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Semiparametric model for the dichotomized functional outcome after stroke: The Northern Manhattan Study

  • Chen, Huaihou
  • Paik, Myunghee Cho
  • Dhamoon, Mandip S.
  • Moon, Yeseon Park
  • Willey, Joshua
  • Sacco, Ralph L.
  • Elkind, Mitchell S.V.
Registered author(s):

    The Northern Manhattan Study (NOMAS) is a prospective, population-based study. One of the goals of NOMAS is to characterize the functional status of stroke survivors over time after stroke. Based on generalized estimating equation models, previous parametric analysis showed that functional status declines over time and the trajectories of decline are different depending on insurance status. The two trends of functional status may not be linear, which motivates our semiparametric modeling. In this paper, we model the time trend nonparametrically, the associated covariates parametrically and an interaction term between the nonparametric time trend and a covariate. We consider both kernel weighted local polynomial-based and regression spline-based approaches for solving the semiparametric model, and propose a statistic to test for the interaction term. To evaluate the performance of the parametric model in the case of model misspecification, we study the bias and efficiency of the estimators from misspecified parametric models. We find that when the adjusted covariates are independent of the time, and the link function is identity, the estimators for those covariates are asymptotically unbiased, even if the time trend is misspecified. In general, however, under other conditions and nonidentity link, the misspecified parametric estimators are biased and less efficient even when they are unbiased. We compute the ARE and also conduct simulation studies and compare power for testing the adjusted covariate when the time trend is modeled parametrically versus nonparametrically. In the simulation studies, we observe significant gain in power of those semiparametric model-based estimators compared to the parametric model-based estimators in the cases when the time trend is nonlinear.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000667
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 8 ()
    Pages: 2598-2608

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2598-2608
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Naisyin Wang & Raymond J. Carroll & Xihong Lin, 2005. "Efficient Semiparametric Marginal Estimation for Longitudinal/Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 147-157, March.
    2. Jianqing Fan & Runze Li, 2004. "New Estimation and Model Selection Procedures for Semiparametric Modeling in Longitudinal Data Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 710-723, January.
    3. Naisyin Wang, 2003. "Marginal nonparametric kernel regression accounting for within-subject correlation," Biometrika, Biometrika Trust, vol. 90(1), pages 43-52, March.
    4. Fan, Jianqing & Huang, Tao & Li, Runze, 2007. "Analysis of Longitudinal Data With Semiparametric Estimation of Covariance Function," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 632-641, June.
    5. Jianhua Z. Huang & Liangyue Zhang & Lan Zhou, 2007. "Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(3), pages 451-477.
    6. Zonghui Hu, 2004. "Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data," Biometrika, Biometrika Trust, vol. 91(2), pages 251-262, June.
    7. Kani Chen & Zhezhen Jin, 2005. "Local polynomial regression analysis of clustered data," Biometrika, Biometrika Trust, vol. 92(1), pages 59-74, March.
    8. Wei Pan, 2001. "Akaike's Information Criterion in Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 57(1), pages 120-125, 03.
    9. Chen, Kani & Jin, Zhezhen, 2006. "Partial Linear Regression Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 195-204, March.
    10. Jianhua Z. Huang, 2002. "Varying-coefficient models and basis function approximations for the analysis of repeated measurements," Biometrika, Biometrika Trust, vol. 89(1), pages 111-128, March.
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