[R-sig-ME] Fitting linear mixed model to longitudinal data with very few data points

[Ben Bolker]

On 13-11-25 09:45 PM, David Westergaard wrote:
> Thank you both for your valuable input. Just to clarify, this is NOT a
> clinical study. This is a first of its kind study, and we are
> interested in generating hypothesis for further investigation and
> experimental evaluation. We accept the limitations of our study, but
> we have a need to estimate these things, given data. Especially
> because the pattern that we observe makes absolutely perfect sense
> biologically.
> 
> @Ben, you could put it like that, I guess. In truth, what we have
> measured is the total gene abundance. We have then binned the
> abundance of individual genes into categories, and its those
> categories that we term Response values.
> 
> Are there any good introductions to working with contrasts in R? When
> I search google, I just get hit by a massive amount of hits, and its a
> bit overwhelming. Also, how would you suggest making the design?

Maybe

http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm
http://ms.mcmaster.ca/~bolker/classes/s4c03/notes/week2B.pdf

  (I'd welcome other suggestions from the list)

> 
> Best,
> David
> 
> 2013/11/25 Ben Bolker <bbolker at gmail.com>:
>> On 13-11-24 09:43 AM, David Westergaard wrote:
>>
>>> To summarise the data: From 2 subjects, 8 response values were
>>> measured at time points T0, T1, T2, T3. At T1, subject 1 underwent
>>> treatment. Subject 1 received no further treatment after T1.
>>
>>>> 1. Is there any observable effect after administering the drug (i.e.
>>>> is the difference between response values significantly greater than
>>>> zero)
>>>> 2. If there is an effect, what is the effect size at each time point
>>>> (i.e. what is the difference between response values)
>>>> 3. How does the effect vary over time
>>>> 4. If there is an effect, is the effect observed from the drug at T1
>>>> still persistant at T3
>>
>>
>>   So you have a total of 64 (2 subjects * 4 times * 8 obs) observations?
>> Overlooking the problem of extrapolating from two individuals to the
>> whole population that might get treated, it seems to me it would be
>> perfectly reasonable to treat this as a regular linear model problem --
>> specifically, ecologists would call this a "before-after-control-impact"
>> design.  If the individuals have different underlying time courses then
>> you won't be able to detect it -- it will be confounded with the
>> treatment effect.  Most of your questions can be set up as contrasts:
>> for example, the effect of the drug is represented by the interaction
>> between (subject) and (T0 vs. {T1,T2,T3}).  (The main effect of subject
>> gives the difference between subjects: the main effect of (T0 vs.
>> {T1,T2,T3}) gives the before-after difference for the untreated subject;
>> the interaction gives the estimated effect size.
>>
>>   And so on.  (This is a reasonable question, but I don't think it can
>> be framed as a mixed model question with this design.)
>>
>>   Ben Bolker
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models