[R] p values for a GEE model

[Prof Brian Ripley]

On Mon, 10 Apr 2006, Tarca, Adi wrote:

> Hi all,
>
> I have a dataset in which the output Y is observed on two groups of
> patients (treatment factor T with 2 levels).
>
> Every subject in each group is observed three times (not time points but
> just technical replication).
>
> I am interested in estimating the treatment effect and take into account
> the fact that I have repeated measurements for every subject.
>
> If I do this with repeated measures ANOVA (in which the patient is
> considered a random effect) I got the following results:
>
>              library(nlme)
>
> data<-read.table("http://146.9.88.18/uploads/dataGEE.txt",header=TRUE)
>
>       res<-lme(Y~T,random=~1|P,data=data)
>       summary(res)
>
> So the p-value for significance of the treatment effect is 0.069.
>
> I would like to use also as a variant analysis a Generalized Estimation
> Equation Model, like
>
>                library(gee)
>                summary(gee(Y~T,id=P,data=data))
>
> Questions:
>
> A) Is the gee approach suitable in this case with the model formulae I
> use?

Yes, but your choice of working correlation probably is not.  Your results 
are basically least-squares here.  I think you want corstr="exchangeable" 
or perhaps some form of AR if the repeated observations have a clear time 
base.

> B) Can I obtain a p-value for the fixed effect T ?

Well, the output is

Coefficients:
              Estimate Naive S.E.   Naive z Robust S.E.  Robust z
(Intercept) 14.781968  0.3686055 40.102410   0.3608597 40.963207
TPTLD        1.857166  0.5259206  3.531266   0.8570370  2.166961

and if you read up on the background you will know that the 'z' scores are 
approximately normally distributed.

There are detailed comparisons of examples of the lme and gee approaches 
in MASS chapter 10.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595