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Clustered Mixed Nonhomogeneous Poisson Process Spline Models for the Analysis of Recurrent Event Panel Data

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  • J. D. Nielsen
  • C. B. Dean

Abstract

Summary A flexible semiparametric model for analyzing longitudinal panel count data arising from mixtures is presented. Panel count data refers here to count data on recurrent events collected as the number of events that have occurred within specific follow‐up periods. The model assumes that the counts for each subject are generated by mixtures of nonhomogeneous Poisson processes with smooth intensity functions modeled with penalized splines. Time‐dependent covariate effects are also incorporated into the process intensity using splines. Discrete mixtures of these nonhomogeneous Poisson process spline models extract functional information from underlying clusters representing hidden subpopulations. The motivating application is an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth. Mature moths arise from hidden, but distinct, subpopulations and monitoring the subpopulation responses was of interest. Within‐cluster random effects are used to account for correlation structures and heterogeneity common to this type of data. An estimating equation approach to inference requiring only low moment assumptions is developed and the finite sample properties of the proposed estimating functions are investigated empirically by simulation.

Suggested Citation

  • J. D. Nielsen & C. B. Dean, 2008. "Clustered Mixed Nonhomogeneous Poisson Process Spline Models for the Analysis of Recurrent Event Panel Data," Biometrics, The International Biometric Society, vol. 64(3), pages 751-761, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:751-761
    DOI: 10.1111/j.1541-0420.2007.00940.x
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    References listed on IDEAS

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    1. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    2. Robert F. Balshaw & C. B. Dean, 2002. "A Semiparametric Model for the Analysis of Recurrent-Event Panel Data," Biometrics, The International Biometric Society, vol. 58(2), pages 324-331, June.
    3. Wenxin Mao & Linda H. Zhao, 2003. "Free‐knot polynomial splines with confidence intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 901-919, November.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    5. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    6. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
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    Cited by:

    1. Wang, Weiwei & Wu, Xianyi & Zhao, Xiaobing & Zhou, Xian, 2018. "Robust variable selection of joint frailty model for panel count data," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 60-78.
    2. Yijun Wang & Weiwei Wang, 2021. "Quantile estimation of semiparametric model with time-varying coefficients for panel count data," PLOS ONE, Public Library of Science, vol. 16(12), pages 1-18, December.
    3. Wang, Yijun & Wang, Weiwei & Zhao, Xiaobing, 2022. "Local logarithm partial likelihood estimation of panel count data model with an unknown link function," Computational Statistics & Data Analysis, Elsevier, vol. 166(C).
    4. 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.

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