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Original Articles

A universal procedure for parametric frailty models

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Pages 1-13 | Published online: 13 May 2010

References

  • Aslanidou , H. , Dey , D. K. and Sinha , D. (1998) . Bayesian analysis of multivariate survival data using Monte Carlo methods . Can. J. Statist. , 26 : 33 – 48 .
  • Benveniste A. Métivier M. Priouret P. (1990) Adaptive Algorithms and Stochastic Approximations Springer New York
  • Chhikara , R. S. and Folks , J. L. (1974) . Estimation of the inverse Gaussian distribution function . J. Amer. Statist. Assoc. , 69 : 250 – 254 .
  • Clayton , D. G. (1991) . A Monte Carlo method for Bayesian inference in frailty models . Biometrics , 47 : 467 – 485 .
  • Clayton , D. G. and Cuzick , J. (1985) . Multivariate generalizations of the proportional hazards model (with discussion) . J. R. Statist. Soc. A , 148 : 82 – 117 .
  • Delyon , B. , Lavielle , E. and Moulines , E. (1999) . Convergence of a stochastic approximation version of the EM algorithm . Ann. Statist. , 27 : 94 – 128 .
  • Duflo M. (1997) Random Iterative Models Springer New York
  • Elbers , C. and Ridder , G. (1982) . True and spurious duration dependence: the identifiability of the proportional hazard model . Review of Economic Studies , 49 : 403 – 409 .
  • Gelfand , A. E. and Smith , A. F. M. (1990) . Sampling based approaches to calculating marginal densities . J. Amer. Statist. Assoc. , 85 : 398 – 409 .
  • Gill , R. D. (1992) . Marginal partial likelihood . Scand. J. Statist. , 19 : 133 – 137 .
  • Gu , M. G. and Kong , F. H. (1998) . A stochastic approximation algorithm with Markov chain Monte Carlo method for incomplete data estimation problems . Proc. Natl. Acad. Sci. USA , 95 : 7270 – 7274 .
  • Gu , M. G. and Zhu , H. T. (2001) . Maximum likelihood estimation for spatial models by Markov chain Carlo stochastic approximation . J. R. Statist. Soc. B , 63 : 339 – 355 .
  • Guo , G. and Rodríguez , G. (1992) . Estimating a multivariate proportional hazard model for clustered data using the EM algorithm . J. Amer. Statist. Assoc. , 87 : 969 – 976 .
  • Ha , I. D. , Lee , Y. and Song , J. K. (2001) . Hierarchical likelihood approach for frailty models . Biometrika , 88 : 233 – 243 .
  • Hastings , W. K. (1970) . Monte Carlo sampling methods using Markov Chains and their applications . Biometrika , 53 : 97 – 109 .
  • Hougaard , P. (1986a) . A class of multivariate failure time distributions . Biometrika , 73 : 671 – 678 .
  • Hougaard , P. (1986b) . Survival models for heterogeneous populations derived from stable distributions . Biometrika , 73 : 387 – 396 .
  • Hougaard , P. , Harvald , B. and Holm , N. V. (1992) . Measuring the similarities between the lifetimes of adult Danish twins born 1881–1930 . J. Amer. Statist. Assoc. , 87 : 17 – 24 .
  • Jalaluddin , M. and Kosorok , M. R. (2000) . An algorithm for robust inference for the Cox model with frailties . J. Computational and Graphical Statistics , 9 : 642 – 652 .
  • Johansen , S. (1983) . An extension of Cox's regression model . Int. Stat. Rev. , 51 : 258 – 262 .
  • Klein , J. P. (1992) . Semiparametric estimation of random effects using the Cox's model based on the EM algorithm . Biometrics , 48 : 795 – 806 .
  • Klein J. P. Moeschberger M. L. Li Y. H. Wang S. T. (1992) Estimating random effects in the Framingham heart study In Klein, J. and Goel, P. (Eds.) Survival Analysis: State of the Art Kluwer Dordrecht
  • Kushner H. J. Yin G. G. (1997) Stochastic Approximation Algorithms and Applications Springer New York
  • Lam , K. F. and Kuk , A. Y. C. (1997) . A marginal likelihood approach to estimation in frailty models . J. Amer. Statist. Assoc. , 92 : 985 – 990 .
  • Li , Y. and Lin , X. H. (2000) . Covariate measurement errors in frailty models for clustered survival data . Biometrika , 87 : 849 – 866 .
  • Lindeboom , M. and Van Den Berg , G. J. (1994) . Heterogeneity in models for bivariate survival: the importance of the mixing distribution . J. R. Statist. Soc. B , 56 : 49 – 60 .
  • Mantel , N. , Bohidar , N. R. and Ciminera , J. L. (1977) . Mantel–Haenszel analysis of litter-matched time-to-response data, with modifications for recovery interlitter information . Cancer Research , 37 : 3863 – 3868 .
  • McGilchrist , C. A. (1993) . REML estimation for survival models with frailty . Biometrics , 49 : 221 – 225 .
  • McGilchrist , C. A. and Aisbett , C. W. (1991) . Regression with frailty in survival analysis . Biometrics , 47 : 461 – 466 .
  • Metropolis , N. , Rosenbluth , A. W. , Rosenbluth , M. N. , Teller , A. H. and Teller , E. (1953) . Equations of state calculations by fast computing machines . J. Chem. Phys. , 21 : 1087 – 1092 .
  • Murphy , S. A. (1994) . Consistency in a proportional hazard model incorporating a random effect . Ann. Statist. , 22 : 712 – 731 .
  • Murphy , S. A. (1995) . Asymptotic theory for the frailty model . Ann. Statist. , 23 : 182 – 198 .
  • Murphy , S. A. and van der Vaart , A. W. (2000) . On profile likelihood . J. Amer. Statist. Assoc. , 95 : 449 – 465 .
  • Nielsen , G. G. , Gill , R. D. , Andersen , P. K. and Sorensen , T. I. A. (1992) . A counting process approach to maximum likelihood estimation in frailty models . Scand. J. Statist. , 19 : 25 – 43 .
  • Parner , E. (1998) . Asymptotic theory for the correlated gamma-frailty model . Ann. Statist. , 26 : 183 – 214 .
  • Petersen , J. H. , Andersen , P. K. and Gill , R. D. (1996) . Variance components models for survival data . Statistica Neerlandica , 50 : 193 – 211 .
  • Polyak , B. T. and Juditski , A. B. (1992) . Acceleration of stochastic approximation by averaging . SIAM J. Control Optimization , 30 : 838 – 855 .
  • Sargent , D. J. (1998) . A general framework for random effects survival analysis in the Cox proportional hazards setting . Biometrics , 54 : 1486 – 1497 .
  • Tanner M. A. (1993) Tools for Statistical Inference Springer New York
  • Tierney , L. (1994) . Markov chains for exploring posterior distributions . Ann. Statist. , 22 : 1701 – 1762 .
  • Vaida , F. and Xu , R. H. (2000) . Proportional hazards model with random effects . Statistics in Medicine , 19 : 3309 – 3324 .

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