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