# [R] Random Effects Model with Interacting Covariates

Dov Stekel d.j.stekel at bham.ac.uk
Mon Jul 31 20:02:51 CEST 2006

```Douglas

That's very helpful! It's just a syntax error in my use of lme (I find
the documentation hard to figure!). I'm actually also using the formula

lme(Measurement~Treatment/When etc)

as this gives the right contrasts to look at the interactions between
each of the treatments and before/after. I'm still working on a model
formula that will give me a single p-value for 'is the difference
between before and after different for different treatments'.

And this all feels much happier than not using a random effects model
and simply using patient as a blocking variable (i.e. Measurement ~
Treat/When + Patient) which seems unsatisfactory for independence
reasons. (I'm not really a statistician - just the most stats-savvy
person in my department!)

Thanks,

Dov

On 31 Jul 2006, at 18:38, Douglas Bates wrote:

> On 7/31/06, Dov Stekel <d.j.stekel at bham.ac.uk> wrote:
>> Hi
>>
>> I have been asked by a colleague to perform a statistical analysis
>> which uses random effects - but I am struggling to get this to work
>> with nlme in R. Help would be very much appreciated!
>>
>> Essentially, the data consists of:
>>
>> 10 patients. Each patient has been given three different treatments
>> (on
>> three separate days). 15 measurements (continuous variable) have been
>> taken from each patient both before and after each of the treatments.
>> So the data looks like:
>>
>> Patient When    Treat   Measurement
>> a               before  A               10.3
>> a               before  A               11.2
>> ...
>> a               after           A               12.4
>> ...
>> a               before  B               11.6
>> ...
>> a               after           B               ...
>>
>> and the same for treatment C, patients, b,c,d, etc.
>>
>> My colleague would like to test to see if the treatments are different
>> from each other. i.e., is the change (before to after) due to the
>> treatments different between the treatments. It would seem to me like
>> a
>> random effects model in which we are interested in the significance of
>> the interaction terms Treat:When, with repeated measures in the
>> patients (who are random effects, but crossed with the covariates).
>> Unfortunately, the groupedData formula only lets me put a single
>> covariate on the LHS - nothing as complicated as this!
>
> I'm not sure I understand what the LHS of a formula for a groupedData
> object has to do with your question.
>
> You will need to specify the model that you wish to fit by lme and,
> for that, you will need to decide which terms should be fixed effects
> and which random effects.  Do you think that the patients contribute
> only an additive shift in the response or do you think that the
> patients may have different initial values and different levels of
> change in the Before/After responses?
>
> It seems that you could begin by fitting
>
> fm1 <- lme(Measurement ~ When*Treat, random = ~ 1 | Patient, data =
> ...)
>
> and
>
> fm2 <- lme(Measurement ~ When*Treat, random = ~ 1|Patient/When, data =
> ...)
>
> There are many other variations that you could consider but we can
> only guess at because we don't know enough of the context of the data.
> For example, it is possible that it would be appropriate to eliminate
> a main effect for Treat because the Treatment cannot be expected to
> influence the measurement before the Treatment is applied.  The
> fixed-effects term would then be specified as
>
> fm3 <- lme(Measurement ~ When + When:Treat, random = ...)
>
>>
>> I could, of course, advise her to simply combine all 30 data points
>> for
>> each treatment in each patient into a single number (representing
>> difference between before and after), but is there a way to use all
>> the
>> data in an LME?
>>
>> Thanks!
>>
>>
>> Dov
>>
>>
>>
>> **************************************************************
>>
>> Dr Dov Stekel
>> Lecturer in Bioinformatics
>> School of Biosciences
>> University of Birmingham
>> Birmingham B15 2TT
>> Tel: +44 121 414 4209
>> Email: d.j.stekel at bham.ac.uk
>>
>> ______________________________________________
>> R-help at stat.math.ethz.ch mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>>

**************************************************************

Dr Dov Stekel
Lecturer in Bioinformatics
School of Biosciences
University of Birmingham
Birmingham B15 2TT
Tel: +44 121 414 4209
Email: d.j.stekel at bham.ac.uk

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