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2013 | OriginalPaper | Buchkapitel

6. Regression Analysis of Panel Count Data II

verfasst von : Jianguo Sun, Xingqiu Zhao

Erschienen in: Statistical Analysis of Panel Count Data

Verlag: Springer New York

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Abstract

This chapter discusses the same problem as in the previous chapter, but under different situations. A basic assumption behind the methods described in the last chapter is that the underlying recurrent event process of interest and the observation process are independent of each other conditional on covariates. As pointed out before, sometimes this assumption may not hold. In other words, the observation process may depend on or contain relevant information about the recurrent event process. In a study on the occurrence of asthma attacks, for example, the observations on or clinical visits of asthma patients may be related to or driven by the numbers of the asthma attacks before the visits. The same can occur for similar recurrent event studies such as these on some disease infections or tumor development. In these situations, it is clear that the methods given in Chap. 5 are not valid as they would lead to biased estimation or wrong conclusions. The data arising from these cases are often referred to as panel count data with informative or dependent observation processes.

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Literatur
Zurück zum Zitat Buzkova, P. (2010). Panel count data regression with informative observation times. The International Journal of Biostatistics, 6, article 30. Buzkova, P. (2010). Panel count data regression with informative observation times. The International Journal of Biostatistics, 6, article 30.
Zurück zum Zitat Cook, R. J. and Lawless, J. F. (2007). The statistical analysis of recurrent events. Springer-Verlag, New York.MATH Cook, R. J. and Lawless, J. F. (2007). The statistical analysis of recurrent events. Springer-Verlag, New York.MATH
Zurück zum Zitat DeGruttola, V. and Tu, X. M. (1994). Modeling progression of CD4-Lymphocyte count and its relationship to survival time. Biometrics, 50, 1003–1014.CrossRef DeGruttola, V. and Tu, X. M. (1994). Modeling progression of CD4-Lymphocyte count and its relationship to survival time. Biometrics, 50, 1003–1014.CrossRef
Zurück zum Zitat Elashoff, R. M., Li, G. and Li, N. (2008). A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics, 64, 762–771.MathSciNetCrossRefMATH Elashoff, R. M., Li, G. and Li, N. (2008). A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics, 64, 762–771.MathSciNetCrossRefMATH
Zurück zum Zitat Ghosh, D. and Lin, D. Y. (2002). Marginal regression models for recurrent and terminal events. Statistica Sinica, 12, 663–688.MathSciNetMATH Ghosh, D. and Lin, D. Y. (2002). Marginal regression models for recurrent and terminal events. Statistica Sinica, 12, 663–688.MathSciNetMATH
Zurück zum Zitat Ghosh, D. and Lin, D. Y. (2003). Semiparametric analysis of recurrent events in the presence of dependent censoring. Biometrics, 59, 877–885.MathSciNetCrossRefMATH Ghosh, D. and Lin, D. Y. (2003). Semiparametric analysis of recurrent events in the presence of dependent censoring. Biometrics, 59, 877–885.MathSciNetCrossRefMATH
Zurück zum Zitat Gibbons, J. D. and Chakraborti, S. (2011). Nonparametric statistical inference, 5th ed., Chapman & Hall. Gibbons, J. D. and Chakraborti, S. (2011). Nonparametric statistical inference, 5th ed., Chapman & Hall.
Zurück zum Zitat He, X., Tong, X. and Sun, J. (2009). Semiparametric analysis of panel count data with correlated observation and follow-up times. Lifetime Data Analysis, 15, 177–196.MathSciNetCrossRefMATH He, X., Tong, X. and Sun, J. (2009). Semiparametric analysis of panel count data with correlated observation and follow-up times. Lifetime Data Analysis, 15, 177–196.MathSciNetCrossRefMATH
Zurück zum Zitat Huang, C. Y. and Wang, M. C. (2004). Joint modeling and estimation for recurrent event processes and failure time data. Journal of the American Statistical Association, 99, 1153–1165.MathSciNetCrossRefMATH Huang, C. Y. and Wang, M. C. (2004). Joint modeling and estimation for recurrent event processes and failure time data. Journal of the American Statistical Association, 99, 1153–1165.MathSciNetCrossRefMATH
Zurück zum Zitat Huang, C. Y., Wang, M. C. and Zhang, Y. (2006). Analyzing panel count data with informative observation times. Biometrika, 93, 763–775.MathSciNetCrossRef Huang, C. Y., Wang, M. C. and Zhang, Y. (2006). Analyzing panel count data with informative observation times. Biometrika, 93, 763–775.MathSciNetCrossRef
Zurück zum Zitat Jin, Z., Liu, M., Albert, S. and Ying, Z. (2006). Analysis of longitudinal health-related quality of life data with terminal events. Lifetime Data Analysis, 12, 169–190.MathSciNetCrossRefMATH Jin, Z., Liu, M., Albert, S. and Ying, Z. (2006). Analysis of longitudinal health-related quality of life data with terminal events. Lifetime Data Analysis, 12, 169–190.MathSciNetCrossRefMATH
Zurück zum Zitat Kalbfleisch, J. D. and Prentice, R. L. (2002). The statistical analysis of failure time data. Second edition, John Wiley: New York.CrossRefMATH Kalbfleisch, J. D. and Prentice, R. L. (2002). The statistical analysis of failure time data. Second edition, John Wiley: New York.CrossRefMATH
Zurück zum Zitat Kim, Y-J. (2006). Analysis of panel count data with dependent observation times. Communications in Statistics - Simulation and Computation, 35, 983–990.MathSciNetCrossRefMATH Kim, Y-J. (2006). Analysis of panel count data with dependent observation times. Communications in Statistics - Simulation and Computation, 35, 983–990.MathSciNetCrossRefMATH
Zurück zum Zitat Li, N. (2011). Semiparametric transformation models for panel count data. Ph.D. Dissertation, University of Missouri, Columbia. Li, N. (2011). Semiparametric transformation models for panel count data. Ph.D. Dissertation, University of Missouri, Columbia.
Zurück zum Zitat Li, N., Sun, L. and Sun, J. (2010). Semiparametric transformation models for panel count data with dependent observation processes. Statistics in Biosciences, 2, 191–210.CrossRef Li, N., Sun, L. and Sun, J. (2010). Semiparametric transformation models for panel count data with dependent observation processes. Statistics in Biosciences, 2, 191–210.CrossRef
Zurück zum Zitat Li, N., Zhao, H. and Sun, J. (2013). Semiparametric transformation models for panel count data with correlated observation and follow-up times. Statistics in Medicine, in press. Li, N., Zhao, H. and Sun, J. (2013). Semiparametric transformation models for panel count data with correlated observation and follow-up times. Statistics in Medicine, in press.
Zurück zum Zitat Liang, Y., Lu, W.B. and Ying, Z. (2009). Joint modeling and analysis of longitudinal data with informative observation times. Biometrics, 65, 377–384.MathSciNetCrossRefMATH Liang, Y., Lu, W.B. and Ying, Z. (2009). Joint modeling and analysis of longitudinal data with informative observation times. Biometrics, 65, 377–384.MathSciNetCrossRefMATH
Zurück zum Zitat Lin, D. Y., Wei, L. J., Yang, I. and Ying, Z. (2000). Semiparametric regression for the mean and rate functions of recurrent events. Journal of Royal Statistical Society Ser B, 62, 711–730.MathSciNetCrossRefMATH Lin, D. Y., Wei, L. J., Yang, I. and Ying, Z. (2000). Semiparametric regression for the mean and rate functions of recurrent events. Journal of Royal Statistical Society Ser B, 62, 711–730.MathSciNetCrossRefMATH
Zurück zum Zitat Lin, D. Y., Wei, L. J. and Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika, 80, 557–572.MathSciNetCrossRefMATH Lin, D. Y., Wei, L. J. and Ying, Z. (1993). Checking the Cox model with cumulative sums of martingale-based residuals. Biometrika, 80, 557–572.MathSciNetCrossRefMATH
Zurück zum Zitat Lin, D. Y., Wei, L. J. and Ying, Z. (2001). Semiparametric transformation models for point processes. Journal of the American Statistical Association, 96, 620–628.MathSciNetCrossRefMATH Lin, D. Y., Wei, L. J. and Ying, Z. (2001). Semiparametric transformation models for point processes. Journal of the American Statistical Association, 96, 620–628.MathSciNetCrossRefMATH
Zurück zum Zitat Lin, H., Scharfstein, D. O. and Rosenheck, D. O. (2004). Analysis of longitudinal data with irregular outcome-dependent follow-up. Journal of Royal Statistical Society, Series B, 66, 791–813.MathSciNetCrossRefMATH Lin, H., Scharfstein, D. O. and Rosenheck, D. O. (2004). Analysis of longitudinal data with irregular outcome-dependent follow-up. Journal of Royal Statistical Society, Series B, 66, 791–813.MathSciNetCrossRefMATH
Zurück zum Zitat Liu, L., Huang, X. and O’Quigley, J. (2008). Analysis of longitudinal data in the presence of informative observational times and a dependent terminal event, with application to medical cost data. Biometrics, 64, 950–958.MathSciNetCrossRefMATH Liu, L., Huang, X. and O’Quigley, J. (2008). Analysis of longitudinal data in the presence of informative observational times and a dependent terminal event, with application to medical cost data. Biometrics, 64, 950–958.MathSciNetCrossRefMATH
Zurück zum Zitat Liu, L., Wolfe, R. A. and Huang, X. (2004). Shared frailty models for recurrent events and a terminal event. Biometrics, 60, 747–756.MathSciNetCrossRefMATH Liu, L., Wolfe, R. A. and Huang, X. (2004). Shared frailty models for recurrent events and a terminal event. Biometrics, 60, 747–756.MathSciNetCrossRefMATH
Zurück zum Zitat Liu, M. and Ying, Z. (2007). Joint analysis of longitudinal data with informative right censoring. Biometrics, 63, 363–371.MathSciNetCrossRefMATH Liu, M. and Ying, Z. (2007). Joint analysis of longitudinal data with informative right censoring. Biometrics, 63, 363–371.MathSciNetCrossRefMATH
Zurück zum Zitat Louis, T. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226–233.MathSciNetMATH Louis, T. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226–233.MathSciNetMATH
Zurück zum Zitat Luo, X. H. and Huang, C. Y. (2010). A comparison of various rate functions of a recurrent event process in the presence of a terminal event. Statistical Methods in Medical Research, 19, 167–182.MathSciNetCrossRef Luo, X. H. and Huang, C. Y. (2010). A comparison of various rate functions of a recurrent event process in the presence of a terminal event. Statistical Methods in Medical Research, 19, 167–182.MathSciNetCrossRef
Zurück zum Zitat Roy, J. and Lin, X. (2002). Analysis of multivariate longitudinal outcomes with nonignorable dropouts and missing covariates: Changes in methadone treatment practices. Journal of the American Statistical Association, 97, 40–52.MathSciNetCrossRefMATH Roy, J. and Lin, X. (2002). Analysis of multivariate longitudinal outcomes with nonignorable dropouts and missing covariates: Changes in methadone treatment practices. Journal of the American Statistical Association, 97, 40–52.MathSciNetCrossRefMATH
Zurück zum Zitat Schoenfeld, D. (1982). Partial residuals for the proportional hazards regression model. Biometrika, 69, 239–241.CrossRef Schoenfeld, D. (1982). Partial residuals for the proportional hazards regression model. Biometrika, 69, 239–241.CrossRef
Zurück zum Zitat Song, X., Davidian, M. and Tsiatis, A.A. (2002). A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics, 58, 742–753.MathSciNetCrossRefMATH Song, X., Davidian, M. and Tsiatis, A.A. (2002). A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics, 58, 742–753.MathSciNetCrossRefMATH
Zurück zum Zitat Song, X., Mu, X. and Sun, L. (2012). Regression analysis of longitudinal data with time-dependent covariates and informative observation times. Scandinavian Journal of Statistics, to appear. Song, X., Mu, X. and Sun, L. (2012). Regression analysis of longitudinal data with time-dependent covariates and informative observation times. Scandinavian Journal of Statistics, to appear.
Zurück zum Zitat Sun, J., Park, D-H., Sun, L. and Zhao, X (2005). Semiparametric regression analysis of longitudinal data with informative observation times. Journal of the American Statistical Association, 100, 882–889.MathSciNetCrossRefMATH Sun, J., Park, D-H., Sun, L. and Zhao, X (2005). Semiparametric regression analysis of longitudinal data with informative observation times. Journal of the American Statistical Association, 100, 882–889.MathSciNetCrossRefMATH
Zurück zum Zitat Sun, J., Sun, L. and Liu, D. (2007a). Regression analysis of longitudinal data in the presence of informative observation and censoring times. Journal of the American Statistical Association, 102, 1397–1406.MathSciNetCrossRefMATH Sun, J., Sun, L. and Liu, D. (2007a). Regression analysis of longitudinal data in the presence of informative observation and censoring times. Journal of the American Statistical Association, 102, 1397–1406.MathSciNetCrossRefMATH
Zurück zum Zitat Sun, J., Tong, X. and He, X. (2007b). Regression analysis of panel count data with dependent observation times. Biometrics, 63, 1053–1059.MathSciNetCrossRefMATH Sun, J., Tong, X. and He, X. (2007b). Regression analysis of panel count data with dependent observation times. Biometrics, 63, 1053–1059.MathSciNetCrossRefMATH
Zurück zum Zitat Sun, L., Song, X., Zhou, J. and Liu, L. (2012). Joint analysis of longitudinal data with informative observation times and a dependent terminal event. Journal of the American Statistical Association, 107, 688–700.MathSciNetCrossRefMATH Sun, L., Song, X., Zhou, J. and Liu, L. (2012). Joint analysis of longitudinal data with informative observation times and a dependent terminal event. Journal of the American Statistical Association, 107, 688–700.MathSciNetCrossRefMATH
Zurück zum Zitat Sun, L. and Tong, X. (2009). Analyzing longitudinal data with informative observation times under biased sampling. Statistics and Probability Letter, 79, 1162–1168.MathSciNetCrossRefMATH Sun, L. and Tong, X. (2009). Analyzing longitudinal data with informative observation times under biased sampling. Statistics and Probability Letter, 79, 1162–1168.MathSciNetCrossRefMATH
Zurück zum Zitat Tsiatis, A. A. and Davidian, M. (2004). An overview of joint modeling of longitudinal and time-to-event data. Statistica Sinica, 14, 793–818.MathSciNet Tsiatis, A. A. and Davidian, M. (2004). An overview of joint modeling of longitudinal and time-to-event data. Statistica Sinica, 14, 793–818.MathSciNet
Zurück zum Zitat Wang, M. C., Qin, J. and Chiang, C. T. (2001). Analyzing recurrent event data with informative censoring. Journal of the American Statistical Association, 96, 1057–1065.MathSciNetCrossRefMATH Wang, M. C., Qin, J. and Chiang, C. T. (2001). Analyzing recurrent event data with informative censoring. Journal of the American Statistical Association, 96, 1057–1065.MathSciNetCrossRefMATH
Zurück zum Zitat Ye, Y., Kalbfleisch, J. D. and Schaubel, D. E. (2007). Semiparametric analysis of correlated recurrent and terminal events. Biometrics, 63, 78–87.MathSciNetCrossRefMATH Ye, Y., Kalbfleisch, J. D. and Schaubel, D. E. (2007). Semiparametric analysis of correlated recurrent and terminal events. Biometrics, 63, 78–87.MathSciNetCrossRefMATH
Zurück zum Zitat Zeng, D. and Cai, J. (2010). A semiparametric additive rate model for recurrent events with an informative terminal event. Biometrika, 97, 699–712.MathSciNetCrossRefMATH Zeng, D. and Cai, J. (2010). A semiparametric additive rate model for recurrent events with an informative terminal event. Biometrika, 97, 699–712.MathSciNetCrossRefMATH
Zurück zum Zitat Zhao, H., Li, Y. and Sun, J. (2013a). Analyzing panel count data with dependent observation process and a terminal event. The Canadian Journal of Statistics, 41, 174–191.MathSciNetCrossRefMATH Zhao, H., Li, Y. and Sun, J. (2013a). Analyzing panel count data with dependent observation process and a terminal event. The Canadian Journal of Statistics, 41, 174–191.MathSciNetCrossRefMATH
Zurück zum Zitat Zhao, X. and Tong, X. (2011). Semiparametric regression analysis of panel count data with informative observation times. Computational Statistics and Data Analysis, 55, 291–300.MathSciNetCrossRefMATH Zhao, X. and Tong, X. (2011). Semiparametric regression analysis of panel count data with informative observation times. Computational Statistics and Data Analysis, 55, 291–300.MathSciNetCrossRefMATH
Zurück zum Zitat Zhao, X., Tong, X. and Sun, J. (2013). Robust estimation for panel count data with informative observation times. Computational Statistics and Data Analysis, 57, 33–40.MathSciNetCrossRef Zhao, X., Tong, X. and Sun, J. (2013). Robust estimation for panel count data with informative observation times. Computational Statistics and Data Analysis, 57, 33–40.MathSciNetCrossRef
Zurück zum Zitat Zhao, X., Zhou, J. and Sun, L. (2011b). Semiparametric transformation models with time-varying coefficients for recurrent and terminal events. Biometrics, 67, 404–414.MathSciNetCrossRefMATH Zhao, X., Zhou, J. and Sun, L. (2011b). Semiparametric transformation models with time-varying coefficients for recurrent and terminal events. Biometrics, 67, 404–414.MathSciNetCrossRefMATH
Zurück zum Zitat Zhu, L., Sun, J., Srivastava, D. K., Tong, X., Leisenring, W., Zhang, H., and Robison, L. L. (2011a). Semiparametric transformation models for joint analysis of multivariate recurrent and terminal events. Statistics in Medicine, 30, 3010–3023.MathSciNetCrossRef Zhu, L., Sun, J., Srivastava, D. K., Tong, X., Leisenring, W., Zhang, H., and Robison, L. L. (2011a). Semiparametric transformation models for joint analysis of multivariate recurrent and terminal events. Statistics in Medicine, 30, 3010–3023.MathSciNetCrossRef
Zurück zum Zitat Zhu, L., Sun, J., Tong, X. and Srivastava, D. K. (2010). Regression analysis of multivariate recurrent event data with a dependent terminal event. Lifetime Data Analysis, 16, 478–490.MathSciNetCrossRef Zhu, L., Sun, J., Tong, X. and Srivastava, D. K. (2010). Regression analysis of multivariate recurrent event data with a dependent terminal event. Lifetime Data Analysis, 16, 478–490.MathSciNetCrossRef
Metadaten
Titel
Regression Analysis of Panel Count Data II
verfasst von
Jianguo Sun
Xingqiu Zhao
Copyright-Jahr
2013
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-8715-9_6