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Sun J, Cook T. A simple and robust parametric shared frailty model for recurrent events with the competing risk of death: An application to the Carvedilol Prospective Randomized Cumulative Survival trial. Stat Methods Med Res 2024; 33:765-793. [PMID: 38625756 DOI: 10.1177/09622802241236934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/18/2024]
Abstract
Many non-fatal events can be considered recurrent in that they can occur repeatedly over time, and some researchers may be interested in the trajectory and relative risk of non-fatal events. With the competing risk of death, the treatment effect on the mean number of recurrent events is non-identifiable since the observed mean is a function of both the recurrent event and terminal event processes. In this paper, we assume independence between the non-fatal and the terminal event process, conditional on the shared frailty, to fit a parametric model that recovers the trajectory of, and identifies the effect of treatment on, the non-fatal event process in the presence of the competing risk of death. Simulation studies are conducted to verify the reliability of our estimators. We illustrate the method and perform model diagnostics using the Carvedilol Prospective Randomized Cumulative Survival trial which involves heart-failure events.
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Affiliation(s)
- Jiren Sun
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA
| | - Thomas Cook
- Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, Madison, WI, USA
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2
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Emura T, Ditzhaus M, Dobler D, Murotani K. Factorial survival analysis for treatment effects under dependent censoring. Stat Methods Med Res 2024; 33:61-79. [PMID: 38069825 DOI: 10.1177/09622802231215805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/13/2024]
Abstract
Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, for example, from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns the proper handling of censoring. So far, all existing factorial analyses for survival data have been developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods for factorial survival analyses under quite general dependent censoring regimes. This will be accomplished by combining existing nonparametric methods for factorial survival analyses with techniques developed for survival copula models. As a result, we will present an appealing F-test that exhibits sound performance in our simulation study. The new methods are illustrated in a real data analysis. We implement the proposed method in an R function surv.factorial(.) in the R package compound.Cox.
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Affiliation(s)
- Takeshi Emura
- Department of Statistical Data Science, The Institute of Statistical Mathematics, Tokyo, Japan
- Biostatistics Center, Kurume University, Kurume, Fukuoka, Japan
| | - Marc Ditzhaus
- Faculty of Mathematics, Otto-von-Guericke University Magdeburg, Saxony-Anhalt, Germany
| | - Dennis Dobler
- Department of Mathematics, Faculty of Science, Vrije Universiteit Amsterdam, Amsterdam, North Holland, The Netherlands
| | - Kenta Murotani
- Biostatistics Center, Kurume University, Kurume, Fukuoka, Japan
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3
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Yeh CT, Liao GY, Emura T. Sensitivity Analysis for Survival Prognostic Prediction with Gene Selection: A Copula Method for Dependent Censoring. Biomedicines 2023; 11:797. [PMID: 36979776 PMCID: PMC10045003 DOI: 10.3390/biomedicines11030797] [Citation(s) in RCA: 12] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2023] [Revised: 02/20/2023] [Accepted: 03/02/2023] [Indexed: 03/08/2023] Open
Abstract
Prognostic analysis for patient survival often employs gene expressions obtained from high-throughput screening for tumor tissues from patients. When dealing with survival data, a dependent censoring phenomenon arises, and thus the traditional Cox model may not correctly identify the effect of each gene. A copula-based gene selection model can effectively adjust for dependent censoring, yielding a multi-gene predictor for survival prognosis. However, methods to assess the impact of various types of dependent censoring on the multi-gene predictor have not been developed. In this article, we propose a sensitivity analysis method using the copula-graphic estimator under dependent censoring, and implement relevant methods in the R package "compound.Cox". The purpose of the proposed method is to investigate the sensitivity of the multi-gene predictor to a variety of dependent censoring mechanisms. In order to make the proposed sensitivity analysis practical, we develop a web application. We apply the proposed method and the web application to a lung cancer dataset. We provide a template file so that developers can modify the template to establish their own web applications.
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Affiliation(s)
- Chih-Tung Yeh
- Department of Information Management, Chang Gung University, Taoyuan 33302, Taiwan
| | - Gen-Yih Liao
- Department of Information Management, Chang Gung University, Taoyuan 33302, Taiwan
| | - Takeshi Emura
- Biostatistics Center, Kurume University, Kurume 830-0011, Japan
- Research Center for Medical and Health Data Science, The Institute of Statistical Mathematics, Tokyo 190-8562, Japan
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4
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Ota S, Kimura M. Statistical injury prediction for professional sumo wrestlers: Modeling and perspectives. PLoS One 2023; 18:e0283242. [PMID: 36930622 PMCID: PMC10022813 DOI: 10.1371/journal.pone.0283242] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2022] [Accepted: 03/03/2023] [Indexed: 03/18/2023] Open
Abstract
In sumo wrestling, a traditional sport in Japan, many wrestlers suffer from injuries through bouts. In 2019, an average of 5.2 out of 42 wrestlers in the top division of professional sumo wrestling were absent in each grand sumo tournament due to injury. As the number of injury occurrences increases, professional sumo wrestling becomes less interesting for sumo fans, requiring systems to prevent future occurrences. Statistical injury prediction is a useful way to communicate the risk of injuries for wrestlers and their coaches. However, the existing statistical methods of injury prediction are not always accurate because they do not consider the long-term effects of injuries. Here, we propose a statistical model of injury occurrences for sumo wrestlers. The proposed model provides the estimated probability of the next potential injury occurrence for a wrestler. In addition, it can support making a risk-based injury prevention scenario for wrestlers. While a previous study modeled injury occurrences by using the Poisson process, we model it by using the Hawkes process to consider the long-term effect of injuries. The proposed model can also be applied to injury prediction for athletes of other sports.
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Affiliation(s)
- Shuhei Ota
- Department of Industrial Engineering and Management, Kanagawa University, Yokohama, Kanagawa, Japan
- * E-mail:
| | - Mitsuhiro Kimura
- Department of Industrial and Systems Engineering, Hosei University, Faculty of Science & Engineering, Tokyo, Japan
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Lin YH, Sun LH, Tseng YJ, Emura T. The Pareto type I joint frailty-copula model for clustered bivariate survival data. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2066694] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Yuan-Hsin Lin
- Graduate Institute of Statistics, National Central University, Taoyuan City, Taiwan
- Department of Information Management, National Central University, Taoyuan City, Taiwan
| | - Li-Hsien Sun
- Graduate Institute of Statistics, National Central University, Taoyuan City, Taiwan
| | - Yi-Ju Tseng
- Department of Computer Science, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
| | - Takeshi Emura
- Biostatistics Center, Kurume University, Kurume, Japan
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6
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Huang XW, Emura T. Computational methods for a copula-based Markov chain model with a binomial time series. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2061514] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Xin-Wei Huang
- Department of Biostatistics, University at Buffalo, State University of New York, Buffalo, NY, USA
| | - Takeshi Emura
- Biostatistics Center, Kurume University, Kurume, Japan
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7
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Copula-Based Estimation Methods for a Common Mean Vector for Bivariate Meta-Analyses. Symmetry (Basel) 2022. [DOI: 10.3390/sym14020186] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Traditional bivariate meta-analyses adopt the bivariate normal model. As the bivariate normal distribution produces symmetric dependence, it is not flexible enough to describe the true dependence structure of real meta-analyses. As an alternative to the bivariate normal model, recent papers have adopted “copula” models for bivariate meta-analyses. Copulas consist of both symmetric copulas (e.g., the normal copula) and asymmetric copulas (e.g., the Clayton copula). While copula models are promising, there are only a few studies on copula-based bivariate meta-analysis. Therefore, the goal of this article is to fully develop the methodologies and theories of the copula-based bivariate meta-analysis, specifically for estimating the common mean vector. This work is regarded as a generalization of our previous methodological/theoretical studies under the FGM copula to a broad class of copulas. In addition, we develop a new R package, “CommonMean.Copula”, to implement the proposed methods. Simulations are performed to check the proposed methods. Two real dataset are analyzed for illustration, demonstrating the insufficiency of the bivariate normal model.
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8
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Emura T, Ha ID. Special feature: Recent statistical methods for survival analysis. JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2021. [DOI: 10.1007/s42081-021-00140-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Emura T, Sofeu CL, Rondeau V. Conditional copula models for correlated survival endpoints: Individual patient data meta-analysis of randomized controlled trials. Stat Methods Med Res 2021; 30:2634-2650. [PMID: 34632882 DOI: 10.1177/09622802211046390] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Correlations among survival endpoints are important for exploring surrogate endpoints of the true endpoint. With a valid surrogate endpoint tightly correlated with the true endpoint, the efficacy of a new drug/treatment can be measurable on it. However, the existing methods for measuring correlation between two endpoints impose an invalid assumption: correlation structure is constant across different treatment arms. In this article, we reconsider the definition of Kendall's concordance measure (tau) in the context of individual patient data meta-analyses of randomized controlled trials. According to our new definition of Kendall's tau, its value depends on the treatment arms. We then suggest extending the existing copula (and frailty) models so that their Kendall's tau can vary across treatment arms. Our newly proposed model, a joint frailty-conditional copula model, is the implementation of the new definition of Kendall's tau in meta-analyses. In order to facilitate our approach, we develop an original R function condCox.reg(.) and make it available in the R package joint.Cox (https://CRAN.R-project.org/package=joint.Cox). We apply the proposed method to a gastric cancer dataset (3288 patients in 14 randomized trials from the GASTRIC group). This data analysis concludes that Kendall's tau has different values between the surgical treatment arm and the adjuvant chemotherapy arm (p-value<0.001), whereas disease-free survival remains a valid surrogate at individual level for overall survival in these trials.
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Affiliation(s)
| | | | - Virginie Rondeau
- INSERM U1219 (Biostatistic), Université Bordeaux Segalen, France
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Shinohara S, Lin YH, Michimae H, Emura T. Dynamic lifetime prediction using a Weibull-based bivariate failure time model: a meta-analysis of individual-patient data. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2020.1855449] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Sayaka Shinohara
- Department of Clinical Medicine (Biostatistics), Kitasato University, Tokyo, Japan
| | - Yuan-Hsin Lin
- Department of Information Management, Chang Gung University, Taoyuan City, Taiwan
| | - Hirofumi Michimae
- Department of Clinical Medicine (Biostatistics), Kitasato University, Tokyo, Japan
| | - Takeshi Emura
- Department of Information Management, Chang Gung University, Taoyuan City, Taiwan
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