title: Review of methods for handling confounding by cluster and informative cluster size in clustered data.
abstract: Clustered data are common in medical research. Typically, one is interested in a regression model for the association between an outcome and covariates. Two complications that can arise when analysing clustered data are informative cluster size (ICS) and confounding by cluster (CBC). ICS and CBC mean that the outcome of a member given its covariates is associated with, respectively, the number of members in the cluster and the covariate values of other members in the cluster. Standard generalised linear mixed models for cluster-specific inference and standard generalised estimating equations for population-average inference assume, in general, the absence of ICS and CBC. Modifications of these approaches have been proposed to account for CBC or ICS. This article is a review of these methods. We express their assumptions in a common format, thus providing greater clarity about the assumptions that methods proposed for handling CBC make about ICS and vice versa, and about when different methods can be used in practice. We report relative efficiencies of methods where available, describe how methods are related, identify a previously unreported equivalence between two key methods, and propose some simple additional methods. Unnecessarily using a method that allows for ICS/CBC has an efficiency cost when ICS and CBC are absent. We review tools for identifying ICS/CBC. A strategy for analysis when CBC and ICS are suspected is demonstrated by examining the association between socio-economic deprivation and preterm neonatal death in Scotland.
authors.affiliation: MRC Biostatistics Unit, Cambridge, CB2 0SR, U.K.
authors.forename: Shaun
authors.initials: S
authors.lastname: Seaman
authors.forename: Menelaos
authors.initials: M
authors.lastname: Pavlou
authors.forename: Andrew
authors.initials: A
authors.lastname: Copas
mesh_terms: D001699:Biometry / Q000379:methods*; D016000:Cluster Analysis; D015986:Confounding Factors, Epidemiologic; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D016014:Linear Models; D016015:Logistic Models; D018401:Sample Size
keywords: conditional maximum likelihood; confounding by cluster; contextual effect; informative cluster size; poor man's method; within-cluster effect
references.citation: Stat Med. 2003 Aug 30;22(16):2591-602
references.pmid: 12898546
references.citation: Biometrika. 2011 Mar;98(1):147-162
references.pmid: 23049125
references.citation: J Nonparametr Stat. 2012 Sep 1;24(3):797-808
references.pmid: 23074359
references.citation: Stat Med. 2011 Jul 10;30(15):1825-36
references.pmid: 21495060
references.citation: Biometrics. 2008 Sep;64(3):772-780
references.pmid: 18047524
references.citation: Am J Epidemiol. 2005 May 1;161(9):891-8
references.pmid: 15840622
references.citation: Stat Med. 2013 Jun 30;32(14):2419-29
references.pmid: 23203817
references.citation: Stat Pap (Berl). 2014 Feb 1;55(1):71-92
references.pmid: 25878396
references.citation: Biostatistics. 2009 Apr;10(2):374-89
references.pmid: 19136448
references.citation: Multivariate Behav Res. 1995 Jan 1;30(1):1-21
references.pmid: 26828342
references.citation: BMJ. 2012 Mar 16;344:e1552
references.pmid: 22427307
references.citation: Stat Med. 2012 Feb 20;31(4):366-82
references.pmid: 22086835
references.citation: J Clin Epidemiol. 1996 Dec;49(12):1373-9
references.pmid: 8970487
references.citation: Biometrics. 1999 Jun;55(2):470-6
references.pmid: 11318202
references.citation: Biometrics. 2014 Jun;70(2):449-56
references.pmid: 24479899
references.citation: Stat Med. 2002 Feb 15;21(3):389-95
references.pmid: 11813225
references.citation: Biometrics. 2003 Sep;59(3):521-30
references.pmid: 14601753
references.citation: Biometrics. 1998 Jun;54(2):638-45
references.pmid: 9629647
references.citation: Biometrics. 2003 Mar;59(1):36-42
references.pmid: 12762439
references.citation: Biometrics. 1996 Jun;52(2):500-11
references.pmid: 10766502
references.citation: Epidemiology. 2003 May;14(3):300-6
references.pmid: 12859030
references.citation: Biometrics. 1995 Mar;51(1):309-17
references.pmid: 7766784
references.citation: Biometrics. 2008 Jun;64(2):501-7
references.pmid: 17970820
references.citation: Stat Methods Med Res. 2004 Feb;13(1):3-16
references.pmid: 14746438
references.citation: Stat Med. 1994 Mar 15-Apr 15;13(5-7):509-22
references.pmid: 8023032
references.citation: Behav Res Methods. 2011 Dec;43(4):1003-13
references.pmid: 21512874
references.citation: Stat Methods Med Res. 2011 Aug;20(4):347-67
references.pmid: 20223781
references.citation: Stat Med. 2013 Apr 15;32(8):1313-24
references.pmid: 22975990
references.citation: Am J Epidemiol. 2003 Aug 1;158(3):280-7
references.pmid: 12882951
references.citation: Epidemiology. 2012 Sep;23(5):751-61
references.pmid: 22828661
references.citation: Biometrics. 2011 Sep;67(3):843-51
references.pmid: 21281273
references.citation: Biometrics. 2005 Sep;61(3):862-6; discussion 866-7
references.pmid: 16135040
references.citation: Biostatistics. 2005 Apr;6(2):241-58
references.pmid: 15772103