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Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models

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  • IL DO HA
  • MAENGSEOK NOH
  • YOUNGJO LEE

Abstract

. Frailty models with a non‐parametric baseline hazard are widely used for the analysis of survival data. However, their maximum likelihood estimators can be substantially biased in finite samples, because the number of nuisance parameters associated with the baseline hazard increases with the sample size. The penalized partial likelihood based on a first‐order Laplace approximation still has non‐negligible bias. However, the second‐order Laplace approximation to a modified marginal likelihood for a bias reduction is infeasible because of the presence of too many complicated terms. In this article, we find adequate modifications of these likelihood‐based methods by using the hierarchical likelihood.

Suggested Citation

  • Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    • Handle: RePEc:bla:scjsta:v:37:y:2010:i:2:p:307-320
    DOI: 10.1111/j.1467-9469.2009.00671.x
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    References listed on IDEAS

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    1. R. Henderson & P. Oman, 1999. "Effect of frailty on marginal regression estimates in survival analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 367-379, April.
    2. Samuli Ripatti & Juni Palmgren, 2000. "Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood," Biometrics, The International Biometric Society, vol. 56(4), pages 1016-1022, December.
    3. Il Do Ha & Youngjo Lee, 2005. "Comparison of hierarchical likelihood versus orthodox best linear unbiased predictor approaches for frailty models," Biometrika, Biometrika Trust, vol. 92(3), pages 717-723, September.
    4. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    Cited by:

    1. Vallejos, Catalina A. & Steel, Mark F.J., 2017. "Incorporating unobserved heterogeneity in Weibull survival models: A Bayesian approach," Econometrics and Statistics, Elsevier, vol. 3(C), pages 73-88.
    2. Il Do Ha & Liming Xiang & Mengjiao Peng & Jong-Hyeon Jeong & Youngjo Lee, 2020. "Frailty modelling approaches for semi-competing risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 109-133, January.

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