title: Bias correction in the hierarchical likelihood approach to the analysis of multivariate survival data.
abstract: Frailty models are useful for measuring unobserved heterogeneity in risk of failures across clusters, providing cluster-specific risk prediction. In a frailty model, the latent frailties shared by members within a cluster are assumed to act multiplicatively on the hazard function. In order to obtain parameter and frailty variate estimates, we consider the hierarchical likelihood (H-likelihood) approach (Ha, Lee and Song, 2001. Hierarchical-likelihood approach for frailty models. Biometrika 88, 233-243) in which the latent frailties are treated as "parameters" and estimated jointly with other parameters of interest. We find that the H-likelihood estimators perform well when the censoring rate is low, however, they are substantially biased when the censoring rate is moderate to high. In this paper, we propose a simple and easy-to-implement bias correction method for the H-likelihood estimators under a shared frailty model. We also extend the method to a multivariate frailty model, which incorporates complex dependence structure within clusters. We conduct an extensive simulation study and show that the proposed approach performs very well for censoring rates as high as 80%. We also illustrate the method with a breast cancer data set. Since the H-likelihood is the same as the penalized likelihood function, the proposed bias correction method is also applicable to the penalized likelihood estimators.
authors.affiliation: Program in Biostatistics and Biomathematics, Fred Hutchinson Cancer Research Center, Seattle, WA 98109, USA. jhjeon@fhcrc.org
authors.forename: Jihyoun
authors.initials: J
authors.lastname: Jeon
authors.forename: Li
authors.initials: L
authors.lastname: Hsu
authors.forename: Malka
authors.initials: M
authors.lastname: Gorfine
mesh_terms: D017668:Age of Onset; D015982:Bias; D001943:Breast Neoplasms / Q000453:epidemiology; D016000:Cluster Analysis; D003198:Computer Simulation; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D015999:Multivariate Analysis; D016019:Survival Analysis
references.citation: Behav Genet. 2007 Jul;37(4):621-30
references.pmid: 17401640
references.citation: Biometrics. 1974 Mar;30(1):89-99
references.pmid: 4813387
references.citation: Stat Med. 2007 Nov 10;26(25):4657-78
references.pmid: 17348081
references.citation: N Engl J Med. 1997 May 15;336(20):1401-8
references.pmid: 9145676
references.citation: Biometrics. 1997 Mar;53(1):131-45
references.pmid: 9147589
references.citation: Lifetime Data Anal. 2005 Jun;11(2):265-84
references.pmid: 15938549
references.citation: Lifetime Data Anal. 2003 Jun;9(2):139-53
references.pmid: 12735493
references.citation: Biometrics. 1992 Sep;48(3):829-38
references.pmid: 1420844
references.citation: Stat Med. 2011 Jul 30;30(17):2144-59
references.pmid: 21563206
references.citation: Ann Stat. 2009;37(3):1489-1517
references.pmid: 19684881