Comparing differences in proportions across different time points and different groups simultaneously

[Brenda Oulo]

Is it possible to compare changes in proportions of a variable across different time points eg baseline and one year later and compare if the changes were significant across four groups. What statistical test would you use to do this at once?

[Bruce Weaver]

Hello Brenda. Do you mean that the outcome variable for each subject at each time point is a proportion (i.e., a value in the range 0-1)? Or do you mean the proportion of events for each group x time point combination, where the outcome variable is dichotomous (1=event, 0=no event)? Thanks for clarifying.

[Joseph Coveney]

Is it possible to compare changes in proportions of a variable across different time points eg baseline and one year later and compare if the changes were significant across four groups. What statistical test would you use to do this at once?

What would I do? This:

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.ÿquietlyÿsetÿobsÿ400

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.ÿgenerateÿbyteÿgrpÿ=ÿmod(_n,ÿ4)ÿ+ÿ1

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.ÿquietlyÿexpandÿ2

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.ÿlabelÿvaluesÿtimÿTimes

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Logÿlikelihoodÿ=ÿ-535.53328ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿÿÿÿÿÿÿ=ÿÿÿÿÿ0.3736
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.ÿ
.ÿ//ÿIfÿIÿwantedÿtoÿtestÿriskÿdifference,ÿmarginalizedÿoverÿgroups
.ÿmarginsÿr.tim

Contrastsÿofÿpredictiveÿmargins
ModelÿVCEÿÿÿÿ:ÿOIM

Expressionÿÿÿ:ÿMarginalÿpredictedÿmean,ÿpredict()

------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿÿchi2ÿÿÿÿÿP>chi2
-------------+----------------------------------
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------------------------------------------------

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ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿDelta-method
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------------------------------+------------------------------------------------
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-------------------------------------------------------------------------------

.ÿ//ÿor
.ÿmarginsÿ,ÿdydx(tim)

AverageÿmarginalÿeffectsÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿNumberÿofÿobsÿÿÿÿÿ=ÿÿÿÿÿÿÿÿ800
ModelÿVCEÿÿÿÿ:ÿOIM

Expressionÿÿÿ:ÿMarginalÿpredictedÿmean,ÿpredict()
dy/dxÿw.r.t.ÿ:ÿ1.tim

---------------------------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿÿÿÿDelta-method
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----------------+----------------------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿtimÿ|
OneÿYearÿLaterÿÿ|ÿÿÿ.0727963ÿÿÿ.0300885ÿÿÿÿÿ2.42ÿÿÿ0.016ÿÿÿÿÿÿ.013824ÿÿÿÿ.1317686
---------------------------------------------------------------------------------
Note:ÿdy/dxÿforÿfactorÿlevelsÿisÿtheÿdiscreteÿchangeÿfromÿtheÿbaseÿlevel.

.ÿ
.ÿ//ÿIfÿinsteadÿIÿwantedÿaÿsimultaneousÿtestÿofÿindividual-groupÿriskÿdifferences
.ÿmarginsÿtim,ÿover(grp)ÿcontrast(waldÿwithinjointÿnoatlevels)

Contrastsÿofÿpredictiveÿmargins
ModelÿVCEÿÿÿÿ:ÿOIM

Expressionÿÿÿ:ÿMarginalÿpredictedÿmean,ÿpredict()
overÿÿÿÿÿÿÿÿÿ:ÿgrp

------------------------------------------------
ÿÿÿÿÿÿÿÿÿÿÿÿÿ|ÿÿÿÿÿÿÿÿÿdfÿÿÿÿÿÿÿÿchi2ÿÿÿÿÿP>chi2
-------------+----------------------------------
ÿÿÿÿÿtim@grpÿ|ÿÿÿÿÿÿÿÿÿÿ4ÿÿÿÿÿÿÿÿ7.41ÿÿÿÿÿ0.1159
------------------------------------------------

.ÿ//ÿor
.ÿquietlyÿmarginsÿtim#grp,ÿpost

.ÿquietlyÿtestÿ0.tim#1.grpÿ=ÿ1.tim#1.grp,ÿnotest

.ÿquietlyÿtestÿ0.tim#2.grpÿ=ÿ1.tim#2.grp,ÿnotestÿaccumulate

.ÿquietlyÿtestÿ0.tim#3.grpÿ=ÿ1.tim#3.grp,ÿnotestÿaccumulate

.ÿtestÿ0.tim#4.grpÿ=ÿ1.tim#4.grp,ÿaccumulate

ÿ(ÿ1)ÿÿ0bn.tim#1bn.grpÿ-ÿ1.tim#1bn.grpÿ=ÿ0
ÿ(ÿ2)ÿÿ0bn.tim#2.grpÿ-ÿ1.tim#2.grpÿ=ÿ0
ÿ(ÿ3)ÿÿ0bn.tim#3.grpÿ-ÿ1.tim#3.grpÿ=ÿ0
ÿ(ÿ4)ÿÿ0bn.tim#4.grpÿ-ÿ1.tim#4.grpÿ=ÿ0

ÿÿÿÿÿÿÿÿÿÿÿchi2(ÿÿ4)ÿ=ÿÿÿÿ7.41
ÿÿÿÿÿÿÿÿÿProbÿ>ÿchi2ÿ=ÿÿÿÿ0.1159

.ÿ
.ÿexit

endÿofÿdo-file


.

The method above assumes that the proportions are not independent. If that's not the case, then come back. (As Bruce mentions, your questions is a little incomplete.)

[Brenda Oulo]

Hi Bruce,
I mean the proportion of events for each group x time point combination eg proportion of respondents replying yes to a specific question at baseline compared to those responding yes to the same question one year later. Then comparing if the difference in proportions between baseline and one year are significantly different across four groups?
Thank you both for responding