1
|
Wen CC, Chen YH. Analyzing recurrent and nonrecurrent terminal events data in discrete time. Biom J 2023; 65:e2100361. [PMID: 36285659 DOI: 10.1002/bimj.202100361] [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] [Received: 11/15/2021] [Revised: 08/22/2022] [Accepted: 09/20/2022] [Indexed: 11/06/2022]
Abstract
Joint analysis of recurrent and nonrecurrent terminal events has attracted substantial attention in literature. However, there lacks formal methodology for such analysis when the event time data are on discrete scales, even though some modeling and inference strategies have been developed for discrete-time survival analysis. We propose a discrete-time joint modeling approach for the analysis of recurrent and terminal events where the two types of events may be correlated with each other. The proposed joint modeling assumes a shared frailty to account for the dependence among recurrent events and between the recurrent and the terminal terminal events. Also, the joint modeling allows for time-dependent covariates and rich families of transformation models for the recurrent and terminal events. A major advantage of our approach is that it does not assume a distribution for the frailty, nor does it assume a Poisson process for the analysis of the recurrent event. The utility of the proposed analysis is illustrated by simulation studies and two real applications, where the application to the biochemists' rank promotion data jointly analyzes the biochemists' citation numbers and times to rank promotion, and the application to the scleroderma lung study data jointly analyzes the adverse events and off-drug time among patients with the symptomatic scleroderma-related interstitial lung disease.
Collapse
Affiliation(s)
- Chi-Chung Wen
- Department of Mathematics, Tamkang University, New Taipei City, Taiwan
| | - Yi-Hau Chen
- Institute of Statistical Science, Academia Sinica, Taipei, Taiwan
| |
Collapse
|
2
|
Chiou SH, Xu G, Yan J, Huang CY. Regression Modeling for Recurrent Events Possibly with an Informative Terminal Event Using R Package reReg. J Stat Softw 2023; 105:5. [PMID: 38586564 PMCID: PMC10997344 DOI: 10.18637/jss.v105.i05] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/09/2024] Open
Abstract
Recurrent event analyses have found a wide range of applications in biomedicine, public health, and engineering, among others, where study subjects may experience a sequence of event of interest during follow-up. The R package reReg offers a comprehensive collection of practical and easy-to-use tools for regression analysis of recurrent events, possibly with the presence of an informative terminal event. The regression framework is a general scale-change model which encompasses the popular Cox-type model, the accelerated rate model, and the accelerated mean model as special cases. Informative censoring is accommodated through a subject-specific frailty without any need for parametric specification. Different regression models are allowed for the recurrent event process and the terminal event. Also included are visualization and simulation tools.
Collapse
Affiliation(s)
- Sy Han Chiou
- Department of Mathematical Sciences, University of Texas at Dallas, 800 W. Campbell Road, Richardson, TX 75080, United States of America
| | - Gongjun Xu
- Department of Statistics, University of Michigan, 1085 South University Avenue, Ann Arbor, MI 48109, United States of America
| | - Jun Yan
- Department of Statistics, University of Connecticut, 215 Glenbrook Road U-4120, Storrs, CT 06269, United States of America
| | - Chiung-Yu Huang
- Department of Epidemiology and Biostatistics, University of California, San Francisco, 550 16th. Street, San Francisco CA 94158, United States of America
| |
Collapse
|
3
|
Wang X, Sun L. Joint modeling of generalized scale-change models for recurrent event and failure time data. LIFETIME DATA ANALYSIS 2023; 29:1-33. [PMID: 36066694 DOI: 10.1007/s10985-022-09573-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2021] [Accepted: 08/13/2022] [Indexed: 06/15/2023]
Abstract
Recurrent event and failure time data arise frequently in many clinical and observational studies. In this article, we propose a joint modeling of generalized scale-change models for the recurrent event process and the failure time, and allow the two processes to be correlated through a shared frailty. The proposed joint model is flexible in that it requires neither the Poisson assumption for the recurrent event process nor a parametric assumption on the frailty distribution. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the resulting estimators are established. Simulation studies are conducted to evaluate the finite sample performances of the proposed method. An application to a medical cost study of chronic heart failure patients is provided.
Collapse
Affiliation(s)
- Xiaoyu Wang
- Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China
| | - Liuquan Sun
- Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People's Republic of China.
| |
Collapse
|
4
|
Jin J, Song X, Sun L. Dynamic semiparametric transformation models for recurrent event data with a terminal event. Stat Med 2022; 41:5432-5447. [PMID: 36121319 DOI: 10.1002/sim.9577] [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: 11/26/2021] [Revised: 08/01/2022] [Accepted: 09/05/2022] [Indexed: 11/06/2022]
Abstract
Recurrent event data with a terminal event commonly arise in many longitudinal follow-up studies. This article proposes a class of dynamic semiparametric transformation models for the marginal mean functions of the recurrent events with a terminal event, where some covariate effects may be time-varying. An estimation procedure is developed for the model parameters, and the asymptotic properties of the resulting estimators are established. In addition, relevant significance tests are suggested for examining whether or not covariate effects vary with time, and a model checking procedure is presented for assessing the adequacy of the proposed models. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a medical cost study of chronic heart failure patients is provided.
Collapse
Affiliation(s)
- Jin Jin
- School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China
| | - Xinyuan Song
- Department of Statistics, The Chinese University of Hong Kong, Hong Kong, China
| | - Liuquan Sun
- Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China.,School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, China
| |
Collapse
|
5
|
|
6
|
|
7
|
Teo YH, Tam WW, Koo CY, Aung AT, Sia CH, Wong RCC, Kong W, Poh KK, Kofidis T, Kojodjojo P, Lee CH. Sleep apnea and recurrent heart failure hospitalizations after coronary artery bypass grafting. J Clin Sleep Med 2021; 17:2399-2407. [PMID: 34216202 DOI: 10.5664/jcsm.9442] [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: 11/13/2022]
Abstract
STUDY OBJECTIVES Sleep apnea is prevalent in patients undergoing coronary artery bypass grafting (CABG). We investigated the relationship between sleep apnea and recurrent heart failure hospitalizations in patient undergoing non-urgent CABG. METHODS Between November 2013 and December 2018, 1007 patients completed a sleep study prior to CABG and were followed up until April 2020. Recurrent heart failure hospitalizations were analyzed by Poisson, negative binomial, Andersen-Gill, and joint frailty models, with partial and full adjustment for covariates. RESULTS At an average follow-up of 3.3 years, the number of patients with 0, 1, or ≥2 heart failure hospitalizations were 908 (90.2%), 62 (6.2%), and 37 (3.7%), respectively. The total number of heart failure hospitalizations was 179, comprising 62 (35%) first and 117 (65%) repeat events. The numbers of heart failure hospitalizations for the sleep apnea (n = 513, 50.9%) and non-sleep apnea groups were 127 and 52, respectively. Negative binomial regression demonstrated that sleep apnea was associated with recurrent heart failure hospitalizations (fully adjusted rate ratio, 1.71; 95% confidence interval [CI], 1.12-2.62; p = 0.013). Similar results were found in Poisson (1.63; 95%CI, 1.15-2.31; p = 0.006), Andersen-Gill (1.66; 95% CI, 1.01-2.75; p = 0.047), and joint frailty models (1.72; 95% CI, 1.00-3.01; p = 0.056). CONCLUSIONS In patients after CABG, repeat events accounted for two-thirds of heart failure hospitalizations. Sleep apnea was independently associated with recurrent heart failure hospitalizations.
Collapse
Affiliation(s)
- Yao Hao Teo
- Yong Loo Lin School of Medicine, National University of Singapore, Singapore
| | - Wilson W Tam
- Alice Lee Centre for Nursing Studies, National University of Singapore, Singapore
| | - Chieh-Yang Koo
- Department of Cardiology, National University Heart Centre Singapore, Singapore
| | - Aye-Thandar Aung
- Department of Cardiology, National University Heart Centre Singapore, Singapore
| | - Ching-Hui Sia
- Department of Cardiology, National University Heart Centre Singapore, Singapore
| | - Raymond C C Wong
- Department of Cardiology, National University Heart Centre Singapore, Singapore
| | - William Kong
- Yong Loo Lin School of Medicine, National University of Singapore, Singapore.,Department of Cardiology, National University Heart Centre Singapore, Singapore
| | - Kian-Keong Poh
- Yong Loo Lin School of Medicine, National University of Singapore, Singapore.,Department of Cardiology, National University Heart Centre Singapore, Singapore
| | - Theodoros Kofidis
- Yong Loo Lin School of Medicine, National University of Singapore, Singapore.,Department of Cardiac, Thoracic and Vascular Surgery, National University Heart Centre, Singapore.,Cardiovascular Research Institute, National University of Singapore, Singapore
| | - Pipin Kojodjojo
- Alice Lee Centre for Nursing Studies, National University of Singapore, Singapore.,Division of Cardiology, Department of Medicine, Ng Teng Fong General Hospital, Singapore
| | - Chi-Hang Lee
- Yong Loo Lin School of Medicine, National University of Singapore, Singapore.,Alice Lee Centre for Nursing Studies, National University of Singapore, Singapore.,Cardiovascular Research Institute, National University of Singapore, Singapore
| |
Collapse
|
8
|
Xu Z, Sinha D, Bradley JR. Joint analysis of recurrence and termination: A Bayesian latent class approach. Stat Methods Med Res 2020; 30:508-522. [PMID: 33050774 DOI: 10.1177/0962280220962522] [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: 11/16/2022]
Abstract
Like many other clinical and economic studies, each subject of our motivating transplant study is at risk of recurrent events of non-fatal tissue rejections as well as the terminating event of death due to total graft rejection. For such studies, our model and associated Bayesian analysis aim for some practical advantages over competing methods. Our semiparametric latent-class-based joint model has coherent interpretation of the covariate (including race and gender) effects on all functions and model quantities that are relevant for understanding the effects of covariates on future event trajectories. Our fully Bayesian method for estimation and prediction uses a complete specification of the prior process of the baseline functions. We also derive a practical and theoretically justifiable partial likelihood-based semiparametric Bayesian approach to deal with the analysis when there is a lack of prior information about baseline functions. Our model and method can accommodate fixed as well as time-varying covariates. Our Markov Chain Monte Carlo tools for both Bayesian methods are implementable via publicly available software. Our Bayesian analysis of transplant study and simulation study demonstrate practical advantages and improved performance of our approach.
Collapse
Affiliation(s)
- Zhixing Xu
- Department of Statistics, 7823Florida State University, Tallahassee, FL, USA
| | - Debajyoti Sinha
- Department of Statistics, 7823Florida State University, Tallahassee, FL, USA
| | - Jonathan R Bradley
- Department of Statistics, 7823Florida State University, Tallahassee, FL, USA
| |
Collapse
|
9
|
Sun X, Ding J, Sun L. A semiparametric additive rates model for the weighted composite endpoint of recurrent and terminal events. LIFETIME DATA ANALYSIS 2020; 26:471-492. [PMID: 31549283 DOI: 10.1007/s10985-019-09486-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2018] [Accepted: 09/17/2019] [Indexed: 06/10/2023]
Abstract
Recurrent event data with a terminal event commonly arise in longitudinal follow-up studies. We use a weighted composite endpoint of all recurrent and terminal events to assess the overall effects of covariates on the two types of events. A semiparametric additive rates model is proposed to analyze the weighted composite event process and the dependence structure among recurrent and terminal events is left unspecified. An estimating equation approach is developed for inference, and the asymptotic properties of the resulting estimators are established. The finite-sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is illustrated.
Collapse
Affiliation(s)
- Xiaowei Sun
- Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
- University of Chinese Academy of Sciences, Beijing, 100049, China
| | - Jieli Ding
- School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, Hubei, China
| | - Liuquan Sun
- Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China.
- University of Chinese Academy of Sciences, Beijing, 100049, China.
| |
Collapse
|
10
|
Chiou SH, Huang CY, Xu G, Yan J. Semiparametric Regression Analysis of Panel Count Data: A Practical Review. Int Stat Rev 2019; 87:24-43. [PMID: 34366547 PMCID: PMC8340851 DOI: 10.1111/insr.12271] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2017] [Accepted: 04/18/2018] [Indexed: 11/26/2022]
Abstract
Panel count data arise in many applications when the event history of a recurrent event process is only examined at a sequence of discrete time points. In spite of the recent methodological developments, the availability of their software implementations has been rather limited. Focusing on a practical setting where the effects of some time-independent covariates on the recurrent events are of primary interest, we review semiparametric regression modelling approaches for panel count data that have been implemented in R package spef. The methods are grouped into two categories depending on whether the examination times are associated with the recurrent event process after conditioning on covariates. The reviewed methods are illustrated with a subset of the data from a skin cancer clinical trial.
Collapse
Affiliation(s)
- Sy Han Chiou
- Department of Mathematical Sciences, University of Texas at Dallas, USA
| | - Chiung-Yu Huang
- Department of Epidemiology and Biostatistics, University of California at San Francisco, USA
| | - Gongjun Xu
- Department of Statistics, University of Michigan, USA
| | - Jun Yan
- Department of Statistics, University of Connecticut, USA
| |
Collapse
|
11
|
Lee J, Thall PF, Lin SH. Bayesian Semiparametric Joint Regression Analysis of Recurrent Adverse Events and Survival in Esophageal Cancer Patients. Ann Appl Stat 2019; 13:221-247. [PMID: 31681453 PMCID: PMC6824476 DOI: 10.1214/18-aoas1182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/15/2023]
Abstract
We propose a Bayesian semiparametric joint regression model for a recurrent event process and survival time. Assuming independent latent subject frailties, we define marginal models for the recurrent event process intensity and survival distribution as functions of the subject's frailty and baseline covariates. A robust Bayesian model, called Joint-DP, is obtained by assuming a Dirichlet process for the frailty distribution. We present a simulation study that compares posterior estimates under the Joint-DP model to a Bayesian joint model with lognormal frailties, a frequentist joint model, and marginal models for either the recurrent event process or survival time. The simulations show that the Joint-DP model does a good job of correcting for treatment assignment bias, and has favorable estimation reliability and accuracy compared with the alternative models. The Joint-DP model is applied to analyze an observational dataset from esophageal cancer patients treated with chemo-radiation, including the times of recurrent effusions of fluid to the heart or lungs, survival time, prognostic covariates, and radiation therapy modality.
Collapse
Affiliation(s)
- Juhee Lee
- Department of Applied Mathematics and Statistics, University California Santa Cruz, Santa Cruz, CA
| | | | - Steven H. Lin
- Department of Radiation Oncology, M.D. Anderson, Huston, TX
| |
Collapse
|
12
|
Yu H, Cheng YJ, Wang CY. Methods for multivariate recurrent event data with measurement error and informative censoring. Biometrics 2018; 74:966-976. [PMID: 29441520 PMCID: PMC6089684 DOI: 10.1111/biom.12857] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Revised: 12/01/2018] [Accepted: 12/01/2017] [Indexed: 11/27/2022]
Abstract
In multivariate recurrent event data regression, observation of recurrent events is usually terminated by other events that are associated with the recurrent event processes, resulting in informative censoring. Additionally, some covariates could be measured with errors. In some applications, an instrumental variable is observed in a subsample, namely a calibration sample, which can be applied for bias correction. In this article, we develop two non-parametric correction approaches to simultaneously correct for the informative censoring and measurement errors in the analysis of multivariate recurrent event data. A shared frailty model is adopted to characterize the informative censoring and dependence among different types of recurrent events. To adjust for measurement errors, a non-parametric correction method using the calibration sample only is proposed. In the second approach, the information from the whole cohort is incorporated by the generalized method of moments. The proposed methods do not require the Poisson-type assumption for the multivariate recurrent event process and the distributional assumption for the frailty. Moreover, we do not need to impose any distributional assumption on the underlying covariates and measurement error. Both methods perform well, but the second approach improves efficiency. The proposed methods are applied to the Nutritional Prevention of Cancer trial to assess the effect of selenium treatment on the recurrences of basal cell carcinoma and squamous cell carcinoma.
Collapse
Affiliation(s)
- Hsiang Yu
- Institute of Statistics, National Tsing-Hua University, Hsin-Chu 300, Taiwan
| | - Yu-Jen Cheng
- Institute of Statistics, National Tsing-Hua University, Hsin-Chu 300, Taiwan
| | - Ching-Yun Wang
- Division of Public Health Sciences, Fred Hutchinson Cancer Research Center, Seattle, Washington, U.S.A
| |
Collapse
|
13
|
Chiou SH, Xu G, Yan J, Huang CY. Semiparametric estimation of the accelerated mean model with panel count data under informative examination times. Biometrics 2017; 74:944-953. [PMID: 29286532 DOI: 10.1111/biom.12840] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/01/2017] [Revised: 11/01/2017] [Accepted: 11/01/2017] [Indexed: 11/29/2022]
Abstract
Panel count data arise when the number of recurrent events experienced by each subject is observed intermittently at discrete examination times. The examination time process can be informative about the underlying recurrent event process even after conditioning on covariates. We consider a semiparametric accelerated mean model for the recurrent event process and allow the two processes to be correlated through a shared frailty. The regression parameters have a simple marginal interpretation of modifying the time scale of the cumulative mean function of the event process. A novel estimation procedure for the regression parameters and the baseline rate function is proposed based on a conditioning technique. In contrast to existing methods, the proposed method is robust in the sense that it requires neither the strong Poisson-type assumption for the underlying recurrent event process nor a parametric assumption on the distribution of the unobserved frailty. Moreover, the distribution of the examination time process is left unspecified, allowing for arbitrary dependence between the two processes. Asymptotic consistency of the estimator is established, and the variance of the estimator is estimated by a model-based smoothed bootstrap procedure. Numerical studies demonstrated that the proposed point estimator and variance estimator perform well with practical sample sizes. The methods are applied to data from a skin cancer chemoprevention trial.
Collapse
Affiliation(s)
- Sy Han Chiou
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75080, U.S.A
| | - Gongjun Xu
- Department of Statistics, University of Michigan, Ann Arbor, Michigan 48109, U.S.A
| | - Jun Yan
- Department of Statistics, University of Connecticut, Storrs, Connecticut 06269, U.S.A
| | - Chiung-Yu Huang
- Department of Epidemiology and Biostatistics, University of California San Francisco, San Francisco, California 94158, U.S.A
| |
Collapse
|
14
|
Choosing between Higher Moment Maximum Entropy Models and Its Application to Homogeneous Point Processes with Random Effects. ENTROPY 2017. [DOI: 10.3390/e19120687] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
|