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The accelerated gap times model

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  • Robert L. Strawderman

Abstract

This paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process. The model is a transparent extension of the accelerated failure time model for univariate survival data. Estimation of the regression parameter is motivated by semiparametric efficiency considerations, extending the class of weighted log-rank estimating functions originally proposed in Prentice (1978) and subsequently studied in detail by Tsiatis (1990) and Ritov (1990). A novel rank-based one-step estimator for the regression parameter is proposed. An Aalen-type estimator for the baseline intensity function is obtained. Asymptotics are handled with empirical process methods, and finite sample properties are studied via simulation. Finally, the new model is applied to the bladder tumour data of Byar (1980). Copyright 2005, Oxford University Press.

Suggested Citation

  • Robert L. Strawderman, 2005. "The accelerated gap times model," Biometrika, Biometrika Trust, vol. 92(3), pages 647-666, September.
    • Handle: RePEc:oup:biomet:v:92:y:2005:i:3:p:647-666
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    File URL: http://hdl.handle.net/10.1093/biomet/92.3.647
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    Citations

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    Cited by:

    1. Xianghua Luo & Chiung-Yu Huang & Lan Wang, 2013. "Quantile Regression for Recurrent Gap Time Data," Biometrics, The International Biometric Society, vol. 69(2), pages 375-385, June.
    2. Jieli Ding & Liuquan Sun, 2017. "Additive mixed effect model for recurrent gap time data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 223-253, April.
    3. V. N. Sreeja & P. G. Sankaran, 2007. "Proportional mean residual life model for gap time distributions of recurrent events," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 319-336.
    4. Kang, Fangyuan & Sun, Liuquan & Zhao, Xingqiu, 2015. "A class of transformed hazards models for recurrent gap times," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 151-167.
    5. Xu Shu & Douglas E. Schaubel, 2017. "Methods for Contrasting Gap Time Hazard Functions: Application to Repeat Liver Transplantation," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 470-488, December.
    6. Kang Fang Yuan, 2018. "The Model and the Inference for the Clustered Recurrent Event," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 5(4), pages 106-107, February.
    7. Chien-Lin Su & Russell J. Steele & Ian Shrier, 2021. "The semiparametric accelerated trend-renewal process for recurrent event data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 357-387, July.
    8. Pang Du & Yihua Jiang & Yuedong Wang, 2011. "Smoothing Spline ANOVA Frailty Model for Recurrent Event Data," Biometrics, The International Biometric Society, vol. 67(4), pages 1330-1339, December.
    9. Jie Fan & Somnath Datta, 2013. "On Mann–Whitney tests for comparing sojourn time distributions when the transition times are right censored," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 149-166, February.
    10. Sankaran, P.G. & Anisha, P., 2012. "Additive hazards models for gap time data with multiple causes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1454-1462.
    11. Fengchang Lin & Jason P. Fine, 2009. "Pseudomartingale estimating equations for modulated renewal process models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 3-23, January.

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