Abstract
For the analysis of correlated survival data mixed linear models are useful alternatives to frailty models. By their use the survival times can be directly modelled, so that the interpretation of the fixed and random effects is straightforward. However, because of intractable integration involved with the use of marginal likelihood the class of models in use has been severely restricted. Such a difficulty can be avoided by using hierarchical-likelihood, which provides a statistically efficient and fast fitting algorithm for multilevel models. The proposed method is illustrated using the chronic granulomatous disease data. A simulation study is carried out to evaluate the performance.
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References
J. R. Batchelor M. Hackett (1970) ArticleTitle“HLA matching in treatment of burned patients with skin allografts” Lancet 2 581–583
W. M. Bolstad S.O.M. Manda (2001) ArticleTitle“Investigating child mortality in Malawi using family and community random effects: a Bayesian analysis,” Journal of the American Statistical Association 96 12–19
H. Chernoff (1954) ArticleTitle“On the distribution of the likelihood ratio” Annals of Mathematical Statistics 25 573–578
T. R. Fleming D.P. Harrington (1991) Counting Processes and Survival Analysis Wiley New York
H. Goldstein (1995) Multilevel Statistical Models Arnold London
R. Gueorguieva (2001) ArticleTitle“A multivariate generalized linear mixed model for joint modelling of clustered outcomes in the exponential family” Statistical Modelling 1 177–193
I. D. Ha, Y. Lee, and G. MacKenzie, “Model selection for frailty models,” manuscript submitted for publication, 2003.
I. D. Ha Y. Lee J.-K. Song (2002) ArticleTitle“Hierarchical likelihood approach for mixed linear models with censored data” Lifetime Data Analysis 8 163–176
C. R. Henderson (1975) ArticleTitle“Best linear unbiased estimation and prediction under a selection model” Biometrics 31 423–447
P. Hougaard (1999) ArticleTitle“Fundamentals of survival data” Biometrics 55 13–22
J. P. Hughes (1999) ArticleTitle“Mixed effects models with censored data with application to HIV RNA levels” Biometrics 55 625–629
J. Jiang (1997) ArticleTitle“Wald consistency and the method of sieves in REML estimation” The Annals of Statistics 25 1781–1803
J. P. Klein C. Pelz M. Zhang (1999) ArticleTitle“Modelling random effects for censored data by a multivariate normal regression model” Biometrics 55 497–506
Y. Lee J. A. Nelder (1996) ArticleTitle“Hierarchical generalized linear models (with discussion)” Journal of the Royal Statistical Society B 58 619–678
Y. Lee J. A. Nelder (2001) ArticleTitle“Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions,” Biometrika 88 987–1006
S. O. M. Manda (2001) ArticleTitle“A comparison of methods for analysing a nested frailty model to child survival in Malawi” Australian and New Zealand Journal of Statistics 43 7–16
W. Pan T. A. Louis (2000) ArticleTitle“A linear mixed-effects model for multivariate censored data” Biometrics 56 160–166
A. N. Pettitt (1986) ArticleTitle“Censored observations, repeated measures and mixed effects models: An approach using the EM algorithm and normal errors,” Biometrika 73 635–643
S. Rabe-Hesketh A. Pickles A. Skrondal (2001) ArticleTitle“Gllamm: A general class of multilevel models and a Stata program,” Multilevel Modelling Newsletter 13 17–23
S. Rabe-Hesketh A. Skrondal A. Pickles (2002) ArticleTitle“Reliable estimation of generalized linear mixed models using adaptive quadrature” The Stata Journal 2 1–21
N. Sastry (1997) ArticleTitle“A nested frailty model for survival data, with application to study of child survival in Northeast Brazil” Journal of the American Statistical Association 92 426–435
S. G. Self K. Y. Liang (1987) ArticleTitle“Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions” Journal of the American Statistical Association 82 605–610
D. O. Stram J. W. Lee (1994) ArticleTitle“Variance components testing in the longitudinal mixed effects model” Biometrics 50 1171–1177
G. Verbeke G. Molenberghs (2003) ArticleTitle“The use of score tests for inference on variance components” Biometrics 59 254–262
H. T. V. Vu M. W. Knuiman (2002) ArticleTitle“A hybrid ML-EM algorithm for calculation of maximum likelihood estimates in semiparametric shared frailty models” Computational Statistics and Data Analysis 40 173–187
H. T. V. Vu M. R. Segal M. W. Knuiman I. R. James (2001) ArticleTitle“Asymptotic and small sample statistical properties of random frailty variance estimates for shared gamma frailty models” Communications in Statistics-Simulation and Computation 30 581–595
R. D. Wolfinger (1993) ArticleTitle“Covariance structure selection in general mixed models” Communications in Statistics-Simulation and Computation 22 1079–1106
R.D. Wolfinger, “Fitting nonlinear mixed models with the new NLMIXED procedure”. Proceedings of the 99 Joint Statistical Meetings,, Paper 287, 1999.
K. K. W. Yau (2001) ArticleTitle“Multilevel models for survival analysis with random effects” Biometrics 57 96–102
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Do Ha, I., Lee, Y. Multilevel Mixed Linear Models for Survival Data. Lifetime Data Anal 11, 131–142 (2005). https://doi.org/10.1007/s10985-004-5644-2
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DOI: https://doi.org/10.1007/s10985-004-5644-2