Skip to main content
SpringerLink
Log in

Other Topics

  • Chapter
  • First Online:
Statistical Analysis of Panel Count Data

Part of the book series: Statistics for Biology and Health ((SBH,volume 80))

  • 2738 Accesses

Abstract

In addition to what discussed in the previous chapters, there exist some other issues or topics about the analysis of panel count data that have been investigated in the literature or could occur in practice. In conducting regression analysis, for example, one can always ask which or if all covariate variables are important or significant enough to be included in the final model for the response variable of interest. That is, one faces a variable selection problem. For the problem, two situations usually occur. One is that the number of covariate variables is fixed and smaller than the sample size as in usual linear or nonlinear regression analysis (Johnson and Wichern, 2002). The other is that the number of covariate or predictor variables is much larger than the sample size and could be over several thousands or hundred thousands. The latter has become a huge and important topic in statistical genetic analysis as well as some other related areas (Beebe et al., 1998; Lee, 2004).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aalen, O. O. (1975). Statistical inference for a family of counting processes. Ph.D. Thesis, University of California, Berkeley.

    Google Scholar 

  • Akaike, H. (1973). Maximum likelihood identification of Gaussian autoregressive moving average models. Biometrika, 60, 255–265.

    Article  MathSciNet  MATH  Google Scholar 

  • Andersen, P. K. and Klein, J. P. (2004). Multi-state models for event history analysis. Statistical Methods in Medical Research, 11, 91–115.

    Article  Google Scholar 

  • Andersen, P. K. and Klein, J. P. (2007). Regression analysis for multistate models based on a pseudo-value approach, with applications to bone marrow transplantation studies. Scandinavian Journal of Statistics, 34, 3–16.

    Article  MathSciNet  MATH  Google Scholar 

  • Bacchetti, P., Boylan, R. D., Terrault, N. A., Monto, A. and Berenguer, M. (2010). Non-Markov multistate modeling using time-varying covariates, with application to progression of liver fibrosis due to Hepatitis C following liver transplant. The International Journal of Biostatistics, 6, Article 7.

    Google Scholar 

  • Bartholomew, D. J. (1983). Some recent developments in social statistics. International Statistical Review, 51, 1–9.

    Article  MathSciNet  MATH  Google Scholar 

  • Beebe, K. R., Pell, R. J. and Seasholtz, M. B. (1998). Chemometrics: A practical guide. John Wiley & Sons, Inc.

    Google Scholar 

  • Breiman, L. (1996). Heuristics of instability and stabilization in model selection. The Annals of Statistics, 24, 2350–2383.

    Article  MathSciNet  MATH  Google Scholar 

  • Cai, Z. and Sun, Y. (2003). Local linear estimation for time-dependent coefficients in Cox’s regression models. Scandinavian Journal of Statistics, 30, 93–111.

    Article  MathSciNet  MATH  Google Scholar 

  • Carroll, R. J., Ruppert, D. and Stefanski, L. A. (1995). Measurement error in nonlinear models. Chapman & Hall, London.

    Book  MATH  Google Scholar 

  • Chen, B., Yi, G. Y. and Cook, R. J. (2010). Analysis of interval-censored disease progression data via multi-state models under a nonignorable inspection process. Statistics in Medicine, 29, 1175–1189.

    Article  MathSciNet  Google Scholar 

  • Chen, B. E. and Cook, R. J. (2003). Regression modeling with recurrent events and time-dependent interval-censored marker data. Lifetime Data Analysis, 9, 275–291.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, H. Y. and Little, R. J. A. (1999). Proportional hazards regression with missing covariates. Journal of the American Statistical Association, 94, 896–908.

    Article  MathSciNet  MATH  Google Scholar 

  • Chen, J. and Li, P. (2009). Hypothesis test for normal mixture models: the EM approach. The Annal of Statistics, 37, 2523–2542.

    Article  MATH  Google Scholar 

  • Chen, J. and Tan, X. (2009). Inference for multivariate normal mixtures. Journal of Multivariate Analysis, 100, 1367–1383.

    Article  MathSciNet  MATH  Google Scholar 

  • Cheng, S. C. and Wei, L. J. (2000). Inferences for a semiparametric model with panel data. Biometrika, 87, 89–97.

    Article  MathSciNet  MATH  Google Scholar 

  • Cox, D. R. and Miller, H. D. (1965). The theory of stochastic processes. London: Chapman and Hall.

    MATH  Google Scholar 

  • Darlington, G. A. and Dixon, S. N. (2013). Event-weighted proportional hazards modelling for recurrent gap time data. Statstics in Medcine, 32, 124–130.

    Article  MathSciNet  Google Scholar 

  • Dicker, L., Huang, B. and Lin, X. (2012). Variable selection and estimation with the seamless-L 0 penalty. Statistica Sinica, to appear.

    Google Scholar 

  • Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association, 96, 1348–1360.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J. and Li, R. (2004). New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. Journal of the American Statistical Association, 99, 710–723.

    Article  MathSciNet  MATH  Google Scholar 

  • Fan, J. and Lv, J. (2010). A selective overview of variable selection in high dimensional feature space. Statistica Sinica, 20, 101–148.

    MathSciNet  MATH  Google Scholar 

  • Fan, J. and Peng, H. (2004). Nonconcave penalized likelihood with a diverging number of parameters. The Annals of Statistics, 32, 928–961.

    Article  MathSciNet  MATH  Google Scholar 

  • Ferguson, T. S. (1973). A Bayesian analysis of some non-parametric problems. The Annals of Statistics, 1, 209–230.

    Article  MathSciNet  MATH  Google Scholar 

  • Ferguson, T. S. (1974). Prior distributions on spaces of probability measures. The Annals of Statistics, 2, 615–629.

    Article  MathSciNet  MATH  Google Scholar 

  • French, J. L. and Ibrahim, J. G. (2002). Bayesian methods for three-state model for rodent carcinogenicity studies. Biometrics, 58, 906–916.

    Article  MathSciNet  MATH  Google Scholar 

  • Gentlemen, R. C., Lawless, J. F. and Lindsey, J. C. (1994). Multi-state Markov models for analysing incomplete diseases history data with illustrations for HIV disease. Statistics in Medicine, 13, 805–821.

    Article  Google Scholar 

  • Gladman, D. D., Farewell, V. T. and Nadeau, C. (1995). Clinical indicators of progression in psoriatic arthritis (PsA): multivariate relative risk model. Journal of Rheumatology, 22, 675–679.

    Google Scholar 

  • Gómez, G., Calle, M. L. and Oller, R. (2004).] Frequentist and Bayesian approaches for interval-censored data. Statistics Papers, 2, 139–173.

    Google Scholar 

  • Gómez, G., Espinal and Lagakos, S. W. (2003).] Inference for a linear regression model with an interval-censored covariate. Statistics in Medicine, 22, 409–425.

    Google Scholar 

  • Hsieh, H. J., Chen, T. H-H. and Chang, S. H. (2002). Assessing chronic disease progression using non-homogeneous exponential regression Markov models: An illustration using a selective breast cancer screening in Taiwan. Statistics in Medicine, 21, 3369–3382.

    Article  Google Scholar 

  • Huang, X. and Liu, L. (2007). A joint frailty model for survival and gap times between recurrent events. Biometrics, 63, 389–397.

    Article  MathSciNet  MATH  Google Scholar 

  • Ibrahim, J. G., Chen, M.-H. and Sinha, D. (2001). Bayesian survival analysis. Springer-Verlag: New York.

    Book  MATH  Google Scholar 

  • Ishwaran, H. and James, L. F. (2004). Computational methods for multiplicative intensity models using weighted gamma processes: proportional hazards, marked point processes, and panel count data. Journal of the American Statistical Association, 99, 175–190.

    Article  MathSciNet  MATH  Google Scholar 

  • James, L. F. (2003). Bayesian calculus for gamma processes with applications to semiparametric intensity models. Sankhya A, 65, 196–223.

    MATH  Google Scholar 

  • Johnson, R. A. and Wichern, D. W. (2002). Applied multivariate statistical analysis. Fifth edition, Prentice Hall, Inc.

    Google Scholar 

  • Joly, P. and Commenges, D. (1999). A penalized likelihood approach for a progressive three-state model with censored and truncated data: Application to AIDS. Biometrics, 55, 887–890.

    Article  MATH  Google Scholar 

  • Joly, P., Commenges, D., Helmer, C. and Letenneur, L. (2002). A penalized likelihood approach for an illness-death model with interval-censored data: Application to age-specific incidence of dementia. Biostatistics, 3, 433–443.

    Article  MATH  Google Scholar 

  • Joly, P., Durand, C., Helmer, C. and Commenges, D. (2009). Estimating life expectancy of demented and institutionalized subjects from interval-censored observations of a multi-state model. Statistical Modelling, 9, 345–360.

    Article  MathSciNet  Google Scholar 

  • Kalbfleisch, J. D. and Lawless, J. F. (1985). The analysis of panel data under a Markov assumption. Journal of the American Statistical Association, 80, 863–871.

    Article  MathSciNet  MATH  Google Scholar 

  • Kay, R. (1986). A Markov model for analyzing cancer markers and diseases states in survival studies. Biometrics, 42, 855–865.

    Article  MATH  Google Scholar 

  • Kim, Y-J. (2007). Analysis of panel count data with measurement errors in the covariates. Journal of Statistical Computation and Simulation, 77, 109–117.

    Article  MathSciNet  MATH  Google Scholar 

  • Lagakos, S. W. and Louis, T. (1988). Use of tumour lethality to interpret tumorigenicity experiments lacking cause-of-death data. Applied Statistics, 37, 169–179.

    Article  Google Scholar 

  • Langohr, K., Gómez, G. and Muga, R. (2004). A parametric survival model with an interval-censored covariate. Statistics in Medicine, 23, 3159–3175.

    Article  Google Scholar 

  • Lawless, J. F. and Zhan, M. (1998). Analysis of interval-grouped recurrent-event data using piecewise constant rate functions. Canadian Journal of Statistics, 26, 549–565.

    Article  MATH  Google Scholar 

  • Lee, M-L. T. (2004). Analysis of microarray gene expression data. Kluwwe Academis Publishers.

    Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, D. Y. and Ying, Z. (2001). Nonparametric tests for the gap time distributions of serial events based on censored data. Biometrics, 57, 369–375.

    Article  MathSciNet  MATH  Google Scholar 

  • Lindsey, J. C. and Ryan, L. M. (1993). A three-state multiplicative model for rodent tumorigenicity experiments. Applied Statistics, 42, 283–300.

    Article  MATH  Google Scholar 

  • Little, R. J. A. and Rubin, D. B. (1987). Statistical analysis with missing data, John Wiley: New York.

    MATH  Google Scholar 

  • Mallows, C. L. (1973). Some comments on Cp. Technometrics, 15, 661–675.

    MATH  Google Scholar 

  • Mclachlan, G. and Peel, D. (2000). Finite mixture models. Wiley: New York.

    Book  MATH  Google Scholar 

  • Nielsen, J. D. and Dean, C. B. (2008). Clustered mixed nonhomogeneous Poisson process spline models for the analysis of recurrent event panel data. Biometrics, 64, 751–761.

    Article  MathSciNet  MATH  Google Scholar 

  • Park, D-H. (2005). Semiparametric and nnonparametric methods for the analysis of longitudinal data. Ph.D. Dissertation, University of Missouri, Columbia.

    Google Scholar 

  • Prentice, R. L. (1982). Covariate measurement errors and parameter estimation in a failure time regression model. Biometrika, 69, 331–342.

    Article  MathSciNet  MATH  Google Scholar 

  • Robison, L., Mertens, A., Boice, J., et al. (2002). Study design and cohort characteristics of the childhood cancer survivor study: A multi-institutional collaborative project. Medical and Pediatric Oncology, 38, 229–239.

    Article  Google Scholar 

  • Rosen, O., Jiang, W. and Tanner, M. A. (2000). Mixtures of marginal models. Biometrika, 87, 391–404.

    Article  MathSciNet  MATH  Google Scholar 

  • Schaubel, D. E. and Cai, J. (2004). Regression methods for gap time hazard functions of sequentially ordered multivariate failure time data. Biometrika, 91, 291–303.

    Article  MathSciNet  MATH  Google Scholar 

  • Scheike, T. H. and Martinussen, T. (2004). On estimation and tests of time-varying effects in the proportional hazards model. Scandinavian Journal of Statistics, 31, 51–62.

    Article  MathSciNet  MATH  Google Scholar 

  • Schwartz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464.

    Article  MathSciNet  Google Scholar 

  • Singer, B. and Spilerman, S. (1976a). The representation of social processes by Markov models. American Journal of Sociology, 82, 1–54.

    Article  Google Scholar 

  • Singer, B. and Spilerman, S. (1976b). Some methodological issues in the analysis of longitudinal surveys. Annals Economic and Sociological Measurement, 5, 447–474.

    Google Scholar 

  • Song, X. and Wang, C. Y. (2008). Semiparametric approaches for joint modeling of longitudinal and survival data with time-varying coefficients. Biometrics, 64, 557–566.

    Article  MathSciNet  MATH  Google Scholar 

  • Staniswalls, J. G., Thall, P. F. and Salch, J. (1997). Semiparametric regression analysis for recurrent event interval counts. Biometrics, 53, 1334–1353.

    Article  MathSciNet  Google Scholar 

  • Sun, J. and Matthews, D. E. (1997). A random-effect regression model for medical follow-up studies. Canadian Journal of Statistics, 25, 101–111.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • Sun, J and Rai, S. N. (2001). Nonparametric tests for the comparison of point processes based on incomplete data. Scand Journal Statistics, 28, 725–732.

    Article  MathSciNet  MATH  Google Scholar 

  • Sun, L., Guo, S. and Chen, M. (2009a). Marginal regression model with time-varying coefficients for panel data. Communications in Statistics, Theory and Methods, 38, 1241–1261.

    Article  MathSciNet  MATH  Google Scholar 

  • Sun, L., Park, D. and Sun, J. (2006). The additive hazards model for recurrent gap times. Statistica Sinica, 16, 919–932.

    MathSciNet  MATH  Google Scholar 

  • Sun, L., Zhu, L. and Sun, J. (2009b). Regression analysis of multivariate recurrent event data with time-varying covariate effects. Journal Multivariate Analysis, 100, 2214–2223.

    Article  MathSciNet  MATH  Google Scholar 

  • Sun, Y. and Wu, H. (2005). Semiparametric time-varying coefficients regression model for longitudinal data. Scandinavian Journal of Statistics, 32, 21–47.

    Article  MathSciNet  MATH  Google Scholar 

  • Susko, E., Kalbfleisch, J. D. and Chen, J. (1998). Constrained nonparametric maximum-likelihood estimation for mixture models. Canadan Journal of Statistics, 26, 601–617.

    Article  MathSciNet  MATH  Google Scholar 

  • Tibshirani, R. J. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society, Series B, 58, 267–288.

    MathSciNet  MATH  Google Scholar 

  • Tibshirani, R. J. (1997). The lasso method for variable selection in the Cox model. Statstics in Medicine, 16, 385–395.

    Article  Google Scholar 

  • Titman, A. C. (2011). Flexible nonhomogeneous Markov models for panel observed data. Biometrics, 67, 780–787.

    Article  MathSciNet  MATH  Google Scholar 

  • Tong, X., He, X., Sun, L. and Sun, J. (2009). Variable selection for panel count data via nonconcave penalized estimating function. Scandinavian Journal of Statistics, 36, 620–635.

    Article  MathSciNet  MATH  Google Scholar 

  • Tsiatis, A. A., DeGruttola, V. and Wulfsohn, M. S. (1995). Modeling the relationship of survival to longitudinal data measured with error. Applications to survival and CD4 counts in patients with AIDS. Journal of the American Statistical Association, 90, 27–37.

    Google Scholar 

  • Tuma, N. B. and Robins, P. K. (1980). A dynamic model of employment behavior: An application to the Seattle and Denver income maintenance experiments. Econometrica, 48, 1031–1-52.

    Google Scholar 

  • Wang, M. C. and Chen, Y. Q. (2000). Nonparametric and semiparametric trend analysis of stratified recurrence time data. Biometrics, 56, 789–794.

    Article  MATH  Google Scholar 

  • Wang, P., Puterman, M. L., Cockburn, I. and Le, N. (1996). Mixed Poisson regression models with covariate dependent rates. Biometrics, 52, 381–400.

    Article  MATH  Google Scholar 

  • Wasserman, S. (1980). Analyzing social networks as stochastic processes. Journal of the American Statistical Association, 75, 280–294.

    Article  MATH  Google Scholar 

  • White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 50, 1–25.

    Article  MathSciNet  MATH  Google Scholar 

  • Wulfsohn, M. S. and Tsiatis, A. A. (1997). A joint model for survival and longitudinal data measured with error. Biometrics, 53, 330–339.

    Article  MathSciNet  MATH  Google Scholar 

  • Yan, J. and Huang, J. (2012). Model selection for Cox models with time-varying coefficients. Biometrics, 68, 419–428.

    Article  MathSciNet  MATH  Google Scholar 

  • Yi, G. Y. and Lawless, J. F. (2012). Likelihood-based and marginal inference methods for recurrent event data with covariate measurement error. Canadian Journal of Statistics, 40, 530–549.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, C. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of Statistics, 38, 894–942.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang, H., Sun, J. and Wang, D. (2013a). Variable selection and estimation for multivariate panel count data via the seamless-L 0 penalty. The Canadian Journal of Statistics, in press.

    Google Scholar 

  • Zhao, Q. and Sun, J. (2006). Semiparametric and nonparametric analysis of recurrent events with observation gaps. Computational Statistics and Data Analysis, 51, 1924–1933.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao, X., Tong, X. and Sun, L. (2012). Joint analysis of longitudinal data with dependent observation times. Statistics Sinica, 22, 317–336.

    MathSciNet  MATH  Google Scholar 

  • Zhao, X., Zhou, J. and Sun, L. (2011b). Semiparametric transformation models with time-varying coefficients for recurrent and terminal events. Biometrics, 67, 404–414.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhao, X. and Zhou, X. (2012). Modeling gap times between recurrent events by marginal rate function. Computational Statistics and Data Analysis, 56, 370–383.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhou, H. and Pepe, M. S. (1995). Auxilliary covariate data in failure time regression analysis. Biometrika, 82, 139–149.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhu, L., Tong, X., Zhao, H., Sun, J., Srivastava, D., Leisenring, W. and Robison, L. (2013). Statistical analysis of mixed recurrent event data with application to cancer survivor study. Statistics in Medicine, to appaer.

    Google Scholar 

  • Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association, 101, 1418–1429.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Missouri, Columbia, MO, USA

    Jianguo Sun

  2. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, Hong Kong SAR

    Xingqiu Zhao

Authors
  1. Jianguo Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xingqiu Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media New York

About this chapter

Cite this chapter

Sun, J., Zhao, X. (2013). Other Topics. In: Statistical Analysis of Panel Count Data. Statistics for Biology and Health, vol 80. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8715-9_8

Download citation

Publish with us

Policies and ethics

Search

Navigation