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Modeling Cumulative Incidences of Dementia and Dementia-Free Death Using a Novel Three-Parameter Logistic Function

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  • Cheng Yu

    (University of Pittsburgh)

Abstract

Parametric modeling of univariate cumulative incidence functions and logistic models have been studied extensively. However, to the best of our knowledge, there is no study using logistic models to characterize cumulative incidence functions. In this paper, we propose a novel parametric model which is an extension of a widely-used four-parameter logistic function for dose-response curves. The modified model can accommodate various shapes of cumulative incidence functions and be easily implemented using standard statistical software. The simulation studies demonstrate that the proposed model is as efficient as or more efficient than its nonparametric counterpart when it is correctly specified, and outperforms the existing Gompertz model when the underlying cumulative incidence function is sigmoidal. The practical utility of the modified three-parameter logistic model is illustrated using the data from the Cache County Study of dementia.

Suggested Citation

  • Cheng Yu, 2009. "Modeling Cumulative Incidences of Dementia and Dementia-Free Death Using a Novel Three-Parameter Logistic Function," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-19, November.
    • Handle: RePEc:bpj:ijbist:v:5:y:2009:i:1:n:29
    DOI: 10.2202/1557-4679.1183
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    References listed on IDEAS

    as
    1. Yu Cheng & Jason P. Fine & Michael R. Kosorok, 2009. "Nonparametric Association Analysis of Exchangeable Clustered Competing Risks Data," Biometrics, The International Biometric Society, vol. 65(2), pages 385-393, June.
    2. Yu Cheng & Jason P. Fine, 2008. "Nonparametric estimation of cause-specific cross hazard ratio with bivariate competing risks data," Biometrika, Biometrika Trust, vol. 95(1), pages 233-240.
    3. Martin G. Larson & Gregg E. Dinse, 1985. "A Mixture Model for the Regression Analysis of Competing Risks Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 201-211, November.
    4. Cheng, Yu & Fine, Jason P. & Kosorok, Michael R., 2007. "Nonparametric Association Analysis of Bivariate Competing-Risks Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1407-1415, December.
    5. Wang Antai, 2007. "The Analysis of Bivariate Truncated Data Using the Clayton Copula Model," The International Journal of Biostatistics, De Gruyter, vol. 3(1), pages 1-18, April.
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    Cited by:

    1. Wang Hao & Cheng Yu, 2014. "Piecewise Cause-Specific Association Analyses of Multivariate Untied or Tied Competing Risks Data," The International Journal of Biostatistics, De Gruyter, vol. 10(2), pages 197-220, November.
    2. S. R. Haile & J.-H. Jeong & X. Chen & Y. Cheng, 2016. "A 3-parameter Gompertz distribution for survival data with competing risks, with an application to breast cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2239-2253, September.

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