/2016] [Indexed: 11/07/2022]
Affiliation(s)
- Jeremias Leão
- Department of Statistics; Universidade Federal do Amazonas; Manaus Brazil
- Department of Statistics; Universidade Federal de São Carlos; São Carlos Brazil
| | - Víctor Leiva
- Faculty of Engineering and Sciences; Universidad Adolfo Ibáñez; Viña del Mar Chile
- School of Industrial Engineering; Pontificia Universidad Católica de Valparaíso; Valparaíso Chile
| | - Helton Saulo
- Institute of Mathematics and Statistics; Universidade Federal de Goiás; Goiânia Brazil
- Department of Statistics; Universidade de Brasília; Brasília Brazil
| | - Vera Tomazella
- Department of Statistics; Universidade Federal de São Carlos; São Carlos Brazil
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Barros M, Galea M, Leiva V, Santos-Neto M. Generalized Tobit models: diagnostics and application in econometrics. J Appl Stat 2016. [DOI: 10.1080/02664763.2016.1268572] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Michelli Barros
- Department of Statistics, Universidade Federal de Campina Grande, Campina Grande, Brazil
| | - Manuel Galea
- Department of Statistics, Pontificia Universidad Católica de Chile, Santiago, Chile
| | - Víctor Leiva
- Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Viña del Mar, Chile
- Faculty of Administration, Accounting and Economics, Universidade Federal de Goiás, Goiânia, Brazil
| | - Manoel Santos-Neto
- Department of Statistics, Universidade Federal de Campina Grande, Campina Grande, Brazil
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Olmos NM, Martínez-Flórez G, Bolfarine H. Bimodal Birnbaum–Saunders distribution with applications to non negative measurements. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2015.1133824] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Neveka M. Olmos
- Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta, Chile
| | - Guillermo Martínez-Flórez
- Departamento de Matemáticas y Estadística, Facultad de Ciencias, Universidad de Córdoba, Córdoba, Colombia
| | - Heleno Bolfarine
- Departamento de Estatítica, IME, Universidade de São Paulo, São Paulo, Brazil
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Marchant C, Leiva V, Cysneiros FJA, Vivanco JF. Diagnostics in multivariate generalized Birnbaum-Saunders regression models. J Appl Stat 2016. [DOI: 10.1080/02664763.2016.1148671] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Carolina Marchant
- Department of Statistics, Universidade Federal de Pernambuco, Recife, Brazil
| | - Víctor Leiva
- Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Viña del Mar, Chile
| | | | - Juan F. Vivanco
- Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Viña del Mar, Chile
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19
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A semiparametric scale-mixture regression model and predictive recursion maximum likelihood. Comput Stat Data Anal 2016. [DOI: 10.1016/j.csda.2015.08.005] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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20
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Santos-Neto M, Cysneiros FJA, Leiva V, Barros M. Reparameterized Birnbaum-Saunders regression models with varying precision. Electron J Stat 2016. [DOI: 10.1214/16-ejs1187] [Citation(s) in RCA: 49] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Leiva V, Tejo M, Guiraud P, Schmachtenberg O, Orio P, Marmolejo-Ramos F. Modeling neural activity with cumulative damage distributions. BIOLOGICAL CYBERNETICS 2015; 109:421-433. [PMID: 25998210 DOI: 10.1007/s00422-015-0651-9] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Accepted: 04/20/2015] [Indexed: 06/04/2023]
Abstract
Neurons transmit information as action potentials or spikes. Due to the inherent randomness of the inter-spike intervals (ISIs), probabilistic models are often used for their description. Cumulative damage (CD) distributions are a family of probabilistic models that has been widely considered for describing time-related cumulative processes. This family allows us to consider certain deterministic principles for modeling ISIs from a probabilistic viewpoint and to link its parameters to values with biological interpretation. The CD family includes the Birnbaum-Saunders and inverse Gaussian distributions, which possess distinctive properties and theoretical arguments useful for ISI description. We expand the use of CD distributions to the modeling of neural spiking behavior, mainly by testing the suitability of the Birnbaum-Saunders distribution, which has not been studied in the setting of neural activity. We validate this expansion with original experimental and simulated electrophysiological data.
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Affiliation(s)
- Víctor Leiva
- Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Viña del Mar, Chile.
- Institute of Statistics, Universidad de Valparaiso, Valparaiso, Chile.
| | - Mauricio Tejo
- Faculty of Natural and Exact Sciences, Universidad de Playa Ancha, Valparaiso, Chile
| | - Pierre Guiraud
- Centro de Investigación y Modelamiento de Fenómenos Aleatorios - Valparaíso, Faculty of Engineering, Universidad de Valparaíso, Valparaiso, Chile
| | - Oliver Schmachtenberg
- Centro Interdisciplinario de Neurociencia de Valparaíso and Institute of Neuroscience, Universidad de Valparaíso, Valparaiso, Chile
| | - Patricio Orio
- Centro Interdisciplinario de Neurociencia de Valparaíso and Institute of Neuroscience, Universidad de Valparaíso, Valparaiso, Chile
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Leiva V, Liu S, Shi L, Cysneiros FJA. Diagnostics in elliptical regression models with stochastic restrictions applied to econometrics. J Appl Stat 2015. [DOI: 10.1080/02664763.2015.1072140] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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23
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Rojas F, Leiva V, Wanke P, Marchant C. Optimization of Contribution Margins in Food Services by Modeling Independent Component Demand. REVISTA COLOMBIANA DE ESTADÍSTICA 2015. [DOI: 10.15446/rce.v38n1.48799] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
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Castro-Kuriss C, Leiva V, Athayde E. Graphical Tools to Assess Goodness-of-Fit in Non-Location-Scale Distributions. REVISTA COLOMBIANA DE ESTADÍSTICA 2014. [DOI: 10.15446/rce.v37n2spe.47941] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022] Open
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