Fitting linear mixed model to longitudinal data with very few data points

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?

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