1
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Ma H, Pang W, Sun L, Xu W. Augmented weighting estimators for the additive rates model under multivariate recurrent event data with missing event type. Stat Med 2022; 41:4285-4298. [PMID: 35764592 DOI: 10.1002/sim.9509] [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: 06/17/2021] [Revised: 04/06/2022] [Accepted: 04/12/2022] [Indexed: 11/10/2022]
Abstract
Multivariate recurrent event data are frequently encountered in biomedical and epidemiological studies when subjects experience multiple types of recurrent events. In practice, the event type information may be missing due to a variety of reasons. In this article, we consider a semiparametric additive rates model for multivariate recurrent event data with missing event types. We develop the augmented inverse probability weighting technique to handle event types that are missing at random. The nonparametric kernel-assisted proposals for the missing mechanisms are studied. The resulting estimator is shown to be consistent and asymptotically normal. Extensive simulation studies and a real data application are provided to illustrate the validity and practical utility of the proposed method.
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Affiliation(s)
- Huijuan Ma
- KLATASDS-MOE, Academy of Statistics and Interdisciplinary Sciences, East China Normal University, Shanghai, China
| | - Weicai Pang
- School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China
| | - Liuquan Sun
- Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
| | - Wei Xu
- Dalla Lana School of Public Health, University of Toronto, Toronto, Ontario, Canada
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2
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Kim YJ. Joint model for bivariate zero-inflated recurrent event data with terminal events. J Appl Stat 2021; 48:738-749. [DOI: 10.1080/02664763.2020.1744539] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Yang-Jin Kim
- Department of Statistics, Sookmyung Women's University, Seoul, South Korea
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3
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Ning J, Cai C, Chen Y, Huang X, Wang MC. Semiparametric modelling and estimation of covariate-adjusted dependence between bivariate recurrent events. Biometrics 2020; 76:1229-1239. [PMID: 31994170 PMCID: PMC7384929 DOI: 10.1111/biom.13229] [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: 11/27/2018] [Revised: 01/02/2020] [Accepted: 01/17/2020] [Indexed: 11/28/2022]
Abstract
A time-dependent measure, termed the rate ratio, was proposed to assess the local dependence between two types of recurrent event processes in one-sample settings. However, the one-sample work does not consider modeling the dependence by covariates such as subject characteristics and treatments received. The focus of this paper is to understand how and in what magnitude the covariates influence the dependence strength for bivariate recurrent events. We propose the covariate-adjusted rate ratio, a measure of covariate-adjusted dependence. We propose a semiparametric regression model for jointly modeling the frequency and dependence of bivariate recurrent events: the first level is a proportional rates model for the marginal rates and the second level is a proportional rate ratio model for the dependence structure. We develop a pseudo-partial likelihood to estimate the parameters in the proportional rate ratio model. We establish the asymptotic properties of the estimators and evaluate the finite sample performance via simulation studies. We illustrate the proposed models and methods using a soft tissue sarcoma study that examines the effects of initial treatments on the marginal frequencies of local/distant sarcoma recurrence and the dependence structure between the two types of cancer recurrence.
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Affiliation(s)
- Jing Ning
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX USA
| | - Chunyan Cai
- Center for Clinical and Translational Sciences, The University of Texas Health Science Center at Houston, Houston, TX USA
| | - Yong Chen
- Department of Biostatistics and Epidemiology, The University of Pennsylvania, Philadelphia, PA USA
| | - Xuelin Huang
- Department of Biostatistics, The University of Texas MD Anderson Cancer Center, Houston, TX USA
| | - Mei-Cheng Wang
- Department of Biostatistics, The Johns Hopkins University, Baltimore, MD USA
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4
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Analysis of cyclic recurrent event data with multiple event types. JAPANESE JOURNAL OF STATISTICS AND DATA SCIENCE 2020; 4:895-915. [DOI: 10.1007/s42081-020-00088-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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5
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Diao G, Zeng D, Hu K, Ibrahim JG. Semiparametric frailty models for zero-inflated event count data in the presence of informative dropout. Biometrics 2019; 75:1168-1178. [PMID: 31106400 DOI: 10.1111/biom.13085] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2018] [Accepted: 05/14/2019] [Indexed: 11/27/2022]
Abstract
Recurrent events data are commonly encountered in medical studies. In many applications, only the number of events during the follow-up period rather than the recurrent event times is available. Two important challenges arise in such studies: (a) a substantial portion of subjects may not experience the event, and (b) we may not observe the event count for the entire study period due to informative dropout. To address the first challenge, we assume that underlying population consists of two subpopulations: a subpopulation nonsusceptible to the event of interest and a subpopulation susceptible to the event of interest. In the susceptible subpopulation, the event count is assumed to follow a Poisson distribution given the follow-up time and the subject-specific characteristics. We then introduce a frailty to account for informative dropout. The proposed semiparametric frailty models consist of three submodels: (a) a logistic regression model for the probability such that a subject belongs to the nonsusceptible subpopulation; (b) a nonhomogeneous Poisson process model with an unspecified baseline rate function; and (c) a Cox model for the informative dropout time. We develop likelihood-based estimation and inference procedures. The maximum likelihood estimators are shown to be consistent. Additionally, the proposed estimators of the finite-dimensional parameters are asymptotically normal and the covariance matrix attains the semiparametric efficiency bound. Simulation studies demonstrate that the proposed methodologies perform well in practical situations. We apply the proposed methods to a clinical trial on patients with myelodysplastic syndromes.
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Affiliation(s)
- Guoqing Diao
- Department of Statistics, George Mason University, Fairfax, VA
| | - Donglin Zeng
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC
| | | | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC
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6
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Charles‐Nelson A, Katsahian S, Schramm C. How to analyze and interpret recurrent events data in the presence of a terminal event: An application on readmission after colorectal cancer surgery. Stat Med 2019; 38:3476-3502. [DOI: 10.1002/sim.8168] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2018] [Revised: 03/27/2019] [Accepted: 03/27/2019] [Indexed: 11/08/2022]
Affiliation(s)
- Anaïs Charles‐Nelson
- Sorbonne Universités, UPMC Univ Paris 06, UMRS 1138Centre de Recherche des Cordeliers Paris France
- INSERM, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Université Paris Descartes, Sorbonne Paris Cité, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Assistance Publique Hôpitaux de Paris, Hôpital Européen Georges‐PompidouUnité d'Épidémiologie et de Recherche Clinique, INSERM, Centre d'Investigation Clinique 1418, Module Épidémiologie Clinique Paris France
| | - Sandrine Katsahian
- INSERM, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Université Paris Descartes, Sorbonne Paris Cité, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Assistance Publique Hôpitaux de Paris, Hôpital Européen Georges‐PompidouUnité d'Épidémiologie et de Recherche Clinique, INSERM, Centre d'Investigation Clinique 1418, Module Épidémiologie Clinique Paris France
| | - Catherine Schramm
- Sorbonne Universités, UPMC Univ Paris 06, UMRS 1138Centre de Recherche des Cordeliers Paris France
- INSERM, UMRS 1138Centre de Recherche des Cordeliers Paris France
- Université Paris Descartes, Sorbonne Paris Cité, UMRS 1138Centre de Recherche des Cordeliers Paris France
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7
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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.
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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
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8
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Abstract
Recurrent event outcomes are ubiquitous among clinical trial data which encourages a conventional approach to analysis. Yet a common feature of these data has received less attention, that is, survival times often comprise multiple types of events that may imply a disparity in cost and disease severity. Typically, we neglect this feature of the data by combining event-types or analyzing each type separately, thus ignoring any interdependence among them. This practice may reflect a dearth of readily available methods and software that more appropriately acknowledge the true data structure. We provide a review of the literature on multitype recurrent events and frailty modelling which reflects a renewed interest in the topic over the past decade and the emergence of software for estimation. Thus, a review of available methods seems timely, if not overdue.
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Affiliation(s)
- Paul M Brown
- Department of Medicine, University of Alberta, Edmonton, Canada
- Canadian VIGOUR Centre, Edmonton, Canada
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9
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Diao G, Zeng D, Hu K, Ibrahim JG. Modeling event count data in the presence of informative dropout with application to bleeding and transfusion events in myelodysplastic syndrome. Stat Med 2017; 36:3475-3494. [PMID: 28560768 DOI: 10.1002/sim.7351] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2016] [Revised: 04/01/2017] [Accepted: 05/05/2017] [Indexed: 11/05/2022]
Abstract
In many biomedical studies, it is often of interest to model event count data over the study period. For some patients, we may not follow up them for the entire study period owing to informative dropout. The dropout time can potentially provide valuable insight on the rate of the events. We propose a joint semiparametric model for event count data and informative dropout time that allows for correlation through a Gamma frailty. We develop efficient likelihood-based estimation and inference procedures. The proposed nonparametric maximum likelihood estimators are shown to be consistent and asymptotically normal. Furthermore, the asymptotic covariances of the finite-dimensional parameter estimates attain the semiparametric efficiency bound. Extensive simulation studies demonstrate that the proposed methods perform well in practice. We illustrate the proposed methods through an application to a clinical trial for bleeding and transfusion events in myelodysplastic syndrome. Copyright © 2017 John Wiley & Sons, Ltd.
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Affiliation(s)
- Guoqing Diao
- Department of Statistics, George Mason University, Fairfax, VA, U.S.A
| | - Donglin Zeng
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, U.S.A
| | - Kuolung Hu
- Amgen Inc., One Amgen Center Drive, Thousand Oaks, CA, U.S.A
| | - Joseph G Ibrahim
- Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC, U.S.A
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10
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Ye P, Zhao X, Sun L, Xu W. A semiparametric additive rates model for multivariate recurrent events with missing event categories. Comput Stat Data Anal 2015. [DOI: 10.1016/j.csda.2015.03.002] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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11
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Smith AR, Schaubel DE. Time-dependent prognostic score matching for recurrent event analysis to evaluate a treatment assigned during follow-up. Biometrics 2015; 71:950-9. [PMID: 26295563 DOI: 10.1111/biom.12361] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2014] [Revised: 04/01/2015] [Accepted: 05/01/2015] [Indexed: 11/30/2022]
Abstract
Recurrent events often serve as the outcome in epidemiologic studies. In some observational studies, the goal is to estimate the effect of a new or "experimental" (i.e., less established) treatment of interest on the recurrent event rate. The incentive for accepting the new treatment may be that it is more available than the standard treatment. Given that the patient can choose between the experimental treatment and conventional therapy, it is of clinical importance to compare the treatment of interest versus the setting where the experimental treatment did not exist, in which case patients could only receive no treatment or the standard treatment. Many methods exist for the analysis of recurrent events and for the evaluation of treatment effects. However, methodology for the intersection of these two areas is sparse. Moreover, care must be taken in setting up the comparison groups in our setting; use of existing methods featuring time-dependent treatment indicators will generally lead to a biased treatment effect since the comparison group construction will not properly account for the timing of treatment initiation. We propose a sequential stratification method featuring time-dependent prognostic score matching to estimate the effect of a time-dependent treatment on the recurrent event rate. The performance of the method in moderate-sized samples is assessed through simulation. The proposed methods are applied to a prospective clinical study in order to evaluate the effect of living donor liver transplantation on hospitalization rates; in this setting, conventional therapy involves remaining on the wait list or receiving a deceased donor transplant.
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Affiliation(s)
- Abigail R Smith
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA
| | - Douglas E Schaubel
- Department of Biostatistics, University of Michigan, Ann Arbor, Michigan, USA
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12
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Wang P, Tong X, Zhao S, Sun J. Regression Analysis of Left-truncated and Case I Interval-censored Data with the Additive Hazards Model. COMMUN STAT-THEOR M 2015. [DOI: 10.1080/03610926.2014.944665] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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13
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Ning J, Chen Y, Cai C, Huang X, Wang MC. On the dependence structure of bivariate recurrent event processes: inference and estimation. Biometrika 2015. [DOI: 10.1093/biomet/asu073] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
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14
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Chen CM, Chuang YW, Shen PS. Two-stage estimation for multivariate recurrent event data with a dependent terminal event. Biom J 2014; 57:215-33. [DOI: 10.1002/bimj.201400001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2014] [Revised: 09/14/2014] [Accepted: 10/01/2014] [Indexed: 11/11/2022]
Affiliation(s)
- Chyong-Mei Chen
- Department of Statistics and Informatics Science; Providence University; Taichung 43301 Taiwan Republic of China
- Department of Financial and Computational Mathematics; Providence University; Taichung 43301 Taiwan Republic of China
| | - Ya-Wen Chuang
- Division of Nephrology; Department of Internal Medicine, Taichung Veterans General Hospital; Taichung 40705 Taiwan Republic of China
| | - Pao-Sheng Shen
- Department of Statistics; Tunghai University; Taichung 40704 Taiwan Republic of China
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15
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Kim YJ. Analysis of Recurrent Gap Time Data with a Binary Time-Varying Covariate. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2014. [DOI: 10.5351/csam.2014.21.5.387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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16
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Mauguen A, Rachet B, Mathoulin-Pélissier S, MacGrogan G, Laurent A, Rondeau V. Dynamic prediction of risk of death using history of cancer recurrences in joint frailty models. Stat Med 2013; 32:5366-80. [DOI: 10.1002/sim.5980] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2012] [Accepted: 08/27/2013] [Indexed: 02/05/2023]
Affiliation(s)
- Audrey Mauguen
- INSERM, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique; F-33000 Bordeaux France
- Univ. Bordeaux, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique; F-33000 Bordeaux France
| | - Bernard Rachet
- Cancer Research UK Cancer Survival Group, Department of Non-Communicable Disease Epidemiology; London School of Hygiene and Tropical Medicine; UK-WC1E7HT London U.K
| | - Simone Mathoulin-Pélissier
- INSERM, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique; F-33000 Bordeaux France
- Unité de recherche et d’épidemiologie cliniques; Institut Bergonié; F-33000 Bordeaux France
- INSERM CIC-EC7; F-33000 Bordeaux France
| | - Gaetan MacGrogan
- Unité de recherche et d’épidemiologie cliniques; Institut Bergonié; F-33000 Bordeaux France
| | - Alexandre Laurent
- INSERM, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique; F-33000 Bordeaux France
- Univ. Bordeaux, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique; F-33000 Bordeaux France
| | - Virginie Rondeau
- INSERM, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique; F-33000 Bordeaux France
- Univ. Bordeaux, ISPED, Centre INSERM U897-Epidémiologie-Biostatistique; F-33000 Bordeaux France
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