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Jin Z, Lu L, Bedair K, Hong Y. Modeling bivariate geyser eruption system with covariate-adjusted recurrent event process. J Appl Stat 2022; 49:2488-2509. [DOI: 10.1080/02664763.2021.1910937] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Zhongnan Jin
- Department of Statistics, Virginia Tech, Blacksburg, VA, USA
| | - Lu Lu
- Department of Mathematics & Statistics, University of South Florida, Tampa, FL, USA
| | - Khaled Bedair
- Department of Statistics & Mathematics, Faculty of Commerce, Tanta University, Tanta, Egypt
- School of Medicine, University of Dundee, Dundee, UK
| | - Yili Hong
- Department of Statistics, Virginia Tech, Blacksburg, VA, USA
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2
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Shin SJ, Li J, Ning J, Bojadzieva J, Strong LC, Wang W. Bayesian estimation of a semiparametric recurrent event model with applications to the penetrance estimation of multiple primary cancers in Li-Fraumeni syndrome. Biostatistics 2021; 21:467-482. [PMID: 30445420 DOI: 10.1093/biostatistics/kxy066] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2017] [Revised: 09/06/2018] [Accepted: 09/09/2018] [Indexed: 11/13/2022] Open
Abstract
A common phenomenon in cancer syndromes is for an individual to have multiple primary cancers (MPC) at different sites during his/her lifetime. Patients with Li-Fraumeni syndrome (LFS), a rare pediatric cancer syndrome mainly caused by germline TP53 mutations, are known to have a higher probability of developing a second primary cancer than those with other cancer syndromes. In this context, it is desirable to model the development of MPC to enable better clinical management of LFS. Here, we propose a Bayesian recurrent event model based on a non-homogeneous Poisson process in order to obtain penetrance estimates for MPC related to LFS. We employed a familywise likelihood that facilitates using genetic information inherited through the family pedigree and properly adjusted for the ascertainment bias that was inevitable in studies of rare diseases by using an inverse probability weighting scheme. We applied the proposed method to data on LFS, using a family cohort collected through pediatric sarcoma patients at MD Anderson Cancer Center from 1944 to 1982. Both internal and external validation studies showed that the proposed model provides reliable penetrance estimates for MPC in LFS, which, to the best of our knowledge, have not been reported in the LFS literature.
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Affiliation(s)
- Seung Jun Shin
- Department of Statistics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, South Korea
| | - Jialu Li
- Department of Bioinformatics and Computational Biology, University of Texas MD Anderson Cancer Center, Pressler St, Houston, TX, USA
| | - Jing Ning
- Department of Biostatistics, University of Texas MD Anderson Cancer Center, Pressler St, Houston, TX, USA
| | - Jasmina Bojadzieva
- Department of Genetics, University of Texas MD Anderson Cancer Center, Pressler St, Houston, TX, USA
| | - Louise C Strong
- Department of Genetics, University of Texas MD Anderson Cancer Center, Pressler St, Houston, TX, USA
| | - Wenyi Wang
- Department of Bioinformatics and Computational Biology, University of Texas MD Anderson Cancer Center, Houston, Pressler St, TX, USA
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Huang XW, Wang W, Emura T. A copula-based Markov chain model for serially dependent event times with a dependent terminal event. JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2020. [DOI: 10.1007/s42081-020-00087-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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4
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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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Tallarita M, De Iorio M, Guglielmi A, Malone-Lee J. Bayesian Autoregressive Frailty Models for Inference in Recurrent Events. Int J Biostat 2019; 16:ijb-2018-0088. [PMID: 31756161 DOI: 10.1515/ijb-2018-0088] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Accepted: 07/19/2019] [Indexed: 11/15/2022]
Abstract
We propose autoregressive Bayesian semi-parametric models for gap times between recurrent events. The aim is two-fold: inference on the effect of possibly time-varying covariates on the gap times and clustering of individuals based on the time trajectory of the recurrent event. Time-dependency between gap times is taken into account through the specification of an autoregressive component for the frailty parameters influencing the response at different times. The order of the autoregression may be assumed unknown and is an object of inference. We consider two alternative approaches to perform model selection under this scenario. Covariates may be easily included in the regression framework and censoring and missing data are easily accounted for. As the proposed methodologies lie within the class of Dirichlet process mixtures, posterior inference can be performed through efficient MCMC algorithms. We illustrate the approach through simulations and medical applications involving recurrent hospitalizations of cancer patients and successive urinary tract infections.
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Affiliation(s)
- Marta Tallarita
- Department of Statistical Science, University College London, London, UK
| | - Maria De Iorio
- Department of Statistical Science, University College London, London, UK
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Affiliation(s)
- Giampiero Marra
- Department of Statistical Science, University College London, London, UK
| | - Rosalba Radice
- Cass Business School, City, University of London, London, UK
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Barthel N, Geerdens C, Czado C, Janssen P. Dependence modeling for recurrent event times subject to right-censoring with D-vine copulas. Biometrics 2019; 75:439-451. [PMID: 30549012 DOI: 10.1111/biom.13014] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Accepted: 12/06/2018] [Indexed: 11/27/2022]
Abstract
In many time-to-event studies, the event of interest is recurrent. Here, the data for each sample unit correspond to a series of gap times between the subsequent events. Given a limited follow-up period, the last gap time might be right-censored. In contrast to classical analysis, gap times and censoring times cannot be assumed independent, i.e., the sequential nature of the data induces dependent censoring. Also, the number of recurrences typically varies among sample units leading to unbalanced data. To model the association pattern between gap times, so far only parametric margins combined with the restrictive class of Archimedean copulas have been considered. Here, taking the specific data features into account, we extend existing work in several directions: we allow for nonparametric margins and consider the flexible class of D-vine copulas. A global and sequential (one- and two-stage) likelihood approach are suggested. We discuss the computational efficiency of each estimation strategy. Extensive simulations show good finite sample performance of the proposed methodology. It is used to analyze the association of recurrent asthma attacks in children. The analysis reveals that a D-vine copula detects relevant insights, on how dependence changes in strength and type over time.
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Affiliation(s)
- Nicole Barthel
- Department of Mathematics, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany
| | - Candida Geerdens
- Center for Statistics, I-BioStat, Universiteit Hasselt, Agoralaan 1, 3590 Diepenbeek, Belgium
| | - Claudia Czado
- Department of Mathematics, Technische Universität München, Boltzmannstraße 3, 85748 Garching, Germany
| | - Paul Janssen
- Center for Statistics, I-BioStat, Universiteit Hasselt, Agoralaan 1, 3590 Diepenbeek, Belgium
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Chatterjee M, Sen Roy S. A copula-based approach for estimating the survival functions of two alternating recurrent events. J STAT COMPUT SIM 2018. [DOI: 10.1080/00949655.2018.1499741] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Romeo JS, Meyer R, Gallardo DI. Bayesian bivariate survival analysis using the power variance function copula. LIFETIME DATA ANALYSIS 2018; 24:355-383. [PMID: 28536818 DOI: 10.1007/s10985-017-9396-1] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2016] [Accepted: 05/16/2017] [Indexed: 06/07/2023]
Abstract
Copula models have become increasingly popular for modelling the dependence structure in multivariate survival data. The two-parameter Archimedean family of Power Variance Function (PVF) copulas includes the Clayton, Positive Stable (Gumbel) and Inverse Gaussian copulas as special or limiting cases, thus offers a unified approach to fitting these important copulas. Two-stage frequentist procedures for estimating the marginal distributions and the PVF copula have been suggested by Andersen (Lifetime Data Anal 11:333-350, 2005), Massonnet et al. (J Stat Plann Inference 139(11):3865-3877, 2009) and Prenen et al. (J R Stat Soc Ser B 79(2):483-505, 2017) which first estimate the marginal distributions and conditional on these in a second step to estimate the PVF copula parameters. Here we explore an one-stage Bayesian approach that simultaneously estimates the marginal and the PVF copula parameters. For the marginal distributions, we consider both parametric as well as semiparametric models. We propose a new method to simulate uniform pairs with PVF dependence structure based on conditional sampling for copulas and on numerical approximation to solve a target equation. In a simulation study, small sample properties of the Bayesian estimators are explored. We illustrate the usefulness of the methodology using data on times to appendectomy for adult twins in the Australian NH&MRC Twin registry. Parameters of the marginal distributions and the PVF copula are simultaneously estimated in a parametric as well as a semiparametric approach where the marginal distributions are modelled using Weibull and piecewise exponential distributions, respectively.
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Affiliation(s)
- Jose S Romeo
- Department of Mathematics, University of Santiago, Santiago, Chile.
- SHORE and Whariki Research Centre, College of Health, Massey University, Auckland, New Zealand.
| | - Renate Meyer
- Department of Statistics, University of Auckland, Auckland, New Zealand
| | - Diego I Gallardo
- Departamento de Matematicas, Facultad de Ingenieria, Universidad de Atacama, Copiapo, Chile
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