Test for clustering

[Jacob John]

In analysing data from a cohort of 6500 children recruited from 3500 families, I would like to examine if the event (developing typhoid) is clustered within households. While multiple events per child is possible, the data is set up as one record per child and only one event per child is included. If clustering within households is present, I will probably use a GEE for analysis else a logistic regression.
Ideally I would like a way of quantifying ICC when the outcome is number of events.
Could someone please provide me an indication of where to look for answers.
Thanks!

Jacob

[Joseph Coveney]

. . . only one event per child is included.
. . . Ideally I would like a way of quantifying ICC when the outcome is number of events.

The outcome, I think, would not be the number of events, but rather the proportion of children with one or more episodes (relapse or re-infection) of typhoid fever, wouldn't it? Anyway, the output below illustrates how to get intraclass correlation coefficient from the setup that you describe.

. . . I will probably use a GEE for analysis else a logistic regression.

I show both below so that you can get an idea of the potential for differences in the magnitude of the household-specific and population-average estimates.

.ÿ
.ÿversionÿ16.0

.ÿ
.ÿclearÿ*

.ÿ
.ÿsetÿseedÿ`=strreverse("1523998")'

.ÿquietlyÿsetÿobsÿ3500

.ÿgenerateÿintÿfidÿ=ÿ_n

.ÿgenerateÿdoubleÿfid_uÿ=ÿrnormal()

.ÿ
.ÿgenerateÿbyteÿepdÿ=ÿ1ÿ+ÿrpoisson(6500ÿ/ÿ3500ÿ-ÿ1)

.ÿsummarizeÿepd,ÿmeanonly

.ÿifÿr(sum)ÿ<ÿ6500ÿquietlyÿreplaceÿepdÿ=ÿepdÿ+ÿ1ÿinÿ1/`=6500ÿ-ÿr(sum)'

.ÿelseÿ{
.ÿÿÿÿÿÿÿÿÿgsortÿ-epd
.ÿÿÿÿÿÿÿÿÿquietlyÿreplaceÿepdÿ=ÿepdÿ-ÿ1ÿinÿ`1/r(sum)ÿ-ÿ6500'
.ÿÿÿÿÿÿÿÿÿassertÿepd
.ÿ}

.ÿquietlyÿexpandÿepd

.ÿ
.ÿ//ÿca.ÿ5%ÿchanceÿchildrenÿdevelopingÿoneÿorÿmoreÿepisodesÿtyphoidÿfever
.ÿgenerateÿdoubleÿxbÿ=ÿfid_uÿ+ÿlogit(0.05)

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

.ÿ
.ÿ*
.ÿ*ÿBeginÿhere
.ÿ*
.ÿmelogitÿtphÿ||ÿfid:ÿ,ÿnolog

Mixed-effectsÿlogisticÿregressionÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ6,500
Groupÿvariable:ÿÿÿÿÿÿÿÿÿÿÿÿÿfidÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿ3,500

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿObsÿperÿgroup:
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ1
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ1.9
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ7

Integrationÿmethod:ÿmvaghermiteÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿIntegrationÿpts.ÿÿ=ÿÿÿÿÿÿÿÿÿÿ7

ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(0)ÿÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿÿ.
Logÿlikelihoodÿ=ÿ-1654.9072ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿÿ.
------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿtphÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-3.007752ÿÿÿ.1186507ÿÿÿ-25.35ÿÿÿ0.000ÿÿÿÿ-3.240303ÿÿÿ-2.775201
-------------+----------------------------------------------------------------
fidÿÿÿÿÿÿÿÿÿÿ|
ÿÿÿvar(_cons)|ÿÿÿÿ1.09515ÿÿÿ.2886757ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ.6532831ÿÿÿÿ1.835886
------------------------------------------------------------------------------
LRÿtestÿvs.ÿlogisticÿmodel:ÿchibar2(01)ÿ=ÿ23.59ÿÿÿÿÿÿÿProbÿ>=ÿchibar2ÿ=ÿ0.0000

.ÿestatÿicc

Intraclassÿcorrelation

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿLevelÿ|ÿÿÿÿÿÿÿÿICCÿÿÿStd.ÿErr.ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-----------------------------+------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿfidÿ|ÿÿÿ.2497481ÿÿÿ.0493908ÿÿÿÿÿÿ.1656754ÿÿÿÿÿ.358169
------------------------------------------------------------------------------

.ÿ
.ÿxtgeeÿtph,ÿi(fid)ÿfamily(binomial)ÿlink(logit)ÿcorr(exchangeable)ÿnolog

GEEÿpopulation-averagedÿmodelÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿ6,500
Groupÿvariable:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿfidÿÿÿÿÿÿNumberÿofÿgroupsÿÿ=ÿÿÿÿÿÿ3,500
Link:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿlogitÿÿÿÿÿÿObsÿperÿgroup:
Family:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿbinomialÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿminÿ=ÿÿÿÿÿÿÿÿÿÿ1
Correlation:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿexchangeableÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿavgÿ=ÿÿÿÿÿÿÿÿ1.9
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿmaxÿ=ÿÿÿÿÿÿÿÿÿÿ7
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿWaldÿchi2(0)ÿÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿÿ.
Scaleÿparameter:ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ1ÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿÿÿÿÿÿ.

------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿtphÿ|ÿÿÿÿÿÿCoef.ÿÿÿStd.ÿErr.ÿÿÿÿÿÿzÿÿÿÿP>|z|ÿÿÿÿÿ[95%ÿConf.ÿInterval]
-------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿ_consÿ|ÿÿ-2.571459ÿÿÿ.0509405ÿÿÿ-50.48ÿÿÿ0.000ÿÿÿÿ-2.671301ÿÿÿ-2.471618
------------------------------------------------------------------------------

.ÿ
.ÿexit

endÿofÿdo-file


.

[Joseph Coveney]

I wrote

quietly replace epd = epd - 1 in `1/r(sum) - 6500'

Good thing that it never got there.

Replace that with

quietly replace epd = epd - 1 in 1/`=r(sum) - 6500'

[Jacob John]

Dear Joseph,
Thank you! Very useful and enlightening. I was travelling to an area without internet and did not have a chance to review this. You are right, I did not mean number of events but the proportion positive.
My choice had to be logistic vs mixed effects logistic vs GEE.
Since in my data the ICC is

famid | .5262349 .0498382 (.4287955 .6217163)

I would assume a simple logistic regression is not the option and either melogit or GEE would be appropriate. Any suggestions which would make more sense? I understand that Mixed effects assess risk at the individual level and GEE at the population level - but what is the meaningful difference if my goal is to predict incidence in a population using these risk factors?