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Leão J, Bourguignon M, Saulo H, Santos-Neto M, Calsavara V. The Negative Binomial Beta Prime Regression Model with Cure Rate: Application with a Melanoma Dataset. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2021. [DOI: 10.1007/s42519-021-00195-y] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
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2
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Molina KC, Calsavara VF, Tomazella VD, Milani EA. Survival models induced by zero-modified power series discrete frailty: Application with a melanoma data set. Stat Methods Med Res 2021; 30:1874-1889. [PMID: 33955295 DOI: 10.1177/09622802211011187] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Survival models with a frailty term are presented as an extension of Cox's proportional hazard model, in which a random effect is introduced in the hazard function in a multiplicative form with the aim of modeling the unobserved heterogeneity in the population. Candidates for the frailty distribution are assumed to be continuous and non-negative. However, this assumption may not be true in some situations. In this paper, we consider a discretely distributed frailty model that allows units with zero frailty, that is, it can be interpreted as having long-term survivors. We propose a new discrete frailty-induced survival model with a zero-modified power series family, which can be zero-inflated or zero-deflated depending on the parameter value. Parameter estimation was obtained using the maximum likelihood method, and the performance of the proposed models was performed by Monte Carlo simulation studies. Finally, the applicability of the proposed models was illustrated with a real melanoma cancer data set.
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Affiliation(s)
- Katy C Molina
- Institute of Mathematics and Computer Sciences, University of São Paulo, São Carlos, SP, Brazil.,Department of Statistics, Federal University of São Carlos, São Carlos, SP, Brazil
| | - Vinicius F Calsavara
- Department of Epidemiology and Statistics, A.C.Camargo Cancer Center, São Paulo, SP, Brazil.,Biostatistics and Bioinformatics Research Center, Cedars-Sinai Medical Center, Los Angeles, CA, USA
| | - Vera D Tomazella
- Department of Statistics, Federal University of São Carlos, São Carlos, SP, Brazil
| | - Eder A Milani
- Institute of Mathematics and Statistics, Federal University of Goiás, Goiânia, Brazil
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Cavenague de Souza HC, Louzada F, de Oliveira MR, Fawole B, Akintan A, Oyeneyin L, Sanni W, Silva Castro Perdoná GD. The Log-Normal zero-inflated cure regression model for labor time in an African obstetric population. J Appl Stat 2021; 49:2416-2429. [DOI: 10.1080/02664763.2021.1896684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | - Francisco Louzada
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, Brazil
| | | | - Bukola Fawole
- Department of Obstetrics and Gynaecology, College of Medicine, University of Ibadan, Ibadan, Nigeria
| | - Adesina Akintan
- Department of Obstetrics and Gynaecology, Mother and Child Hospital, Akure, Ondo State, Nigeria
| | - Lawal Oyeneyin
- Department of Obstetrics and Gynaecology, Mother and Child Hospital, Ondo, Ondo State, Nigeria
| | | | - Gleici da Silva Castro Perdoná
- Department of Social Medicine, Ribeirão Preto School of Medicine, University of São Paulo, Ribeirão Preto, São Paulo Brazil
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4
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Calsavara VF, Milani EA, Bertolli E, Tomazella V. Long-term frailty modeling using a non-proportional hazards model: Application with a melanoma dataset. Stat Methods Med Res 2019; 29:2100-2118. [DOI: 10.1177/0962280219883905] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The semiparametric Cox regression model is often fitted in the modeling of survival data. One of its main advantages is the ease of interpretation, as long as the hazards rates for two individuals do not vary over time. In practice the proportionality assumption of the hazards may not be true in some situations. In addition, in several survival data is common a proportion of units not susceptible to the event of interest, even if, accompanied by a sufficiently large time, which is so-called immune, “cured,” or not susceptible to the event of interest. In this context, several cure rate models are available to deal with in the long term. Here, we consider the generalized time-dependent logistic (GTDL) model with a power variance function (PVF) frailty term introduced in the hazard function to control for unobservable heterogeneity in patient populations. It allows for non-proportional hazards, as well as survival data with long-term survivors. Parameter estimation was performed using the maximum likelihood method, and Monte Carlo simulation was conducted to evaluate the performance of the models. Its practice relevance is illustrated in a real medical dataset from a population-based study of incident cases of melanoma diagnosed in the state of São Paulo, Brazil.
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Affiliation(s)
- Vinicius F Calsavara
- Department of Epidemiology and Statistics, A.C.Camargo Cancer Center, São Paulo, Brazil
| | - Eder A Milani
- Institute of Mathematics and Statistics, Federal University of Goiás, Goiânia, Brazil
| | - Eduardo Bertolli
- Skin Cancer Department, A.C.Camargo Cancer Center, São Paulo, Brazil
| | - Vera Tomazella
- Department of Statistics, Federal University of São Carlos, São Carlos, Brazil
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Calsavara VF, Rodrigues AS, Rocha R, Louzada F, Tomazella V, Souza ACRLA, Costa RA, Francisco RPV. Zero-adjusted defective regression models for modeling lifetime data. J Appl Stat 2019. [DOI: 10.1080/02664763.2019.1597029] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Vinicius F. Calsavara
- Department of Epidemiology and Statistics, A.C.Camargo Cancer Center, São Paulo, SP, Brazil
| | - Agatha S. Rodrigues
- Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, Brazil
- Department of Obstetrics and Gynecology, São Paulo University Medical School, São Paulo, SP, Brazil
| | - Ricardo Rocha
- Department of Statistics, Federal University of Bahia, Salvador, BA, Brazil
| | - Francisco Louzada
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, SP, Brazil
| | - Vera Tomazella
- Department of Statistics, Federal University of São Carlos, São Carlos, SP, Brazil
| | - Ana C. R. L. A. Souza
- Department of Obstetrics and Gynecology, São Paulo University Medical School, São Paulo, SP, Brazil
| | - Rafaela A. Costa
- Department of Obstetrics and Gynecology, São Paulo University Medical School, São Paulo, SP, Brazil
| | - Rossana P. V. Francisco
- Department of Obstetrics and Gynecology, São Paulo University Medical School, São Paulo, SP, Brazil
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Calsavara VF, Rodrigues AS, Rocha R, Tomazella V, Louzada F. Defective regression models for cure rate modeling with interval-censored data. Biom J 2019; 61:841-859. [PMID: 30868619 DOI: 10.1002/bimj.201800056] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2018] [Revised: 10/17/2018] [Accepted: 02/22/2019] [Indexed: 11/11/2022]
Abstract
Regression models in survival analysis are most commonly applied for right-censored survival data. In some situations, the time to the event is not exactly observed, although it is known that the event occurred between two observed times. In practice, the moment of observation is frequently taken as the event occurrence time, and the interval-censored mechanism is ignored. We present a cure rate defective model for interval-censored event-time data. The defective distribution is characterized by a density function whose integration assumes a value less than one when the parameter domain differs from the usual domain. We use the Gompertz and inverse Gaussian defective distributions to model data containing cured elements and estimate parameters using the maximum likelihood estimation procedure. We evaluate the performance of the proposed models using Monte Carlo simulation studies. Practical relevance of the models is illustrated by applying datasets on ovarian cancer recurrence and oral lesions in children after liver transplantation, both of which were derived from studies performed at A.C. Camargo Cancer Center in São Paulo, Brazil.
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Affiliation(s)
- Vinicius F Calsavara
- Department of Epidemiology and Statistics, A.C. Camargo Cancer Center, São Paulo, SP, Brazil
| | - Agatha S Rodrigues
- Institute of Mathematics and Statistics, University of São Paulo, São Paulo, SP, Brazil.,Department of Obstetrics and Gynecology, São Paulo University Medical School, São Paulo, SP, Brazil
| | - Ricardo Rocha
- Department of Statistics, Federal University of Bahia, Salvador, BA, Brazil
| | - Vera Tomazella
- Department of Statistics, Federal University of São Carlos, São Carlos, SP, Brazil
| | - Francisco Louzada
- Institute of Mathematical Science and Computing, University of São Paulo, São Carlos, SP, Brazil
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7
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Scudilio J, Calsavara VF, Rocha R, Louzada F, Tomazella V, Rodrigues AS. Defective models induced by gamma frailty term for survival data with cured fraction. J Appl Stat 2018. [DOI: 10.1080/02664763.2018.1498464] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Juliana Scudilio
- Maths Science Institute and Computing, University of São Paulo, São Carlos, Brazil
- Department of Statistics, Federal University of São Carlos, São Carlos, Brazil
| | - Vinicius F. Calsavara
- Department of Epidemiology and Statistics, A.C.Camargo Cancer Center, São Paulo, Brazil
| | - Ricardo Rocha
- Maths Science Institute and Computing, University of São Paulo, São Carlos, Brazil
| | - Francisco Louzada
- Maths Science Institute and Computing, University of São Paulo, São Carlos, Brazil
| | - Vera Tomazella
- Department of Statistics, Federal University of São Carlos, São Carlos, Brazil
| | - Agatha S. Rodrigues
- Institute of Mathematics and Statistics, University of São Paulo, São Paulo, Brazil
- Department of Obstetrics and Gynecology, Faculty of Medicine, University of São Paulo, São Paulo, Brazil
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