×

zbMATH — the first resource for mathematics

Correlated versus uncorrelated frailty Cox models: a comparison of different estimation procedures. (English) Zbl 1358.62093
Summary: In many studies in medicine, including clinical trials and epidemiological investigations, data are clustered into groups such as health centers or herds in veterinary medicine. Such data are usually analyzed by hierarchical regression models to account for possible variation between groups. When such variation is large, it is of potential interest to explore whether additionally the effect of a within-group predictor varies between groups. In survival analysis, this may be investigated by including two frailty terms at group level in a Cox proportional hazards model. Several estimation methods have been proposed to estimate this type of frailty Cox models. We review four of these methods, apply them to real data from veterinary medicine, and compare them using a simulation study.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
62N05 Reliability and life testing
62-07 Data analysis (statistics) (MSC2010)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Bender, Generating survival times to simulate Cox proportional hazards models, Statistics in Medicine 24 pp 1712– (2005) · doi:10.1002/sim.2059
[2] Breslow, Approximate inference in generalized linear models, Journal of the American Statistical Association 88 pp 9– (1993) · Zbl 0775.62195
[3] Christensen, The influence of selected litter and herd factors on treatments for lameness in suckling piglets from 35 Danish herds, Preventive Veterinary Medicine 26 pp 107– (1996) · doi:10.1016/0167-5877(95)00523-4
[4] Cortiñas, A version of the EM algorithm for proportional hazard model with random effects, Biometrical Journal 47 pp 847– (2005) · doi:10.1002/bimj.200410141
[5] Cortiñas, Comparison of different estimation procedures for proportional hazards model with random effects, Computational Statistics and Data Analysis 51 pp 3913– (2007) · Zbl 1161.62415 · doi:10.1016/j.csda.2006.03.009
[6] Duchateau, The Frailty Model (2008) · Zbl 1210.62153
[7] Feng, Frailty survival model analysis of the national deceased donor kidney transplant dataset using Poisson variance structures, Journal of the American Statistical Association 100 pp 718– (2005) · Zbl 1117.62333 · doi:10.1198/016214505000000123
[8] Feng, Laplace’s approximation for relative risk frailty models, Lifetime Data Analysis 15 pp 343– (2009) · Zbl 1282.62216 · doi:10.1007/s10985-009-9112-x
[9] Hirsch, Software for semiparametric shared gamma and log-normal frailty models: an overview, Computer Methods and Programs in Biomedicine 107 pp 582– (2012) · doi:10.1016/j.cmpb.2011.05.004
[10] Joly, A penalized likelihood approach for arbitrarily censored and truncated data: application to age-specific incidence of dementia, Biometrics 54 pp 185– (1998) · Zbl 1058.62618 · doi:10.2307/2534006
[11] Kalbfleish, Nonparametric Bayesian analysis of survival time data, Journal of the Royal Statistical Society: Series B 40 pp 214– (1978)
[12] Legrand, A Bayesian approach to jointly estimate centre and treatment by centre heterogeneity in a proportional hazards model, Statistics in Medicine 24 pp 3789– (2005) · doi:10.1002/sim.2475
[13] Ma, Random effects Cox models: A Poisson modelling approach, Biometrika 90 pp 157– (2003) · Zbl 1035.62114 · doi:10.1093/biomet/90.1.157
[14] Marquardt, An algorithm for least-squares estimation of nonlinear parameters, SIAM Journal on Applied Mathematics 11 pp 431– (1963) · Zbl 0112.10505 · doi:10.1137/0111030
[15] Massonnet, Fitting conditional survival models to meta-analytic data by using a transformation toward mixed-effects models, Biometrics 64 pp 834– (2008) · Zbl 1146.62094 · doi:10.1111/j.1541-0420.2007.00960.x
[16] McGilchrist, REML estimation for survival models with frailty, Biometrics 49 pp 221– (1993) · doi:10.2307/2532615
[17] Pinheiro, Approximations to the log-likelihood function in the nonlinear mixed-effects model, Journal of Computational and Graphical Statistics 4 pp 12– (1995)
[18] Plummer, CODA: convergence diagnosis and output analysis for MCMC, R News 6 pp 7– (2006)
[19] Rabe-Hesketh, Categorical Responses, Counts, and Survival II (2012) · Zbl 1274.62033
[20] Ramsay, Monotone regression splines in action, Statistical Science 3 pp 425– (1988) · doi:10.1214/ss/1177012761
[21] Ripatti, Estimation of multivariate frailty models using penalized partial likelihood, Biometrics 56 pp 1016– (2000) · Zbl 1060.62564 · doi:10.1111/j.0006-341X.2000.01016.x
[22] Rondeau, Maximum penalized likelihood estimation in a Gamma-frailty model, Lifetime Data Analysis 9 pp 139– (2003) · Zbl 1116.62408 · doi:10.1023/A:1022978802021
[23] Rondeau, Investigating trial and treatment heterogeneity in an individual patient data meta-analysis of survival data by means of the penalized maximum likelihood approach, Statistics in Medicine 27 pp 1894– (2008) · doi:10.1002/sim.3161
[24] Rondeau, frailtypack: an R package for the analysis of correlated survival data with frailty models using penalized likelihood estimation or parametrical estimation, Journal of Statistical Software 47 (2012) · doi:10.18637/jss.v047.i04
[25] Stryhn, The analysis-hierarchical models: past, present and future, Preventive Veterinary Medicine 113 pp 304– (2013) · doi:10.1016/j.prevetmed.2013.10.001
[26] Sturtz, R2WinBUGS: a package for running WinBUGS from R, Journal of Statistical Software 12 (2005) · doi:10.18637/jss.v012.i03
[27] Therneau, Modelling Survival Data, Extending the Cox model (2000) · doi:10.1007/978-1-4757-3294-8
[28] Therneau , T. 2011 http://cran.r-project.org/web/packages/coxme/
[29] Vaida, Proportional hazards model with random effects, Statistics in Medicine 19 pp 3309– (2000) · doi:10.1002/1097-0258(20001230)19:24<3309::AID-SIM825>3.0.CO;2-9
[30] Wienke, A comparison of different bivariate correlated frailty models and estimation strategies, Mathematical Biosciences 198 pp 1– (2005) · Zbl 1077.62085 · doi:10.1016/j.mbs.2004.11.010
[31] Wienke, Frailty Models in Survival Analysis (2010) · doi:10.1201/9781420073911
[32] Xue, Bivariate frailty model for the analysis of multivariate survival time, Lifetime Data Analysis 2 pp 227– (1996) · Zbl 0862.62085 · doi:10.1007/BF00128978
[33] Yamaguchi, Investigating centre effects in a multicentre clinical trial of superficial bladder cancer, Statistics in Medicine 18 pp 1961– (1999) · doi:10.1002/(SICI)1097-0258(19990815)18:15<1961::AID-SIM170>3.0.CO;2-3
[34] Yamaguchi, Proportional hazards models with random effects to examine centre effects in multicentre cancer clinical trials, Statistical Methods in Medical Research 11 pp 221– (2002) · Zbl 1121.62679 · doi:10.1191/0962280202sm284ra
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.