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Accelerated Recurrence Time Models

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  • YIJIAN HUANG
  • LIMIN PENG

Abstract

. For the analysis with recurrent events, we propose a generalization of the accelerated failure time model to allow for evolving covariate effects. These so‐called accelerated recurrence time models postulate that the time to expected recurrence frequency, upon transformation, is a linear function of covariates with frequency‐dependent coefficients. This modelling strategy shares the same spirit as quantile regression. An estimation and inference procedure is developed by generalizing the celebrated Powell's (J. Econometrics 25, 1984, 303; J. Econometrics 32, 1986, 143) estimator for censored quantile regression. Consistency and asymptotic normality of the proposed estimator are established. An algorithm is devised to attain good computational efficiency. Simulations demonstrate that this proposal performs well under practical settings. This methodology is illustrated in an application to the well‐known bladder cancer study.

Suggested Citation

  • Yijian Huang & Limin Peng, 2009. "Accelerated Recurrence Time Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 636-648, December.
    • Handle: RePEc:bla:scjsta:v:36:y:2009:i:4:p:636-648
    DOI: 10.1111/j.1467-9469.2009.00645.x
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    References listed on IDEAS

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    1. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(3), pages 295-317, September.
    2. Lai, Tze Leung & Ying, Zhiliang, 1988. "Stochastic integrals of empirical-type processes with applications to censored regression," Journal of Multivariate Analysis, Elsevier, vol. 27(2), pages 334-358, November.
    3. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
    4. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
    5. Portnoy S., 2003. "Censored Regression Quantiles," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1001-1012, January.
    6. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    7. Chin-Tsang Chiang & Mei-Cheng Wang, 2009. "Varying-coefficient model for the occurrence rate function of recurrent events," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 197-213, March.
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    Cited by:

    1. Xiaoyan Sun & Limin Peng & Yijian Huang & HuiChuan J. Lai, 2016. "Generalizing Quantile Regression for Counting Processes With Applications to Recurrent Events," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 145-156, March.
    2. Xiaoyi Wen & Jinfeng Xu, 2022. "Generalized Accelerated Failure Time Models for Recurrent Events," Mathematics, MDPI, vol. 10(15), pages 1-14, July.
    3. Shahedul A. Khan & Nyla Basharat, 2022. "Accelerated failure time models for recurrent event data analysis and joint modeling," Computational Statistics, Springer, vol. 37(4), pages 1569-1597, September.
    4. Shuang Ji & Limin Peng & Yu Cheng & HuiChuan Lai, 2012. "Quantile Regression for Doubly Censored Data," Biometrics, The International Biometric Society, vol. 68(1), pages 101-112, March.
    5. Huijuan Ma & Limin Peng & Zhumin Zhang & HuiChuan J. Lai, 2018. "Generalized accelerated recurrence time model for multivariate recurrent event data with missing event type," Biometrics, The International Biometric Society, vol. 74(3), pages 954-965, September.
    6. Yijian Huang, 2017. "Restoration of Monotonicity Respecting in Dynamic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 613-622, April.

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