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Loubna H, Goual H, Alghamdi FM, Mustafa MS, Tekle Mekiso G, Ali MM, Al-Nefaie AH, Alsuhabi H, Ibrahim M, Yousof HM. The quasi-xgamma frailty model with survival analysis under heterogeneity problem, validation testing, and risk analysis for emergency care data. Sci Rep 2024; 14:8973. [PMID: 38637600 PMCID: PMC11026502 DOI: 10.1038/s41598-024-59137-w] [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: 08/18/2023] [Accepted: 04/08/2024] [Indexed: 04/20/2024] Open
Abstract
Frailty models are important for survival data because they allow for the possibility of unobserved heterogeneity problem. The problem of heterogeneity can be existed due to a variety of factors, such as genetic predisposition, environmental factors, or lifestyle choices. Frailty models can help to identify these factors and to better understand their impact on survival. In this study, we suggest a novel quasi xgamma frailty (QXg-F) model for the survival analysis. In this work, the test of Rao-Robson and Nikulin is employed to test the validity and suitability of the probabilistic model, we examine the distribution's properties and evaluate its performance in comparison with many relevant cox-frailty models. To show how well the QXg-F model captures heterogeneity and enhances model fit, we use simulation studies and real data applications, including a fresh dataset gathered from an emergency hospital in Algeria. According to our research, the QXg-F model is a viable replacement for the current frailty modeling distributions and has the potential to improve the precision of survival analyses in a number of different sectors, including emergency care. Moreover, testing the ability and the importance of the new QXg-F model in insurance is investigated using simulations via different methods and application to insurance data.
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Affiliation(s)
- Hamami Loubna
- Laboratory of Probabilities and Statistics LaPS, Department of Mathematics, Faculty of Sciences, Badji Mokhtar Annaba University, Annaba, Algeria
| | - Hafida Goual
- Laboratory of Probabilities and Statistics LaPS, Department of Mathematics, Faculty of Sciences, Badji Mokhtar Annaba University, Annaba, Algeria
| | - Fatimah M Alghamdi
- Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia
| | | | - Getachew Tekle Mekiso
- Department of Statistics, College of Natural and Computational Science, Wachemo University, Hossana, Ethiopia.
| | - M Masoom Ali
- Department of Mathematical Sciences, Ball State University, Muncie, IN, USA
| | - Abdullah H Al-Nefaie
- Department of Quantitative Methods, School of Business, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
| | - Hassan Alsuhabi
- Department of Mathematics, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia
| | - Mohamed Ibrahim
- Department of Quantitative Methods, School of Business, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
- Department of Applied, Mathematical and Actuarial Statistics, Faculty of Commerce, Damietta University, Damietta, Egypt
| | - Haitham M Yousof
- Department of Statistics, Mathematics and Insurance, Benha University, Benha, Egypt
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2
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Liu K, Balakrishnan N, He M, Xie L. Likelihood inference for Birnbaum–Saunders frailty model with an application to bone marrow transplant data. J STAT COMPUT SIM 2023. [DOI: 10.1080/00949655.2023.2174543] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Affiliation(s)
- Kai Liu
- School of Statistics and Mathematics, Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
| | - N. Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
| | - Mu He
- Department of Mathematical Sciences, Xi'an Jiaotong-Liverpool University, Suzhou, People's Republic of China
| | - Lingfang Xie
- School of Finance, Shanghai Lixin University of Accounting and Finance, Shanghai, People's Republic of China
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3
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Mota A, Milani EA, Leão J, Ramos PL, Ferreira PH, Junior OG, Tomazella VLD, Louzada F. A new cure rate frailty regression model based on a weighted Lindley distribution applied to stomach cancer data. STAT METHOD APPL-GER 2022. [DOI: 10.1007/s10260-022-00673-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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4
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Wang P, Pal S. A two-way flexible generalized gamma transformation cure rate model. Stat Med 2022; 41:2427-2447. [PMID: 35262947 DOI: 10.1002/sim.9363] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2021] [Revised: 02/11/2022] [Accepted: 02/14/2022] [Indexed: 02/01/2023]
Abstract
We propose a two-way flexible cure rate model. The first flexibility is provided by considering a family of Box-Cox transformation cure models that include the commonly used cure models as special cases. The second flexibility is provided by proposing the wider class of generalized gamma distributions to model the associated lifetime. The advantage of this two-way flexibility is that it allows us to carry out tests of hypotheses to select an adequate cure model (within the family of Box-Cox transformation cure models) and a suitable lifetime distribution (within the wider class of generalized gamma distributions) that jointly provides the best fit to a given data. First, we study the maximum likelihood estimation of the generalized gamma Box-Cox transformation (GGBCT) model parameters. Then, we use the flexibility of our proposed model to carry out power studies to demonstrate the power of likelihood ratio test in rejecting mis-specified models. Furthermore, we study the bias and efficiency of the estimators of the cure rates under model mis-specification. Our findings strongly suggest the importance of selecting a correct lifetime distribution and a correct cure rate model, which can be achieved through the proposed two-way flexible model. Finally, we illustrate the applicability of our proposed model using a data from a breast cancer study and show that our model provides a better fit than the existing semiparametric Box-Cox transformation cure model with piecewise exponential approximation to the lifetime distribution.
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Affiliation(s)
- Pei Wang
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA
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5
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Hernández-Herrera G, Moriña D, Navarro A. Left-censored recurrent event analysis in epidemiological studies: a proposal for when the number of previous episodes is unknown. BMC Med Res Methodol 2022; 22:20. [PMID: 35034622 PMCID: PMC8761288 DOI: 10.1186/s12874-022-01503-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2021] [Accepted: 01/03/2022] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND When dealing with recurrent events in observational studies it is common to include subjects who became at risk before follow-up. This phenomenon is known as left censoring, and simply ignoring these prior episodes can lead to biased and inefficient estimates. We aimed to propose a statistical method that performs well in this setting. METHODS Our proposal was based on the use of models with specific baseline hazards. In this, the number of prior episodes were imputed when unknown and stratified according to whether the subject had been at risk of presenting the event before t = 0. A frailty term was also used. Two formulations were used for this "Specific Hazard Frailty Model Imputed" based on the "counting process" and "gap time." Performance was then examined in different scenarios through a comprehensive simulation study. RESULTS The proposed method performed well even when the percentage of subjects at risk before follow-up was very high. Biases were often below 10% and coverages were around 95%, being somewhat conservative. The gap time approach performed better with constant baseline hazards, whereas the counting process performed better with non-constant baseline hazards. CONCLUSIONS The use of common baseline methods is not advised when knowledge of prior episodes experienced by a participant is lacking. The approach in this study performed acceptably in most scenarios in which it was evaluated and should be considered an alternative in this context. It has been made freely available to interested researchers as R package miRecSurv.
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Affiliation(s)
- Gilma Hernández-Herrera
- Instituto de Investigaciones Médicas, Facultad de Medicina, Universidad de Antioquia, Medellín, Colombia.,Methodology of Biomedical Research and Public Health, Autonomous University of Barcelona, Cerdanyola del Vallès, Spain
| | - David Moriña
- Department of Econometrics, Statistics and Applied Economics, Riskcenter-IREA, University of Barcelona (UB), Barcelona, Spain. .,Centre de Recerca Matemàtica (CRM), Cerdanyola del Vallès, Spain. .,Facultat d'Economia i Empresa, Universitat de Barcelona (UB), Avinguda Diagonal, 690-694, 08034, Barcelona, Spain.
| | - Albert Navarro
- Psychosocial Risks, Organization of Work and Health (POWAH), Autonomous University of Barcelona (UAB), Cerdanyola del Vallès, Spain.,Biostatistics Unit, Faculty of Medicine, Autonomous University of Barcelona (UAB), Cerdanyola del Vallès, Spain
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6
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Rakhmawati TW, Ha ID, Lee H, Lee Y. Penalized variable selection for cause-specific hazard frailty models with clustered competing-risks data. Stat Med 2021; 40:6541-6557. [PMID: 34541690 DOI: 10.1002/sim.9197] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2020] [Revised: 08/27/2021] [Accepted: 08/28/2021] [Indexed: 11/08/2022]
Abstract
Competing risks data usually arise when an occurrence of an event precludes other types of events from being observed. Such data are often encountered in a clustered clinical study such as a multi-center clinical trial. For the clustered competing-risks data which are correlated within a cluster, competing-risks models allowing for frailty terms have been recently studied. To the best of our knowledge, however, there is no literature on variable selection methods for cause-specific hazard frailty models. In this article, we propose a variable selection procedure for fixed effects in cause-specific competing risks frailty models using a penalized h-likelihood (HL). Here, we study three penalty functions, LASSO, SCAD, and HL. Simulation studies demonstrate that the proposed procedure using the HL penalty works well, providing a higher probability of choosing the true model than LASSO and SCAD methods without losing prediction accuracy. The proposed method is illustrated by using two kinds of clustered competing-risks cancer data sets.
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Affiliation(s)
| | - Il Do Ha
- Department of Statistics, Pukyong National University, Busan, South Korea
| | - Hangbin Lee
- Department of Statistics, Seoul National University, Seoul, South Korea
| | - Youngjo Lee
- Department of Statistics, Seoul National University, Seoul, South Korea
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7
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Liu K, Balakrishnan N, He M. Generalized Birnbaum–Saunders mixture cure frailty model: inferential method and an application to bone marrow transplant data. COMMUN STAT-SIMUL C 2021. [DOI: 10.1080/03610918.2021.1995753] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Kai Liu
- School of Statistics and Mathematics, Interdisciplinary Research Institute of Data Science, Shanghai Lixin University of Accounting and Finance, Shanghai, P.R. China
| | | | - Mu He
- The Department of Foundational Mathematics, Xi’an Jiaotong-Liverpool University, Suzhou, P.R. China
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8
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Mota A, Milani EA, Calsavara VF, Tomazella VLD, Leão J, Ramos PL, Ferreira PH, Louzada F. Weighted Lindley frailty model: estimation and application to lung cancer data. LIFETIME DATA ANALYSIS 2021; 27:561-587. [PMID: 34331190 DOI: 10.1007/s10985-021-09529-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/29/2020] [Accepted: 07/14/2021] [Indexed: 06/13/2023]
Abstract
In this paper, we propose a novel frailty model for modeling unobserved heterogeneity present in survival data. Our model is derived by using a weighted Lindley distribution as the frailty distribution. The respective frailty distribution has a simple Laplace transform function which is useful to obtain marginal survival and hazard functions. We assume hazard functions of the Weibull and Gompertz distributions as the baseline hazard functions. A classical inference procedure based on the maximum likelihood method is presented. Extensive simulation studies are further performed to verify the behavior of maximum likelihood estimators under different proportions of right-censoring and to assess the performance of the likelihood ratio test to detect unobserved heterogeneity in different sample sizes. Finally, to demonstrate the applicability of the proposed model, we use it to analyze a medical dataset from a population-based study of incident cases of lung cancer diagnosed in the state of São Paulo, Brazil.
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Affiliation(s)
- Alex Mota
- Institute of Mathematical and Computer Sciences, University of São Paulo, São Paulo, São Carlos, 13566-590, Brazil.
- Department of Statistics, Federal University of São Carlos, São Paulo, São Carlos, 13565-905, Brazil.
- Institute of Mathematical and Statistics, Federal University of Goiás, Goiânia, Goiâs, 74690-900, Brazil.
| | - Eder A Milani
- Institute of Mathematical and Statistics, Federal University of Goiás, Goiânia, Goiâs, 74690-900, Brazil
| | - Vinicius F Calsavara
- Department of Epidemiology and Statistics, A.C.Camargo Cancer Center, São Paulo, 01508-010, Brazil
- Biostatistics and Bioinformatics Research Center, Cedars-Sinai Medical Center, Los Angeles, CA, USA
| | - Vera L D Tomazella
- Department of Statistics, Federal University of São Carlos, São Paulo, São Carlos, 13565-905, Brazil
| | - Jeremias Leão
- Department of Statistics, Federal University of Amazonas, Manaus, Amazonas, 69067-005, Brazil
| | - Pedro L Ramos
- Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Macul, Santiago, 7820436, Chile
| | - Paulo H Ferreira
- Department of Statistics, Federal University of Bahia, Salvador, Bahia, 40170-110, Brazil
| | - Francisco Louzada
- Institute of Mathematical and Computer Sciences, University of São Paulo, São Paulo, São Carlos, 13566-590, Brazil
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9
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Gazon AB, Milani EA, Mota AL, Louzada F, Tomazella VLD, Calsavara VF. Nonproportional hazards model with a frailty term for modeling subgroups with evidence of long-term survivors: Application to a lung cancer dataset. Biom J 2021; 64:105-130. [PMID: 34569095 DOI: 10.1002/bimj.202000292] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2020] [Revised: 06/12/2021] [Accepted: 07/19/2021] [Indexed: 11/09/2022]
Abstract
With advancements in medical treatments for cancer, an increase in the life expectancy of patients undergoing new treatments is expected. Consequently, the field of statistics has evolved to present increasingly flexible models to explain such results better. In this paper, we present a lung cancer dataset with some covariates that exhibit nonproportional hazards (NPHs). Besides, the presence of long-term survivors is observed in subgroups. The proposed modeling is based on the generalized time-dependent logistic model with each subgroup's effect time and a random term effect (frailty). In practice, essential covariates are not observed for several reasons. In this context, frailty models are useful in modeling to quantify the amount of unobservable heterogeneity. The frailty distribution adopted was the weighted Lindley distribution, which has several interesting properties, such as the Laplace transform function on closed form, flexibility in the probability density function, among others. The proposed model allows for NPHs and long-term survivors in subgroups. Parameter estimation was performed using the maximum likelihood method, and Monte Carlo simulation studies were conducted to evaluate the estimators' performance. We exemplify this model's use by applying data of patients diagnosed with lung cancer in the state of São Paulo, Brazil.
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Affiliation(s)
- Amanda B Gazon
- Department of Statistics, Federal University of São Carlos, São Carlos, São Paulo, Brazil
| | - Eder A Milani
- Institute of Mathematical and Statistics, Federal University of Goiás, Goiânia, Goiás, Brazil.,Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo, Brazil
| | - Alex L Mota
- Department of Statistics, Federal University of São Carlos, São Carlos, São Paulo, Brazil.,Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo, Brazil
| | - Francisco Louzada
- Institute of Mathematics and Computer Science, University of São Paulo, São Carlos, São Paulo, Brazil
| | - Vera L D Tomazella
- Department of Statistics, Federal University of São Carlos, São Carlos, São Paulo, Brazil
| | - Vinicius F Calsavara
- Department of Epidemiology and Statistics, A.C.Camargo Cancer Center, São Paulo, São Paulo, Brazil.,Samuel Oschin Comprehensive Cancer Institute, Cedars-Sinai Medical Center, Los Angeles, CA, USA
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10
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Ngari MM, Schmitz S, Maronga C, Mramba LK, Vaillant M. A systematic review of the quality of conduct and reporting of survival analyses of tuberculosis outcomes in Africa. BMC Med Res Methodol 2021; 21:89. [PMID: 33906605 PMCID: PMC8080365 DOI: 10.1186/s12874-021-01280-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 04/12/2021] [Indexed: 12/18/2022] Open
Abstract
BACKGROUND Survival analyses methods (SAMs) are central to analysing time-to-event outcomes. Appropriate application and reporting of such methods are important to ensure correct interpretation of the data. In this study, we systematically review the application and reporting of SAMs in studies of tuberculosis (TB) patients in Africa. It is the first review to assess the application and reporting of SAMs in this context. METHODS Systematic review of studies involving TB patients from Africa published between January 2010 and April 2020 in English language. Studies were eligible if they reported use of SAMs. Application and reporting of SAMs were evaluated based on seven author-defined criteria. RESULTS Seventy-six studies were included with patient numbers ranging from 56 to 182,890. Forty-three (57%) studies involved a statistician/epidemiologist. The number of published papers per year applying SAMs increased from two in 2010 to 18 in 2019 (P = 0.004). Sample size estimation was not reported by 67 (88%) studies. A total of 22 (29%) studies did not report summary follow-up time. The survival function was commonly presented using Kaplan-Meier survival curves (n = 51, (67%) studies) and group comparisons were performed using log-rank tests (n = 44, (58%) studies). Sixty seven (91%), 3 (4.1%) and 4 (5.4%) studies reported Cox proportional hazard, competing risk and parametric survival regression models, respectively. A total of 37 (49%) studies had hierarchical clustering, of which 28 (76%) did not adjust for the clustering in the analysis. Reporting was adequate among 4.0, 1.3 and 6.6% studies for sample size estimation, plotting of survival curves and test of survival regression underlying assumptions, respectively. Forty-five (59%), 52 (68%) and 73 (96%) studies adequately reported comparison of survival curves, follow-up time and measures of effect, respectively. CONCLUSION The quality of reporting survival analyses remains inadequate despite its increasing application. Because similar reporting deficiencies may be common in other diseases in low- and middle-income countries, reporting guidelines, additional training, and more capacity building are needed along with more vigilance by reviewers and journal editors.
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Affiliation(s)
- Moses M Ngari
- KEMRI/Wellcome Trust Research Programme, P.O Box 230, Kilifi, 80108, Kenya.
- The Childhood Acute Illness & Nutrition Network (CHAIN), Nairobi, Kenya.
- Competence Center for Methodology and Statistics, Department of Population Health, Luxembourg Institute of Health, Strassen, Luxembourg.
| | - Susanne Schmitz
- Competence Center for Methodology and Statistics, Department of Population Health, Luxembourg Institute of Health, Strassen, Luxembourg
| | - Christopher Maronga
- KEMRI/Wellcome Trust Research Programme, P.O Box 230, Kilifi, 80108, Kenya
- The Childhood Acute Illness & Nutrition Network (CHAIN), Nairobi, Kenya
| | - Lazarus K Mramba
- Department of Biostatistics and Data Science, University of Kansas Medical Center, Kansas, USA
| | - Michel Vaillant
- Competence Center for Methodology and Statistics, Department of Population Health, Luxembourg Institute of Health, Strassen, Luxembourg
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11
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Piancastelli LSC, Barreto-Souza W, Mayrink VD. Generalized inverse-Gaussian frailty models with application to TARGET neuroblastoma data. ANN I STAT MATH 2020. [DOI: 10.1007/s10463-020-00774-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
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12
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Tran TMP, Abrams S, Braekers R. A general frailty model to accommodate individual heterogeneity in the acquisition of multiple infections: An application to bivariate current status data. Stat Med 2020; 39:1695-1714. [PMID: 32129520 DOI: 10.1002/sim.8506] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2018] [Revised: 11/12/2019] [Accepted: 01/20/2020] [Indexed: 11/11/2022]
Abstract
The analysis of multivariate time-to-event (TTE) data can become complicated due to the presence of clustering, leading to dependence between multiple event times. For a long time, (conditional) frailty models and (marginal) copula models have been used to analyze clustered TTE data. In this article, we propose a general frailty model employing a copula function between the frailty terms to construct flexible (bivariate) frailty distributions with the application to current status data. The model has the advantage to impose a less restrictive correlation structure among latent frailty variables as compared to traditional frailty models. Specifically, our model uses a copula function to join the marginal distributions of the frailty vector. In this article, we considered different copula functions, and we relied on marginal gamma distributions due to their mathematical convenience. Based on a simulation study, our novel model outperformed the commonly used additive correlated gamma frailty model, especially in the case of a negative association between the frailties. At the end of the article, the new methodology is illustrated on real-life data applications entailing bivariate serological survey data.
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Affiliation(s)
- Thao M P Tran
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, Data Science Institute, Hasselt University, Diepenbeek, Belgium
| | - Steven Abrams
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, Data Science Institute, Hasselt University, Diepenbeek, Belgium.,Global Health Institute, Department of Epidemiology and Social Medicine, University of Antwerp, Antwerp, Belgium
| | - Roel Braekers
- Interuniversity Institute for Biostatistics and statistical Bioinformatics, Data Science Institute, Hasselt University, Diepenbeek, Belgium.,Interuniversity Institute for Biostatistics and statistical Bioinformatics, KU Leuven, Leuven, Belgium
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13
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Vila R, Ferreira L, Saulo H, Prataviera F, Ortega E. A bimodal gamma distribution: properties, regression model and applications. STATISTICS-ABINGDON 2020. [DOI: 10.1080/02331888.2020.1764560] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Roberto Vila
- Departamento de Estatística, Universidade de Brasília, Brasília, Brazil
| | - Letícia Ferreira
- Departamento de Estatística, Universidade de Brasília, Brasília, Brazil
| | - Helton Saulo
- Departamento de Estatística, Universidade de Brasília, Brasília, Brazil
| | - Fábio Prataviera
- Departamento de Ciências Exatas, Universidade de São Paulo, São Paulo, Brazil
| | - Edwin Ortega
- Departamento de Ciências Exatas, Universidade de São Paulo, São Paulo, Brazil
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14
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Li Z, Chinchilli VM, Wang M. A time‐varying Bayesian joint hierarchical copula model for analysing recurrent events and a terminal event: an application to the Cardiovascular Health Study. J R Stat Soc Ser C Appl Stat 2019. [DOI: 10.1111/rssc.12382] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Zheng Li
- Penn State College of Medicine Hershey USA
| | | | - Ming Wang
- Penn State College of Medicine Hershey USA
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15
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Cancho VG, Barriga G, Leão J, Saulo H. Survival model induced by discrete frailty for modeling of lifetime data with long-term survivors and change-point. COMMUN STAT-THEOR M 2019. [DOI: 10.1080/03610926.2019.1648826] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Vicente G. Cancho
- Department of Mathematics and Statistics, Universidade de São Paulo, São Carlos, Brazil
| | - Gladys Barriga
- Department of Producing Engineering, Universidade Estadual Paulista Júlio de Mesquita Filho, São Paulo, Brazil
| | - Jeremias Leão
- Department of Statistics, Universidade Federal Do Amazonas, Manaus, Brazil
| | - Helton Saulo
- Department of Statistics, Universidade de Brasília, Brasília, Brazil
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16
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Kim G. Posterior consistency in frailty models and simulation studies to test the presence of random effects. J Korean Stat Soc 2019. [DOI: 10.1016/j.jkss.2018.10.004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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17
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Yu H, Cheng YJ, Wang CY. Semiparametric Regression Estimation for Recurrent Event Data with Errors in Covariates under Informative Censoring. Int J Biostat 2018; 12:/j/ijb.ahead-of-print/ijb-2016-0001/ijb-2016-0001.xml. [PMID: 27497870 DOI: 10.1515/ijb-2016-0001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Recurrent event data arise frequently in many longitudinal follow-up studies. Hence, evaluating covariate effects on the rates of occurrence of such events is commonly of interest. Examples include repeated hospitalizations, recurrent infections of HIV, and tumor recurrences. In this article, we consider semiparametric regression methods for the occurrence rate function of recurrent events when the covariates may be measured with errors. In contrast to the existing works, in our case the conventional assumption of independent censoring is violated since the recurrent event process is interrupted by some correlated events, which is called informative drop-out. Further, some covariates may be measured with errors. To accommodate for both informative censoring and measurement error, the occurrence of recurrent events is modelled through an unspecified frailty distribution and accompanied with a classical measurement error model. We propose two corrected approaches based on different ideas, and we show that they are numerically identical when estimating the regression parameters. The asymptotic properties of the proposed estimators are established, and the finite sample performance is examined via simulations. The proposed methods are applied to the Nutritional Prevention of Cancer trial for assessing the effect of the plasma selenium treatment on the recurrence of squamous cell carcinoma.
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18
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Pal S, Balakrishnan N. Expectation Maximization Algorithm for Box–Cox Transformation Cure Rate Model and Assessment of Model Misspecification Under Weibull Lifetimes. IEEE J Biomed Health Inform 2018; 22:926-934. [DOI: 10.1109/jbhi.2017.2704920] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
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19
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20
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Bayesian estimation of generalized gamma shared frailty model. Comput Stat 2018. [DOI: 10.1007/s00180-017-0728-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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21
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Abd-Elfattah EF. Saddlepoint density and distribution functions for the ratio of two linear functions and the product of generalized gamma variates. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2016.1277758] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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22
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Wiangnak P, Pal S. Gamma lifetimes and associated inference for interval-censored cure rate model with COM–Poisson competing cause. COMMUN STAT-THEOR M 2017. [DOI: 10.1080/03610926.2017.1321769] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Piyachart Wiangnak
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA
| | - Suvra Pal
- Department of Mathematics, University of Texas at Arlington, Arlington, Texas, USA
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23
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Pal S, Balakrishnan N. Likelihood inference for COM-Poisson cure rate model with interval-censored data and Weibull lifetimes. Stat Methods Med Res 2017; 26:2093-2113. [DOI: 10.1177/0962280217708686] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In this paper, we consider a competing cause scenario and assume the number of competing causes to follow a Conway–Maxwell Poisson distribution which can capture both over and under dispersion that is usually encountered in discrete data. Assuming the population of interest having a component cure and the form of the data to be interval censored, as opposed to the usually considered right-censored data, the main contribution is in developing the steps of the expectation maximization algorithm for the determination of the maximum likelihood estimates of the model parameters of the flexible Conway–Maxwell Poisson cure rate model with Weibull lifetimes. An extensive Monte Carlo simulation study is carried out to demonstrate the performance of the proposed estimation method. Model discrimination within the Conway–Maxwell Poisson distribution is addressed using the likelihood ratio test and information-based criteria to select a suitable competing cause distribution that provides the best fit to the data. A simulation study is also carried out to demonstrate the loss in efficiency when selecting an improper competing cause distribution which justifies the use of a flexible family of distributions for the number of competing causes. Finally, the proposed methodology and the flexibility of the Conway–Maxwell Poisson distribution are illustrated with two known data sets from the literature: smoking cessation data and breast cosmesis data.
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Affiliation(s)
- Suvra Pal
- Department of Mathematics, University of Texas, Arlington, TX, USA
| | - N Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, ON, Canada
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24
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de Souza D, Cancho VG, Rodrigues J, Balakrishnan N. Bayesian cure rate models induced by frailty in survival analysis. Stat Methods Med Res 2017; 26:2011-2028. [DOI: 10.1177/0962280217708671] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Frailty models provide a convenient way of modeling unobserved dependence and heterogeneity in survival data which, if not accounted for duly, would result incorrect inference. Gamma frailty models are commonly used for this purpose, but alternative continuous distributions are possible as well. However, with cure rate being present in survival data, these continuous distributions may not be appropriate since individuals with long-term survival times encompass zero frailty. So, we propose here a flexible probability distribution induced by a discrete frailty, and then present some special discrete probability distributions. We specifically focus on a special hyper-Poisson distribution and then develop the corresponding Bayesian simulation, influence diagnostics and an application to real dataset by means of intensive Markov chain Monte Carlo algorithm. These illustrate the usefulness of the proposed model as well as the inferential results developed here.
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Affiliation(s)
- Daiane de Souza
- Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos, Brazil
| | - Vicente G Cancho
- Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos, Brazil
| | - Josemar Rodrigues
- Department of Applied Mathematics and Statistics, University of São Paulo, São Carlos, Brazil
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Su PF, Chung CH, Wang YW, Chi Y, Chang YJ. Power and sample size calculation for paired recurrent events data based on robust nonparametric tests. Stat Med 2017; 36:1823-1838. [PMID: 28183151 DOI: 10.1002/sim.7241] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2016] [Revised: 12/28/2016] [Accepted: 01/17/2017] [Indexed: 11/08/2022]
Abstract
The purpose of this paper is to develop a formula for calculating the required sample size for paired recurrent events data. The developed formula is based on robust non-parametric tests for comparing the marginal mean function of events between paired samples. This calculation can accommodate the associations among a sequence of paired recurrent event times with a specification of correlated gamma frailty variables for a proportional intensity model. We evaluate the performance of the proposed method with comprehensive simulations including the impacts of paired correlations, homogeneous or nonhomogeneous processes, marginal hazard rates, censoring rate, accrual and follow-up times, as well as the sensitivity analysis for the assumption of the frailty distribution. The use of the formula is also demonstrated using a premature infant study from the neonatal intensive care unit of a tertiary center in southern Taiwan. Copyright © 2017 John Wiley & Sons, Ltd.
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Affiliation(s)
- Pei-Fang Su
- Department of Statistics, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Chia-Hua Chung
- Department of Statistics, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Yu-Wen Wang
- Institute of Allied Health Science, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Yunchan Chi
- Department of Statistics, National Cheng Kung University, Tainan, 70101, Taiwan
| | - Ying-Ju Chang
- Institute of Allied Health Science, National Cheng Kung University, Tainan, 70101, Taiwan.,Department of Nursing, National Cheng Kung University, Tainan, 70101, Taiwan
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26
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Li X, Chen Y, Li R. A frailty model for recurrent events during alternating restraint and non-restraint time periods. Stat Med 2017; 36:643-654. [PMID: 27757970 DOI: 10.1002/sim.7150] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2016] [Revised: 08/29/2016] [Accepted: 09/26/2016] [Indexed: 11/05/2022]
Abstract
We consider recurrent events of the same type that occur during alternating restraint and non-restraint time periods. This research is motivated by a study on juvenile recidivism, where the probationers were followed for re-offenses during alternating placement periods and free-time periods. During the placement periods, the probationers were under a restricted environment with direct supervision of the probation officers. During the free-time periods, the probationers were released to home and not under direct supervision. Although re-offenses can occur during both types of time periods, the intensities of the re-offenses are very different. Thus, these two types of time periods should be modeled differently. The same data structure also arises in many biomedical settings, as exemplified by tumor metastases during chemotherapy and chemo-free periods. In this paper, we propose a joint modeling framework that explicitly accounts for the different types of time periods, as well as the within-subject dependence during the same type and between different types of time periods. The estimation procedure is implemented in SAS and is easily accessible to practical investigators. We evaluate the proposed method through simulation studies under several realistic scenarios and demonstrate the feasibility of the proposed method by applying it to the juvenile recidivism dataset. Copyright © 2016 John Wiley & Sons, Ltd.
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Affiliation(s)
- Xiaoqi Li
- Department of Physical Medicine and Rehabilitation, Baylor College of Medicine, Houston, 77030, TX, U.S.A
| | - Yong Chen
- Department of Biostatistics and Epidemiology, University of Pennsylvania, PA, 19104, Philadelphia, U.S.A
| | - Ruosha Li
- Department of Biostatistics, The University of Texas Health Science Center at Houston, TX, 77030, U.S.A
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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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28
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Navarro A, Casanovas G, Alvarado S, Moriña D. Analyzing recurrent events when the history of previous episodes is unknown or not taken into account: proceed with caution. GACETA SANITARIA 2016; 31:227-234. [PMID: 27863821 DOI: 10.1016/j.gaceta.2016.09.004] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/23/2016] [Revised: 08/29/2016] [Accepted: 09/08/2016] [Indexed: 11/18/2022]
Abstract
OBJECTIVE Researchers in public health are often interested in examining the effect of several exposures on the incidence of a recurrent event. The aim of the present study is to assess how well the common-baseline hazard models perform to estimate the effect of multiple exposures on the hazard of presenting an episode of a recurrent event, in presence of event dependence and when the history of prior-episodes is unknown or is not taken into account. METHODS Through a comprehensive simulation study, using specific-baseline hazard models as the reference, we evaluate the performance of common-baseline hazard models by means of several criteria: bias, mean squared error, coverage, confidence intervals mean length and compliance with the assumption of proportional hazards. RESULTS Results indicate that the bias worsen as event dependence increases, leading to a considerable overestimation of the exposure effect; coverage levels and compliance with the proportional hazards assumption are low or extremely low, worsening with increasing event dependence, effects to be estimated, and sample sizes. CONCLUSIONS Common-baseline hazard models cannot be recommended when we analyse recurrent events in the presence of event dependence. It is important to have access to the history of prior-episodes per subject, it can permit to obtain better estimations of the effects of the exposures.
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Affiliation(s)
- Albert Navarro
- GRAAL-Unitat de Bioestadística, Facultat de Medicina, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain.
| | - Georgina Casanovas
- GRAAL-Unitat de Bioestadística, Facultat de Medicina, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
| | - Sergio Alvarado
- Programa de Salud Ambiental, Escuela de Salud Pública, Facultad de Medicina, Universidad de Chile, Chile; Facultad de Ciencias de la Salud, Universidad de Tarapacá, Arica, Chile
| | - David Moriña
- GRAAL-Unitat de Bioestadística, Facultat de Medicina, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain; Unit of Infections and Cancer (UNIC), Cancer Epidemiology Research Program (CERP), Catalan Institute of Oncology (ICO)-IDIBELL, Barcelona, Spain
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29
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Pal S, Balakrishnan N. An EM type estimation procedure for the destructive exponentially weighted Poisson regression cure model under generalized gamma lifetime. J STAT COMPUT SIM 2016. [DOI: 10.1080/00949655.2016.1247843] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Barmalzan G, Najafabadi ATP, Balakrishnan N. Orderings for series and parallel systems comprising heterogeneous exponentiated Weibull-geometric components. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2016.1222432] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Ghobad Barmalzan
- Department of Statistics, University of Zabol, Sistan and Baluchestan, Iran
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32
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Balakrishnan N, Pal S. Expectation maximization-based likelihood inference for flexible cure rate models with Weibull lifetimes. Stat Methods Med Res 2016; 25:1535-63. [DOI: 10.1177/0962280213491641] [Citation(s) in RCA: 38] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Recently, a flexible cure rate survival model has been developed by assuming the number of competing causes of the event of interest to follow the Conway–Maxwell–Poisson distribution. This model includes some of the well-known cure rate models discussed in the literature as special cases. Data obtained from cancer clinical trials are often right censored and expectation maximization algorithm can be used in this case to efficiently estimate the model parameters based on right censored data. In this paper, we consider the competing cause scenario and assuming the time-to-event to follow the Weibull distribution, we derive the necessary steps of the expectation maximization algorithm for estimating the parameters of different cure rate survival models. The standard errors of the maximum likelihood estimates are obtained by inverting the observed information matrix. The method of inference developed here is examined by means of an extensive Monte Carlo simulation study. Finally, we illustrate the proposed methodology with a real data on cancer recurrence.
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Affiliation(s)
- Narayanaswamy Balakrishnan
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
- Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia
| | - Suvra Pal
- Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
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33
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Pal S, Balakrishnan N. Likelihood inference for the destructive exponentially weighted Poisson cure rate model with Weibull lifetime and an application to melanoma data. Comput Stat 2016. [DOI: 10.1007/s00180-016-0660-8] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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Olivera MJ, Cucunubá ZM, Álvarez CA, Nicholls RS. Safety Profile of Nifurtimox and Treatment Interruption for Chronic Chagas Disease in Colombian Adults. Am J Trop Med Hyg 2015; 93:1224-1230. [PMID: 26392162 PMCID: PMC4674239 DOI: 10.4269/ajtmh.15-0256] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/31/2015] [Accepted: 07/27/2015] [Indexed: 12/29/2022] Open
Abstract
Nifurtimox (NFX) is one of the approved drugs used to treat Chagas disease. Safety profile studies and models on risk factors for treatment interruption in adults are scarce in Latin America. This study evaluated retrospectively the medical records of adult Chagas disease patients treated with NFX between 2007 and 2012 in Bogotá, Colombia. An accelerated failure time model was used, and associations were expressed as time ratio (TR). In total, 76 adult patients with NFX were included: 60 (79.0%) completed 60 days of treatment, 61 (80.3%) presented adverse drug reactions (ADRs), and 16 (21.0%) required treatment interruption. The predominant symptoms were epigastric pain (23.7%), nauseas (18.4%), sleep disturbances (18.4%), loss of appetite (17.1%), and temporary loss of memory (15.2%). ADRs were classified as mild (64.5%), moderate (30.4%), and severe (5.1%). Time of treatment was significantly longer when presenting ≤ 3 ADRs (TR: 1.78; 95% CI: 1.04–3.03), presence of non-severe ADRs (TR: 6.52; 95% CI: 3.24–13.1), doses of NFX ≤ 8 mg/kg/day (TR: 1.78; 95% CI: 0.90–3.49), and age < 48 years (TR: 1.57; 95% CI: 0.90–2.74). Treatment with NFX in adults caused a high frequency of ADRs, but most of the cases were mild and did not require treatment interruption. Severity and number of ADRs were the main predictors for treatment interruption.
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Affiliation(s)
| | - Zulma M. Cucunubá
- *Address correspondence to Zulma M. Cucunubá, Grupo de Parasitología, Instituto Nacional de Salud, Avenida Calle 22 51-20, Bogotá DC, Colombia. E-mail:
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35
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Balakrishnan N, Pal S. Likelihood Inference for Flexible Cure Rate Models with Gamma Lifetimes. COMMUN STAT-THEOR M 2015. [DOI: 10.1080/03610926.2014.964807] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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36
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Balakrishnan N, Pal S. An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetime and model discrimination using likelihood- and information-based methods. Comput Stat 2014. [DOI: 10.1007/s00180-014-0527-9] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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37
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Enki DG, Noufaily A, Farrington CP. A time-varying shared frailty model with application to infectious diseases. Ann Appl Stat 2014. [DOI: 10.1214/13-aoas693] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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38
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39
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Balakrishnan N, Pal S. Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM-Poisson family. Comput Stat Data Anal 2013. [DOI: 10.1016/j.csda.2013.04.018] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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40
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Balakrishnan N, Mitra D. Some Further Issues Concerning Likelihood Inference for Left Truncated and Right Censored Lognormal Data. COMMUN STAT-SIMUL C 2013. [DOI: 10.1080/03610918.2012.703749] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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41
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Balakrishnan N, Chimitova E, Galanova N, Vedernikova M. Testing Goodness of Fit of Parametric AFT and PH Models with Residuals. COMMUN STAT-SIMUL C 2013. [DOI: 10.1080/03610918.2012.659824] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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42
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Chen P, Zhang J, Zhang R. Estimation of the accelerated failure time frailty model under generalized gamma frailty. Comput Stat Data Anal 2013. [DOI: 10.1016/j.csda.2013.01.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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43
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Balakrishnan N, Mitra D. Left truncated and right censored Weibull data and likelihood inference with an illustration. Comput Stat Data Anal 2012. [DOI: 10.1016/j.csda.2012.05.004] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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44
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Balakrishnan N, Pal S. EM Algorithm-Based Likelihood Estimation for Some Cure Rate Models. JOURNAL OF STATISTICAL THEORY AND PRACTICE 2012. [DOI: 10.1080/15598608.2012.719803] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Abstract
Clustered survival data arise when groups of failure times share a common ingredient; typically, they refer to the same individual or individuals with a common factor. When the association between failure times within the same cluster is of interest, statistical methods called frailty models have been used. The frailty is an unobserved random component which affects the risk level, changing from cluster to cluster but shared by all observations within the same cluster. Various probability distributions have been proposed for the frailty term, with special emphasis on the gamma and log-normal distribution. Since adequate modelling of the frailty distribution is essential to properly investigate the dependence structure, we introduce a new class of frailty models with a flexible distribution form. Specifically, we adopt the skew-normal distribution for the log-transformed frailty, leading to an extension of the log-normal model. After presenting the methodology connected to this choice, we illustrate it with a case study of multiple myeloma patients with autologous stem cells transplantation.
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Affiliation(s)
- A Callegaro
- Department of Statistical Sciences, University of Padua, 35121 Padua, Italy
| | - S Iacobelli
- University Tor Vergata, Rome, Italy on behalf of the EBMT Chronic Leukemia Working Party
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46
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Song H, Peng Y, Tu D. A new approach for joint modelling of longitudinal measurements and survival times with a cure fraction. CAN J STAT 2012. [DOI: 10.1002/cjs.11127] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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47
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Paddy Farrington C, Unkel S, Anaya-Izquierdo K. The relative frailty variance and shared frailty models. J R Stat Soc Series B Stat Methodol 2012. [DOI: 10.1111/j.1467-9868.2011.01021.x] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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48
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49
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Herberich E, Hothorn T. Dunnett-type inference in the frailty Cox model with covariates. Stat Med 2011; 31:45-55. [DOI: 10.1002/sim.4403] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2010] [Revised: 07/19/2011] [Accepted: 08/01/2011] [Indexed: 11/08/2022]
Affiliation(s)
- Esther Herberich
- Institut für Statistik; Ludwig-Maximilians-Universität München; DE-80539 Munich Germany
| | - Torsten Hothorn
- Institut für Statistik; Ludwig-Maximilians-Universität München; DE-80539 Munich Germany
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50
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Balakrishnan N, Mitra D. Likelihood inference for lognormal data with left truncation and right censoring with an illustration. J Stat Plan Inference 2011. [DOI: 10.1016/j.jspi.2011.05.007] [Citation(s) in RCA: 28] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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