A varying-coefficient model for gap times between recurrent events
Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events consider the time scale measured from the study origin and assume constant effects of covariates. In many applications, however...
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| Published in | Lifetime data analysis Vol. 27; no. 3; pp. 437 - 459 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.07.2021
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1380-7870 1572-9249 1572-9249 |
| DOI | 10.1007/s10985-021-09523-7 |
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| Abstract | Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events consider the time scale measured from the study origin and assume constant effects of covariates. In many applications, however, gap times between recurrent events are of natural interest and moreover the effects may actually vary over time. In this article, we propose a marginal varying-coefficient model for gap times between recurrent events that allows for the intra-individual correlation between events. Estimation and inference procedures are developed for the varying coefficients. Consistency and weak convergence of the proposed estimator are established. Monte Carlo simulation studies demonstrate that the proposed method works well with practical sample sizes. The proposed method is illustrated with an analysis of bladder tumor clinical data. |
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| AbstractList | Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events consider the time scale measured from the study origin and assume constant effects of covariates. In many applications, however, gap times between recurrent events are of natural interest and moreover the effects may actually vary over time. In this article, we propose a marginal varying-coefficient model for gap times between recurrent events that allows for the intra-individual correlation between events. Estimation and inference procedures are developed for the varying coefficients. Consistency and weak convergence of the proposed estimator are established. Monte Carlo simulation studies demonstrate that the proposed method works well with practical sample sizes. The proposed method is illustrated with an analysis of bladder tumor clinical data. Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events consider the time scale measured from the study origin and assume constant effects of covariates. In many applications, however, gap times between recurrent events are of natural interest and moreover the effects may actually vary over time. In this article, we propose a marginal varying-coefficient model for gap times between recurrent events that allows for the intra-individual correlation between events. Estimation and inference procedures are developed for the varying coefficients. Consistency and weak convergence of the proposed estimator are established. Monte Carlo simulation studies demonstrate that the proposed method works well with practical sample sizes. The proposed method is illustrated with an analysis of bladder tumor clinical data.Recurrent events often arise in follow-up studies where a subject may experience multiple occurrences of the same type of event. Most regression models for recurrent events consider the time scale measured from the study origin and assume constant effects of covariates. In many applications, however, gap times between recurrent events are of natural interest and moreover the effects may actually vary over time. In this article, we propose a marginal varying-coefficient model for gap times between recurrent events that allows for the intra-individual correlation between events. Estimation and inference procedures are developed for the varying coefficients. Consistency and weak convergence of the proposed estimator are established. Monte Carlo simulation studies demonstrate that the proposed method works well with practical sample sizes. The proposed method is illustrated with an analysis of bladder tumor clinical data. |
| Author | Huang, Yijian Soh, J. E. |
| Author_xml | – sequence: 1 givenname: J. E. orcidid: 0000-0003-0234-8986 surname: Soh fullname: Soh, J. E. email: statsoh@gmail.com organization: Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University – sequence: 2 givenname: Yijian orcidid: 0000-0003-4364-3199 surname: Huang fullname: Huang, Yijian organization: Department of Biostatistics and Bioinformatics, Rollins School of Public Health, Emory University |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/33963982$$D View this record in MEDLINE/PubMed |
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| Cites_doi | 10.1214/aos/1176345976 10.1093/biomet/68.2.373 10.1111/1467-9868.00259 10.1198/016214508000000355 10.1214/aos/1176347865 10.1023/A:1025892922453 10.1080/01621459.1999.10473831 10.1080/01621459.2016.1149070 10.1093/biomet/asm058 10.1214/aos/1176345338 10.1093/biomet/asu004 10.1093/biomet/asq050 10.1111/j.2517-6161.1972.tb00899.x 10.1093/biomet/91.3.683 10.1080/01621459.1993.10476346 10.1007/978-1-4757-3294-8 10.1007/978-0-387-74978-5 10.1080/00401706.1995.10484300 10.2307/2337051 10.1007/s10463-007-0129-1 |
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| DOI | 10.1007/s10985-021-09523-7 |
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| Keywords | Event history analysis Multivariate survival data Marginal modeling Multiplier bootstrap Varying-effects model Renewal Process |
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| References | PengLHuangYSurvival analysis with temporal covariate effectsBiometrika2007943719733241001910.1093/biomet/asm058 KosorokMRIntroduction to Empirical Processes and Semiparametric Inference2008New YorkSpringer-Verlag10.1007/978-0-387-74978-5 PepeMSCaiJSome graphical displays and marginal regression analyses for recurrent failure times and time dependent covariatesJ Am Stat Assoc19938842381182010.1080/01621459.1993.10476346 PengLHuangYSurvival analysis with quantile regression modelsJ Am Stat Assoc2008103482637649243546810.1198/016214508000000355 WangM-CChangS-HNonparametric estimation of a recurrent survival functionJ Am Stat Assoc199994445146153168922010.1080/01621459.1999.10473831 FineJPYanJKosorokMRTemporal process regressionBiometrika2004913683703209063010.1093/biomet/91.3.683 QianJPengLCensored quantile regression with partially functional effectsBiometrika2010974839850274615510.1093/biomet/asq050 GillRDJohansenSA survey of product-integration with a view toward application in survival analysisAnnal Stat199018415011555107442210.1214/aos/1176347865 HuangYChenYQMarginal regression of gaps between recurrent eventsLifetime Data Anal200393293303201662410.1023/A:1025892922453 ByarDPThe Veterans Administration Study of Chemoprophylaxis for Recurrent Stage I Bladder Tumours: Comparisons of Placebo. Pyridoxine and Topical Thiotepa1980US, Boston, MASpringer HuangYRestoration of monotonicity respecting in dynamic regressionJ Am Stat Assoc2017112518613622367175610.1080/01621459.2016.1149070 HuangYBootstrap for the case-cohort designBiometrika20141012465476321536010.1093/biomet/asu004 LinDFlemingTWeiLConfidence bands for survival curves under the proportional: Hazards modelBiometrika19948117381127965710.2307/2337051 AndersenPKGillRDCox’s regression model for counting processes: A large sample studyAnnal Stat19821041100112067364610.1214/aos/1176345976 AndersenPKBorganØGillRDKeidingNStatistical Models Based on Counting Processes. Springer Series in Statistics1993New YorkSpringer0769.62061 Cox DR (1972) ‘Regression models and life-tables’, Journal of the Royal Statistical Society. Series B (Methodological) 34(2):187–220 LawlessJFNadeauCSome simple robust methods for the analysis of recurrent eventsTechnometrics1995372158168133319410.1080/00401706.1995.10484300 PrenticeRWilliamsBPetersonAOn the regression analysis of multivariate failure time dataBiometrika198168237337962639610.1093/biomet/68.2.373 RubinDBThe bayesian bootstrapAnnal Stat19819113013460053810.1214/aos/1176345338 TherneauTMGrambschPMModeling Survival Data: Extending the Cox Model2000New YorkSpringer-Verlag10.1007/978-1-4757-3294-8 ChiangCTWangMCVarying-coefficient model for the occurrence rate function of recurrent eventsAnn Inst Stat Math2009611197213248103410.1007/s10463-007-0129-1 CookRJLawlessJThe Statistical Analysis of Recurrent Events2007New YorkSpringer-Verlag1159.62061 LinDYWeiLJYangIYingZSemiparametric regression for the mean and rate functions of recurrent eventsJ R Stat Soc: Series B (Stat Methodol)2000624711730179628710.1111/1467-9868.00259 RD Gill (9523_CR8) 1990; 18 Y Huang (9523_CR10) 2017; 112 Y Huang (9523_CR9) 2014; 101 J Qian (9523_CR20) 2010; 97 Y Huang (9523_CR11) 2003; 9 DY Lin (9523_CR15) 2000; 62 DB Rubin (9523_CR21) 1981; 9 RJ Cook (9523_CR5) 2007 PK Andersen (9523_CR1) 1993 MR Kosorok (9523_CR12) 2008 L Peng (9523_CR16) 2007; 94 D Lin (9523_CR14) 1994; 81 MS Pepe (9523_CR18) 1993; 88 TM Therneau (9523_CR22) 2000 L Peng (9523_CR17) 2008; 103 R Prentice (9523_CR19) 1981; 68 CT Chiang (9523_CR4) 2009; 61 DP Byar (9523_CR3) 1980 PK Andersen (9523_CR2) 1982; 10 JF Lawless (9523_CR13) 1995; 37 JP Fine (9523_CR7) 2004; 91 M-C Wang (9523_CR23) 1999; 94 9523_CR6 |
| References_xml | – reference: HuangYBootstrap for the case-cohort designBiometrika20141012465476321536010.1093/biomet/asu004 – reference: ByarDPThe Veterans Administration Study of Chemoprophylaxis for Recurrent Stage I Bladder Tumours: Comparisons of Placebo. Pyridoxine and Topical Thiotepa1980US, Boston, MASpringer – reference: QianJPengLCensored quantile regression with partially functional effectsBiometrika2010974839850274615510.1093/biomet/asq050 – reference: WangM-CChangS-HNonparametric estimation of a recurrent survival functionJ Am Stat Assoc199994445146153168922010.1080/01621459.1999.10473831 – reference: AndersenPKBorganØGillRDKeidingNStatistical Models Based on Counting Processes. Springer Series in Statistics1993New YorkSpringer0769.62061 – reference: KosorokMRIntroduction to Empirical Processes and Semiparametric Inference2008New YorkSpringer-Verlag10.1007/978-0-387-74978-5 – reference: FineJPYanJKosorokMRTemporal process regressionBiometrika2004913683703209063010.1093/biomet/91.3.683 – reference: HuangYRestoration of monotonicity respecting in dynamic regressionJ Am Stat Assoc2017112518613622367175610.1080/01621459.2016.1149070 – reference: LinDYWeiLJYangIYingZSemiparametric regression for the mean and rate functions of recurrent eventsJ R Stat Soc: Series B (Stat Methodol)2000624711730179628710.1111/1467-9868.00259 – reference: CookRJLawlessJThe Statistical Analysis of Recurrent Events2007New YorkSpringer-Verlag1159.62061 – reference: GillRDJohansenSA survey of product-integration with a view toward application in survival analysisAnnal Stat199018415011555107442210.1214/aos/1176347865 – reference: PrenticeRWilliamsBPetersonAOn the regression analysis of multivariate failure time dataBiometrika198168237337962639610.1093/biomet/68.2.373 – reference: TherneauTMGrambschPMModeling Survival Data: Extending the Cox Model2000New YorkSpringer-Verlag10.1007/978-1-4757-3294-8 – reference: AndersenPKGillRDCox’s regression model for counting processes: A large sample studyAnnal Stat19821041100112067364610.1214/aos/1176345976 – reference: Cox DR (1972) ‘Regression models and life-tables’, Journal of the Royal Statistical Society. Series B (Methodological) 34(2):187–220 – reference: LinDFlemingTWeiLConfidence bands for survival curves under the proportional: Hazards modelBiometrika19948117381127965710.2307/2337051 – reference: PengLHuangYSurvival analysis with quantile regression modelsJ Am Stat Assoc2008103482637649243546810.1198/016214508000000355 – reference: ChiangCTWangMCVarying-coefficient model for the occurrence rate function of recurrent eventsAnn Inst Stat Math2009611197213248103410.1007/s10463-007-0129-1 – reference: LawlessJFNadeauCSome simple robust methods for the analysis of recurrent eventsTechnometrics1995372158168133319410.1080/00401706.1995.10484300 – reference: PengLHuangYSurvival analysis with temporal covariate effectsBiometrika2007943719733241001910.1093/biomet/asm058 – reference: PepeMSCaiJSome graphical displays and marginal regression analyses for recurrent failure times and time dependent covariatesJ Am Stat Assoc19938842381182010.1080/01621459.1993.10476346 – reference: HuangYChenYQMarginal regression of gaps between recurrent eventsLifetime Data Anal200393293303201662410.1023/A:1025892922453 – reference: RubinDBThe bayesian bootstrapAnnal Stat19819113013460053810.1214/aos/1176345338 – volume: 10 start-page: 1100 issue: 4 year: 1982 ident: 9523_CR2 publication-title: Annal Stat doi: 10.1214/aos/1176345976 – volume: 68 start-page: 373 issue: 2 year: 1981 ident: 9523_CR19 publication-title: Biometrika doi: 10.1093/biomet/68.2.373 – volume: 62 start-page: 711 issue: 4 year: 2000 ident: 9523_CR15 publication-title: J R Stat Soc: Series B (Stat Methodol) doi: 10.1111/1467-9868.00259 – volume: 103 start-page: 637 issue: 482 year: 2008 ident: 9523_CR17 publication-title: J Am Stat Assoc doi: 10.1198/016214508000000355 – volume-title: Statistical Models Based on Counting Processes. Springer Series in Statistics year: 1993 ident: 9523_CR1 – volume: 18 start-page: 1501 issue: 4 year: 1990 ident: 9523_CR8 publication-title: Annal Stat doi: 10.1214/aos/1176347865 – volume: 9 start-page: 293 issue: 3 year: 2003 ident: 9523_CR11 publication-title: Lifetime Data Anal doi: 10.1023/A:1025892922453 – volume: 94 start-page: 146 issue: 445 year: 1999 ident: 9523_CR23 publication-title: J Am Stat Assoc doi: 10.1080/01621459.1999.10473831 – volume: 112 start-page: 613 issue: 518 year: 2017 ident: 9523_CR10 publication-title: J Am Stat Assoc doi: 10.1080/01621459.2016.1149070 – volume: 94 start-page: 719 issue: 3 year: 2007 ident: 9523_CR16 publication-title: Biometrika doi: 10.1093/biomet/asm058 – volume: 9 start-page: 130 issue: 1 year: 1981 ident: 9523_CR21 publication-title: Annal Stat doi: 10.1214/aos/1176345338 – volume-title: The Statistical Analysis of Recurrent Events year: 2007 ident: 9523_CR5 – volume-title: The Veterans Administration Study of Chemoprophylaxis for Recurrent Stage I Bladder Tumours: Comparisons of Placebo. Pyridoxine and Topical Thiotepa year: 1980 ident: 9523_CR3 – volume: 101 start-page: 465 issue: 2 year: 2014 ident: 9523_CR9 publication-title: Biometrika doi: 10.1093/biomet/asu004 – volume: 97 start-page: 839 issue: 4 year: 2010 ident: 9523_CR20 publication-title: Biometrika doi: 10.1093/biomet/asq050 – ident: 9523_CR6 doi: 10.1111/j.2517-6161.1972.tb00899.x – volume: 91 start-page: 683 issue: 3 year: 2004 ident: 9523_CR7 publication-title: Biometrika doi: 10.1093/biomet/91.3.683 – volume: 88 start-page: 811 issue: 423 year: 1993 ident: 9523_CR18 publication-title: J Am Stat Assoc doi: 10.1080/01621459.1993.10476346 – volume-title: Modeling Survival Data: Extending the Cox Model year: 2000 ident: 9523_CR22 doi: 10.1007/978-1-4757-3294-8 – volume-title: Introduction to Empirical Processes and Semiparametric Inference year: 2008 ident: 9523_CR12 doi: 10.1007/978-0-387-74978-5 – volume: 37 start-page: 158 issue: 2 year: 1995 ident: 9523_CR13 publication-title: Technometrics doi: 10.1080/00401706.1995.10484300 – volume: 81 start-page: 73 issue: 1 year: 1994 ident: 9523_CR14 publication-title: Biometrika doi: 10.2307/2337051 – volume: 61 start-page: 197 issue: 1 year: 2009 ident: 9523_CR4 publication-title: Ann Inst Stat Math doi: 10.1007/s10463-007-0129-1 |
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| SubjectTerms | Bladder Bladder cancer Coefficients Economics Finance Health Sciences Insurance Management Mathematics and Statistics Medicine Monte Carlo simulation Operations Research/Decision Theory Quality Control Regression models Reliability Safety and Risk Statistics Statistics for Business Statistics for Life Sciences Time measurement |
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| Title | A varying-coefficient model for gap times between recurrent events |
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