Intraclass correlation coefficient calculated by gee

[Alfono leiva]

I am trying to report the ICC form a cluster clinical trial. The outcome is a dichotomous variable and I calculated OR by gee. How can I calculate icc based on the gee estimations?

[Joseph Coveney]

Don't you get what's called a working correlation with GEE? If you want what most would call an ICC, wouldn't you want to use -xtlogit- or -melogit-?

.ÿ
.ÿversionÿ16.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1525325")'

.ÿ
.ÿ//ÿClinics
.ÿquietlyÿsetÿobsÿ30

.ÿgenerateÿbyteÿcidÿ=ÿ_n

.ÿgenerateÿdoubleÿcid_uÿ=ÿrnormal()

.ÿ
.ÿgenerateÿbyteÿtrtÿ=ÿmod(_n,ÿ2)ÿ//ÿ"clusterÿclinicalÿtrial"

.ÿ
.ÿ//ÿPatients
.ÿquietlyÿexpandÿ50

.ÿ
.ÿ//ÿOutcomes
.ÿgenerateÿdoubleÿxbÿ=ÿ0ÿ*ÿtrtÿ+ÿcid_u

.ÿgenerateÿbyteÿoutÿ=ÿrbinomial(1,ÿinvlogit(xb))

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿ
.ÿ//ÿICC
.ÿmelogitÿoutÿi.trtÿ||ÿcid:ÿ,ÿnolog

Mixed-effectsÿlogisticÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ1,500
Groupÿvariable:ÿÿÿÿÿÿÿÿÿÿÿÿÿcidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ30

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ50
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ50.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ50

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿÿÿÿ0.07
Logÿlikelihoodÿ=ÿ-947.74355ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.7884
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ1.trtÿ|ÿÿÿÿ.097411ÿÿÿ.3628641ÿÿÿÿÿ0.27ÿÿÿ0.788ÿÿÿÿ-.6137895ÿÿÿÿ.8086115
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.0972996ÿÿÿ.2578787ÿÿÿÿ-0.38ÿÿÿ0.706ÿÿÿÿ-.6027326ÿÿÿÿ.4081334
-------------+----------------------------------------------------------------
cidÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿvar(_cons)|ÿÿÿ.8869553ÿÿÿ.2700865ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.4883178ÿÿÿÿÿ1.61102
------------------------------------------------------------------------------
LRÿtestÿvs.ÿlogisticÿmodel:ÿchibar2(01)ÿ=ÿ180.88ÿÿÿÿÿÿProbÿ>=ÿchibar2ÿ=ÿ0.0000

.ÿestatÿicc

Residualÿintraclassÿcorrelation

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿLevelÿ|ÿÿÿÿÿÿÿÿICCÿÿÿStd.ÿErr.ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿcidÿ|ÿÿÿ.2123516ÿÿÿ.0509318ÿÿÿÿÿÿ.1292466ÿÿÿÿÿÿ.32872
------------------------------------------------------------------------------

.ÿ/*ÿorÿ*/
.ÿxtlogitÿoutÿi.trt,ÿi(cid)ÿreÿnolog

Random-effectsÿlogisticÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ1,500
Groupÿvariable:ÿcidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ30

Randomÿeffectsÿu_iÿ~ÿGaussianÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ50
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ50.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ50

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿ12

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿÿÿÿ0.07
Logÿlikelihoodÿÿ=ÿ-947.74356ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.7884

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ1.trtÿ|ÿÿÿ.0974083ÿÿÿ.3629142ÿÿÿÿÿ0.27ÿÿÿ0.788ÿÿÿÿ-.6138905ÿÿÿÿ.8087071
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.0972954ÿÿÿ.2579467ÿÿÿÿ-0.38ÿÿÿ0.706ÿÿÿÿ-.6028616ÿÿÿÿ.4082708
-------------+----------------------------------------------------------------
ÿÿÿÿ/lnsig2uÿ|ÿÿ-.1200228ÿÿÿ.3045386ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ-.7169076ÿÿÿÿ.4768619
-------------+----------------------------------------------------------------
ÿÿÿÿÿsigma_uÿ|ÿÿÿ.9417538ÿÿÿ.1434002ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.6987559ÿÿÿÿ1.269256
ÿÿÿÿÿÿÿÿÿrhoÿ|ÿÿÿ.2123412ÿÿÿ.0509348ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.1292333ÿÿÿÿ.3287188
------------------------------------------------------------------------------
LRÿtestÿofÿrho=0:ÿchibar2(01)ÿ=ÿ180.87ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>=ÿchibar2ÿ=ÿ0.000

.ÿdisplayÿinÿsmclÿasÿtextÿ"ICCÿ=ÿ"ÿasÿresultÿ%04.2fÿe(rho)
ICCÿ=ÿ0.21

.ÿ
.ÿ
.ÿ//ÿGEEÿworkingÿcorrelation
.ÿxtgeeÿoutÿi.trt,ÿi(cid)ÿfamily(binomial)ÿlink(logit)ÿcorr(exchangeable)ÿnolog

GEEÿpopulation-averagedÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ1,500
Groupÿvariable:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿcidÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿÿÿÿ30
Link:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlogitÿÿÿÿÿÿObsÿperÿgroup:
Family:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿbinomialÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿ50
Correlation:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿexchangeableÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿ50.0
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿ50
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(1)ÿÿÿÿÿÿ=ÿÿÿÿÿÿÿ0.19
Scaleÿparameter:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.6594

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿoutÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ1.trtÿ|ÿÿÿ.1335085ÿÿÿ.3029401ÿÿÿÿÿ0.44ÿÿÿ0.659ÿÿÿÿ-.4602431ÿÿÿÿ.7272602
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-.1281752ÿÿÿ.2144303ÿÿÿÿ-0.60ÿÿÿ0.550ÿÿÿÿ-.5484509ÿÿÿÿ.2921005
------------------------------------------------------------------------------

.ÿestatÿwcorrelation,ÿcompact

Errorÿstructure:ÿexchangeable
Estimatedÿwithin-cidÿcorrelation:ÿ.1548164

.ÿ
.ÿexit

endÿofÿdo-file


.