Abstract
In [13], Schaubel et al. proposed a semiparametric partially linear rate model for the statistical analysis of recurrent event data. But they only considered the model with time-independent covariate effects. In this paper, rate function of the recurrent event is modeled by a semiparametric partially linear function which can include the time-varying effects. We propose the method of generalized estimating equations to make inferences about both the time-varying effects and time-independent effects. The large sample properties are established, while extensive simulation studies are carried out to examine the proposed procedures. At last, we apply the procedures to the well-known bladder cancer study.
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References
Anderson, P., Gill, R. Cox’s regression model for counting processes: a large sample study. Annals of Statistics, 10: 1100–1120 (1982)
Byar, D.P. The Veterans Administration study of chemoprophylaxis for recurrent stage I bladder tumors: Comparisons of placebo, pyridoxine, and topical thiotepa. In: Bladder Tumors and Other Topics in Urological Oncology, ed. by Pavane-Macaluso P, Smith P H and Edsmyr F, Plenum, New York, 1980, 363–370
Bilias, Y., Gu, M., Ying, Z. Towards a general asymptotic theory for the Cox model with staggered entry. Annals of Statistics, 25: 662–682 (1997)
Cai, J., Schaubel, Z. Marginal means/rates models for multiple type recurrent event data. Lifetime Data Analysis, 10: 121–138 (2004)
Kalbfleisch, J., Prentice, R. The statistical analysis of failure time data. Wiley, New York, 2002
Liang, K., Zeger, S. Longitudinal data analysis using generalized linear models. Biometrika, 73: 13–22 (1986)
Lin, D., Wei, L., Ying, Z. Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika, 80: 557–572 (1993)
Lin, D., Wei, L., Ying, Z. Semiparametric regression for the mean and rate functions of recurrent events. Journal of the Royal Statistical Soecity (Series B), 62:711–730 (2000)
Mckeague, I.W., Sasieni, P.D. A partly parametric additive risk model. Biometrika, 81: 501–514 (1994)
Pollard, D. Empirical processes:theory and application. Institute of Mathematical Statistics, Hyward, 1990
Prentice, R., Williams, B., Peterson, A. On the regression analysis of multivariate failure time data. Biometrika, 68: 373–379 (1981)
Schaubel, Z., Cai, J. Semiparametric methods for clustered recurrent event data. Lifetime Data Analysis, 11: 405–425 (2005)
Schaubel, Z., Zeng, D., Cai, J. A semiparametric additive rates model for recurrent event data. Lifetime Data Analysis, 12: 389–406 (2006)
Scheike, T.H. The additive nonparametric and semiparametric Aalen model as the rate function for a counting process. Lifetime Data Analysis, 8: 247–262 (2002)
Sen, P., Singer, J. Large sample methods in statistics. Chapman & Hall, New York, 1993
Sun, L.Q., Zhu, L., Sun, J.G. Regression analysis of multivariate recurrent event data with time-varying covariate effects. Journal of Multivariate Analysis, 100: 2214–2223 (2009)
Zhao, X., Zhou, J., Sun, L. Semiparametric Transformation Models with Time-Varying Coefficients for Recurrent and Terminal Events. Biometrics, 67: 404–414 (2011)
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Supported by the National Natural Science Foundation of China (No.11326184) and the Fundamental Research Funds for the Central Universities (No.14CX02146A).
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Chen, Xl. Partially time-varying coefficient linear rate model for the recurrent event data. Acta Math. Appl. Sin. Engl. Ser. 30, 681–698 (2014). https://doi.org/10.1007/s10255-014-0425-5
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DOI: https://doi.org/10.1007/s10255-014-0425-5