Skip to main content
Log in

Semiparametric additive marginal regression models for multiple type recurrent events

  • Published:
Lifetime Data Analysis Aims and scope Submit manuscript

Abstract

Recurrent event data are often encountered in biomedical research, for example, recurrent infections or recurrent hospitalizations for patients after renal transplant. In many studies, there are more than one type of events of interest. Cai and Schaube (Lifetime Data Anal 10:121–138, 2004) advocated a proportional marginal rate model for multiple type recurrent event data. In this paper, we propose a general additive marginal rate regression model. Estimating equations approach is used to obtain the estimators of regression coefficients and baseline rate function. We prove the consistency and asymptotic normality of the proposed estimators. The finite sample properties of our estimators are demonstrated by simulations. The proposed methods are applied to the India renal transplant study to examine risk factors for bacterial, fungal and viral infections.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abu-Libdeh H, Turnbull B, Clark L (1990) Analysis of multi-type recurrent events in longitudinal studies: Application to a skin cancer prevention trial. Biometrics 46: 1017–1034

    Article  Google Scholar 

  • Anderson P, Gill R (1982) Cox’s regression model for counting processes: a large sample study. Ann Stat 10: 1100–1120

    Article  Google Scholar 

  • Bilias Y, Gu M, Ying Z (1997) Towards a general asymptotic theory for the cox model with ataggered entry. Ann Stat 25: 662–682

    Article  MathSciNet  MATH  Google Scholar 

  • Cai J, Schaubel D (2004) Marginal means/rates models for multiple type recurrent event data. Lifetime Data Anal 10: 121–138

    Article  MathSciNet  MATH  Google Scholar 

  • Chen B, Cook R, Lawless F, Zhan M (2005) Statistical methods for multivariate interval-censored recurrent events. Stat Med 24: 671–691

    Article  MathSciNet  Google Scholar 

  • Chen B, Cook R (2009) The analysis of multivariate recurrent events with partially missing event types. Lifetime Data Anal 15: 41–58

    Article  MathSciNet  MATH  Google Scholar 

  • Ghosh D, Lin D (2000) Nonparametric analysis of recurrent events and death. Biometrics 56: 554–562

    Article  MathSciNet  MATH  Google Scholar 

  • Ghosh D, Lin D (2002) Marginal regression models for recurrent and terminal events. Stat Sinica 12: 88–663

    MathSciNet  Google Scholar 

  • Kalbfleisch J, Prentice R (2002) The statistical analysis of failure time data. Wiley, New York

    Book  MATH  Google Scholar 

  • Lawless J, Nadeau C (1995) Some simple robust methods for the analysis of recurrent events. Technometrics 37: 68–158

    Article  MathSciNet  Google Scholar 

  • Lawless J, Wigg M, Tuli S, Drake J, Lamberti-Pasculli M (2001) Analysis of repeated failures or durations, with application to shunt failures for patients with paediatric hydrocephalus. Appl Stat 50: 449–465

    MathSciNet  MATH  Google Scholar 

  • Liang K, Zeger S (1986) Longitudinal data analysis using generalized linear models. Biometrika 73: 13–22

    Article  MathSciNet  MATH  Google Scholar 

  • Lin D, Wei L, Ying Z (1993) Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika 80: 72–557

    MathSciNet  Google Scholar 

  • Lin D, Fleming T, Wei L (1994) Confidence bands for survival curves under the proportional hazards model. Biometrika 81: 73–81

    Article  MathSciNet  MATH  Google Scholar 

  • Lin D, Wei L, Ying Z (1998) Accelerated failure time models for counting processes. Biometrika 85: 605–618

    Article  MathSciNet  MATH  Google Scholar 

  • Lin D, Wei L, Ying Z (2000) Semiparametric regression for the mean and rate functions of recurrent events. J R Stat Soc B 62: 30–711

    Article  MathSciNet  Google Scholar 

  • Liu L, Wolfe R, Huang X (2004) Shared frailty models for recurrent events and a terminal event. Biometrics 60: 747–756

    Article  MathSciNet  MATH  Google Scholar 

  • Liu Y, Wu Y, Cai J, Zhou H (2010) Additive-multiplicative rates model for recurrent events. Lifetime Data Anal 16: 353–373

    Article  MathSciNet  Google Scholar 

  • Ng E, Cook R (1999) Robust inference for bivariate point processes. Can J Stat 27: 509–524

    Article  MathSciNet  MATH  Google Scholar 

  • Pepe M, Cai J (1993) Some graphical displays and marginal regression analyses for recurrent failure times and time-dependent covariates. J Am Stat Assoc 88: 20–811

    Article  Google Scholar 

  • Pollard D (1990) Empirical processes:theory and application. Institute of Mathematical Statistics, Hyward

    Google Scholar 

  • Prentice R, Williams B, Peterson A (1981) On the regression analysis of multivariate failure time data. Biometrika 68: 79–373

    Article  MathSciNet  Google Scholar 

  • Schaubel D, Zeng D, Cai J (2006) A semiparametric additive rates model for recurrent event data. Lifetime Data Anal 12: 389–406

    Article  MathSciNet  MATH  Google Scholar 

  • Schaubel D, Cai J (2006a) Rate/mean regression for multiple-sequence recurrent event data with missing event category. Scand J Stat 33: 191–207

    Article  MathSciNet  MATH  Google Scholar 

  • Schaubel D, Cai J (2006b) Multiple imputation methods for recurrent event data with missing event category. Can J Stat 34: 677–692

    Article  MathSciNet  MATH  Google Scholar 

  • Sen P, Singer J (1993) Large sample methods in statistics. Chapman & Hall, New York

    MATH  Google Scholar 

  • Spiekerman C, Lin D (1998) Marginal regression models for multivariate failure time data. J Am Stat Assoc 93: 75–1164

    Article  MathSciNet  Google Scholar 

  • Sun L, Zhu L, Sun J (2009) Regression analysis of multivariate recurrent event data with time-varying covariate effects. J Multivar Anal 100: 2214–2223

    Article  MathSciNet  MATH  Google Scholar 

  • Van der Vaart A, Wellner J (1996) Weak convergence and empirical processes. Springer, New York

    MATH  Google Scholar 

  • Zeng D, Cai J (2010) A semiparametric additive rate model for recurrent events with an informative terminal event. Biometrika 97: 699–712

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Qihua Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chen, X., Wang, Q., Cai, J. et al. Semiparametric additive marginal regression models for multiple type recurrent events. Lifetime Data Anal 18, 504–527 (2012). https://doi.org/10.1007/s10985-012-9226-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10985-012-9226-4

Keywords

Mathematical Subject Classification (2000)

Navigation