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

[Ben Bolker]

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