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Modeling gap times between recurrent events by marginal rate function

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  • Zhao, Xiaobing
  • Zhou, Xian

Abstract

Gap times between recurrent events are often encountered in longitudinal follow-up studies related to medical science, biostatistics, econometrics, reliability, criminology, demography, and other areas. There have been many models to fit such data, such as proportional hazards (PH) model and additive hazards (AH) model, among others. Standard partial likelihood can be employed to draw their statistical inference. The inference from a direct PH or AH assumption on the gap times, however, is less intuitive and straightforward than marginal rate models–which are often preferred by practitioners due to their more direct interpretations for identifying risk factors. In addition, the existing models have not adequately considered zero-recurrence subjects often encountered in recurrent event data. To overcome these shortcomings, we propose an alternative gap time model using an additive marginal rate function that accounts for zero-recurrence subjects. Local profile-likelihood is applied to estimate the model attributes, and the asymptotic properties of the estimators are established as well. The performance of the proposed estimators is evaluated by a simulation study. The proposed model is applied to analyze a set of data on pulmonary exacerbations and rhDNase treatment.

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  • Zhao, Xiaobing & Zhou, Xian, 2012. "Modeling gap times between recurrent events by marginal rate function," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 370-383.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:2:p:370-383
    DOI: 10.1016/j.csda.2011.07.015
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    1. Jianwen Cai & Jianqing Fan & Jiancheng Jiang & Haibo Zhou, 2008. "Partially linear hazard regression with varying coefficients for multivariate survival data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 141-158, February.
    2. Yining Ye & John D. Kalbfleisch & Douglas E. Schaubel, 2007. "Semiparametric Analysis of Correlated Recurrent and Terminal Events," Biometrics, The International Biometric Society, vol. 63(1), pages 78-87, March.
    3. Mei-Cheng Wang & Ying-Qing Chen, 2000. "Nonparametric and Semiparametric Trend Analysis for Stratified Recurrence Times," Biometrics, The International Biometric Society, vol. 56(3), pages 789-794, September.
    4. Chiung-Yu Huang & Mei-Cheng Wang, 2004. "Joint Modeling and Estimation for Recurrent Event Processes and Failure Time Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 1153-1165, December.
    5. Douglas E. Schaubel, 2004. "Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data," Biometrika, Biometrika Trust, vol. 91(2), pages 291-303, June.
    6. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    7. Yip, Karen C.H. & Yau, Kelvin K.W., 2005. "On modeling claim frequency data in general insurance with extra zeros," Insurance: Mathematics and Economics, Elsevier, vol. 36(2), pages 153-163, April.
    8. J. Fan & J. Chen, 1999. "One‐step local quasi‐likelihood estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 927-943.
    9. J. Fan & M. Farmen & I. Gijbels, 1998. "Local maximum likelihood estimation and inference," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(3), pages 591-608.
    10. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    11. Wang M-C. & Qin J. & Chiang C-T., 2001. "Analyzing Recurrent Event Data With Informative Censoring," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1057-1065, September.
    12. Chin‐Tsang Chiang & Mei‐Cheng Wang & Chiung‐Yu Huang, 2005. "Kernel Estimation of Rate Function for Recurrent Event Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 77-91, March.
    13. John W. McDonald & Alessandro Rosina, 2001. "Mixture modelling of recurrent event times with long-term survivors: Analysis of Hutterite birth intervals," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 10(1), pages 257-272, January.
    14. Yanyuan Ma & Jeffrey D. Hart, 2007. "Constrained local likelihood estimators for semiparametric skew-normal distributions," Biometrika, Biometrika Trust, vol. 94(1), pages 119-134.
    15. Boucher, Jean-Philippe & Denuit, Michel, 2008. "Credibility premiums for the zero-inflated Poisson model and new hunger for bonus interpretation," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 727-735, April.
    16. Zhao, Xiaobing & Zhou, Xian, 2006. "Proportional hazards models for survival data with long-term survivors," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1685-1693, September.
    17. Jean-Philippe Boucher & Michel Denuit & Montserrat Guillén, 2007. "Risk Classification for Claim Counts," North American Actuarial Journal, Taylor & Francis Journals, vol. 11(4), pages 110-131.
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    2. Wang, Jixian & Quartey, George, 2013. "A semi-parametric approach to analysis of event duration and prevalence," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 248-257.

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