Statistical model / test for difference in change over time for two conditions

Question

I have data from an experiment that looks like this:

rep 1 T=0	rep 2 T=0	rep 1 treatment	rep 2 treatment	rep 1 control	rep 2 control
0	3	3	7	2	4
1	4	3	8	1	4
...	...	...	...	...	...

The statistical question I'm trying to answer is whether all observations (all rows) differed in their change after T=0 in the treatment group versus the control group (whether observations as a whole significantly differed in their response to treatment compared to control).

What is the most appropriate statistical approach to test this hypothesis using all available data? I believe it is a mixed effects model but am not quite sure how to set it up.

Edit: Note that data are "paired" - each row represents two replicates, each an independent unit that is split in half and each half independently exposed to both treatment and control. Each row is a biological replicate and each "replicate" column is a technical replicate thereof.

Answer 1

The first point is about the pairing. It depends on how exactly the independent units are "split in half", and what exactly the variable you measure is. Are the 2 halves of Rep1 really identical, at least from the perspective of the variable being measured? And are these 2 halves identical (again wrt the measured variable) to the whole unit? Since there are no details about it, we can not really assess. Therefore, I will take assume that they indeed are, as the OP describes.
In this case, you can then re-arrange your data. You currently have a 6xN table (where $N$ is the total number of "pairs"; re-arrange it as a 3x$2N$ table such as

| T=0 | treatment | control | | ------- | --------- | ------- | | 0 | 3 | 2 | | 3 | 7 | 4 | | 1 | 3 | 1 | | 4 | 8 | 4 | | ... | ... | ... | Then compute the differences $Treatment-T_0$ and $Control-T_0$ and run paired tests (e.g. paired t-test, for comparing means, or paired Sign test for comparing medians, etc.).
Note that the paired tests are executed on a variable which simplifies to just $Treatment - Control$, so the measurements at $T_0$ are not used... So you can directly jump to that difference, and run 1-sample tests on it...
But if you had not split the units in half (so, no pairing), you would have needed the $T_0$ measurement, to adjust for any initial difference between treatment and control group. And you would have to use 2-sample tests, which have lower power...