IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v97y2016icp47-59.html
   My bibliography  Save this article

Semiparametric regression analysis of panel count data allowing for within-subject correlation

Author

Listed:
  • Yao, Bin
  • Wang, Lianming
  • He, Xin

Abstract

In this paper, a maximum likelihood approach is proposed for analyzing panel count data under the gamma frailty non-homogeneous Poisson process model. The approach allows one to estimate the baseline mean function and the regression parameters jointly while taking the within-subject correlation into account. The within-subject correlation is quantified explicitly by Pearson’s correlation coefficient. Monotone splines are adopted to approximate the unspecified nondecreasing baseline mean function in the model. An expectation–maximization (EM) algorithm is derived to facilitate the computation by exploiting a data augmentation based on Poisson latent variables. The EM algorithm is robust to initial values, easy to implement, converges fast, and provides closed-form variance estimates. It can be also applied to the non-homogeneous Poisson model without frailty. The proposed approach is evaluated through simulations and illustrated by two real-life examples coming from a skin cancer study and a bladder tumor study. A companion R package PCDSpline has been developed and is available on R CRAN for public use.

Suggested Citation

  • Yao, Bin & Wang, Lianming & He, Xin, 2016. "Semiparametric regression analysis of panel count data allowing for within-subject correlation," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 47-59.
    • Handle: RePEc:eee:csdana:v:97:y:2016:i:c:p:47-59
    DOI: 10.1016/j.csda.2015.11.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794731500300X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.11.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jianguo Sun, 2003. "A nonparametric test for panel count data," Biometrika, Biometrika Trust, vol. 90(1), pages 199-208, March.
    2. Ying Zhang & Mortaza Jamshidian, 2003. "The Gamma-Frailty Poisson Model for the Nonparametric Estimation of Panel Count Data," Biometrics, The International Biometric Society, vol. 59(4), pages 1099-1106, December.
    3. Lu, Minggen & Zhang, Ying & Huang, Jian, 2009. "Semiparametric Estimation Methods for Panel Count Data Using Monotone B-Splines," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1060-1070.
    4. Ying Zhang, 2006. "Nonparametric k-sample tests with panel count data," Biometrika, Biometrika Trust, vol. 93(4), pages 777-790, December.
    5. Minggen Lu & Ying Zhang & Jian Huang, 2007. "Estimation of the mean function with panel count data using monotone polynomial splines," Biometrika, Biometrika Trust, vol. 94(3), pages 705-718.
    6. X. Joan Hu & Jianguo Sun & Lee‐Jen Wei, 2003. "Regression Parameter Estimation from Panel Counts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 25-43, March.
    7. J. Sun & L. J. Wei, 2000. "Regression analysis of panel count data with covariate‐dependent observation and censoring times," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 293-302.
    8. Cai, Bo & Lin, Xiaoyan & Wang, Lianming, 2011. "Bayesian proportional hazards model for current status data with monotone splines," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2644-2651, September.
    9. Lianming Wang & David B. Dunson, 2011. "Semiparametric Bayes' Proportional Odds Models for Current Status Data with Underreporting," Biometrics, The International Biometric Society, vol. 67(3), pages 1111-1118, September.
    10. Ying Zhang, 2002. "A semiparametric pseudolikelihood estimation method for panel count data," Biometrika, Biometrika Trust, vol. 89(1), pages 39-48, March.
    11. Zhang, Haixiang & Zhao, Hui & Sun, Jianguo & Wang, Dehui & Kim, KyungMann, 2013. "Regression analysis of multivariate panel count data with an informative observation process," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 71-80.
    12. Li, Yang & Zhao, Hui & Sun, Jianguo & Kim, KyungMann, 2014. "Nonparametric tests for panel count data with unequal observation processes," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 103-111.
    13. Zhao, Xingqiu & Tong, Xingwei & Sun, Jianguo, 2013. "Robust estimation for panel count data with informative observation times," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 33-40.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. John D. Rice & Robert L. Strawderman & Brent A. Johnson, 2018. "Regularity of a renewal process estimated from binary data," Biometrics, The International Biometric Society, vol. 74(2), pages 566-574, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gang Cheng & Ying Zhang & Liqiang Lu, 2011. "Efficient algorithms for computing the non and semi-parametric maximum likelihood estimates with panel count data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 567-579.
    2. Xin He & Xuenan Feng & Xingwei Tong & Xingqiu Zhao, 2017. "Semiparametric partially linear varying coefficient models with panel count data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(3), pages 439-466, July.
    3. Zhao, Xingqiu & Tong, Xingwei & Sun, Jianguo, 2013. "Robust estimation for panel count data with informative observation times," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 33-40.
    4. Zhao, Xingqiu & Tong, Xingwei, 2011. "Semiparametric regression analysis of panel count data with informative observation times," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 291-300, January.
    5. Xingqiu Zhao & N. Balakrishnan & Jianguo Sun, 2011. "Nonparametric inference based on panel count data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 1-42, May.
    6. Yang Li & Xin He & Haiying Wang & Jianguo Sun, 2016. "Regression analysis of longitudinal data with correlated censoring and observation times," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 343-362, July.
    7. Xingqiu Zhao & Jianguo Sun, 2011. "Nonparametric Comparison for Panel Count Data with Unequal Observation Processes," Biometrics, The International Biometric Society, vol. 67(3), pages 770-779, September.
    8. N. Balakrishnan & Xingqiu Zhao, 2011. "A class of multi-sample nonparametric tests for panel count data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(1), pages 135-156, February.
    9. Chunling Wang & Xiaoyan Lin, 2022. "Bayesian Semiparametric Regression Analysis of Multivariate Panel Count Data," Stats, MDPI, vol. 5(2), pages 1-17, May.
    10. Jie Zhou & Haixiang Zhang & Liuquan Sun & Jianguo Sun, 2017. "Joint analysis of panel count data with an informative observation process and a dependent terminal event," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(4), pages 560-584, October.
    11. Li, Yang & He, Xin & Wang, Haiying & Zhang, Bin & Sun, Jianguo, 2015. "Semiparametric regression of multivariate panel count data with informative observation times," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 209-219.
    12. Sy Han Chiou & Gongjun Xu & Jun Yan & Chiung‐Yu Huang, 2018. "Semiparametric estimation of the accelerated mean model with panel count data under informative examination times," Biometrics, The International Biometric Society, vol. 74(3), pages 944-953, September.
    13. Balakrishnan, N. & Zhao, Xingqiu, 2010. "A nonparametric test for the equality of counting processes with panel count data," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 135-142, January.
    14. Li, Yang & Zhao, Hui & Sun, Jianguo & Kim, KyungMann, 2014. "Nonparametric tests for panel count data with unequal observation processes," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 103-111.
    15. Zhang, Haixiang & Zhao, Hui & Sun, Jianguo & Wang, Dehui & Kim, KyungMann, 2013. "Regression analysis of multivariate panel count data with an informative observation process," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 71-80.
    16. Hangjin Jiang & Wen Su & Xingqiu Zhao, 2020. "Robust estimation for panel count data with informative observation times and censoring times," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 65-84, January.
    17. Faysal Satter & Yichuan Zhao & Ni Li, 2024. "Empirical likelihood inference for the panel count data with informative observation process," Statistical Papers, Springer, vol. 65(5), pages 3039-3061, July.
    18. Jianhong Wang & Xiaoyan Lin, 2020. "A Bayesian approach for semiparametric regression analysis of panel count data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 402-420, April.
    19. Fei Qin & Zhangsheng Yu, 2021. "Penalized spline estimation for panel count data model with time-varying coefficients," Computational Statistics, Springer, vol. 36(4), pages 2413-2434, December.
    20. Weiwei Wang & Yijun Wang & Xiaobing Zhao, 2022. "Semiparametric analysis of multivariate panel count data with nonlinear interactions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 89-115, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:97:y:2016:i:c:p:47-59. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.