Abstract
Panel count data occur in many clinical and observational studies and in some situations the observation process is informative. In this article, we propose a new joint model for the analysis of panel count data with time-dependent covariates and possibly in the presence of informative observation process via two latent variables. For the inference on the proposed model, a class of estimating equations is developed and the resulting estimators are shown to be consistent and asymptotically normal. In addition, a lack-of-fit test is provided for assessing the adequacy of the model. The finite-sample behavior of the proposed methods is examined through Monte Carlo simulation studies which suggest that the proposed approach works well for practical situations. Also an illustrative example is provided.
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References
Balakrishnan, N., Zhao, X. New multi-sample nonparametric tests for panel count data. Annals of Statistics, 37: 1112–1149 (2009)
Buzkova, P., (2010). Panel count data regression with informative observation times. The International Journal of Biostatistics, 6(1): Article 30 (2010)
He, X., Tong, X., Sun, J., Cook, R. Regression analysis of multivariate panel count data. Biostatistics, 9: 234–248 (2008)
He, X., Tong, X., Sun, J. Semiparametric analysis of panel count data with correlated observation and follow-up times. Lifetime Data Analysis, 15: 177–196 (2009)
Huang, C.Y., Wang, M.C., Zhang, Y. Analysing panel count data with informative observation times. Biometrika, 93: 763–775 (2006)
Kalbfleisch, J.D., Lawless, J.F. The analysis of panel data under a Markov assumption. Journal of the American Statistical Association, 80: 863–871 (1985)
Lin, D.Y., Wei, L.J., Yang, I., Ying, Z. Semiparametric regression for the mean and rate functions of recurrent events. Journal of the Royal Statistical Society, Series B, 62: 711–730 (2000)
Lin, D.Y., Wei, L.J., Ying, Z. Semiparametric transformation models for point processes. Journal of the America Statistical Association, 96: 620–628 (2001)
Lin, D.Y., Ying, Z. Semiparametric and nonparametric regression analysis of longitudinal data. Journal of the American Statistical Association, 96: 103–126 (2001)
Ross, S. Simulation, 4th ed. Academic Press, New York, 2006
Sun, J., Fang, H.B. A nonparametric test for panel count data. Biometrika, 90: 199–208 (2003)
Sun, J., Kalbfleisch, J.D. Estimation of the mean function of point processes based on panel count data. Statistica Sinica, 5: 279–290 (1985)
Sun, J., Tong, X., He, X. Regression analysis of panel count data with dependent observation times. Biometrics, 63: 1053–1059 (2007)
Sun, J., Wei, L.J. Regression analysis of panel count data with covariate-dependent observation and censoring times. Journal of the Royal Statistical Society, Series B, 62: 293–302 (2000)
Sun, J., Zhao, X. The Statistical Analysis of Panel Count Data. Springer Science + Business Inc., 2013
Sun, L., Song, X., Zhou, J., Liu, L. Joint analysis of longitudinal data with informative observation times and a dependent terminal event. Journal of the American Statistical Association, 107: 688–700 (2012)
Thall, P.F., Lachin, J.M. Analysis of recurrent events: nonparametric methods for random-interval count data. Journal of the American Statistical Association, 83: 339–347 (1988)
Tong, X., He, X., Sun, L., Sun, J. Variable selection for panel count data via non-concave penalized estimating function. Scandinavian Journal of Statistics, 36: 620–635 (2009)
Wellner, J.A., Zhang, Y. Two estimators of the mean of a counting process with panel count data. Annals of Statistics, 28: 779–814 (2000)
Zhang, H., Sun, J., Wang, D. Variable selection and estimation for multivariate panel count data via the seamless-L 0 penalty. The Canadian Journal of Statistics, 41(2): 368–385 (2013)
Zhang, H., Zhao, H., Sun, J., Wang, D., Kim, K. Regression analysis of multivariate panel count data with an informative observation process. Journal of Multivariate Analysis, 119: 71–80 (2013)
Zhang, Y. Nonparametric k-sample tests for panel count data. Biometrika, 93: 777–790 (2006)
Zhao, X., Tong, X. Semiparametric regression analysis of panel count data with information observation times. Computational Statistics and Data Analysis, 55: 291–300 (2011)
Zhao, X., Tong, X., Sun, J. Robust estimation for panel count data with informative observation times. Computational Statistics and Data Analysis, 57: 33–40 (2013)
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The work of Sha Fang is partially supported by National Natural Science Foundation of China (11671267), Scientific Research Level Improvement Quota Project of Capital University of Economics and Business and Scientific Research Foundation for Young Teachers of Capital University of Economics and Business (00591654490336). The work of Haixiang Zhang is partially supported by the National Natural Science Foundation of China (Nos. 11301212, 11401146). The work of Liuquan Sun is partially supported by the National Natural Science Foundation of China Grants (No. 11231010, 11171330 and 11021161) and Key Laboratory of RCSDS, CAS (No.2008DP173182). The work of Dehui Wang is partly supported by National Natural Science Foundation of China (11271155), Specialized Research Fund for the Doctoral Program of Higher Education (20110061110003), Scientific Research Fund of Jilin University (201100011) and Jilin Province Natural Science Foundation (20101596).
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Fang, S., Zhang, Hx., Sun, Lq. et al. Analysis of panel count data with time-dependent covariates and informative observation process. Acta Math. Appl. Sin. Engl. Ser. 33, 147–156 (2017). https://doi.org/10.1007/s10255-017-0645-6
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DOI: https://doi.org/10.1007/s10255-017-0645-6