Is it possible to test if the response difference over two time points is significantly different between groups when there are no repeated subjects?

Question

I currently have a dataset where I've collected data between two groups (disease versus control). The experimental design is to evaluate how the response variable changes over time. Thus, we have 4 time points, and the response variable is quantified at every time point. The kicker here is that I can't do a paired t test (assuming normality which is whole other problem) because no subject has multiple time points; i.e. at timepoint 1, subject A's response is quantified and that will be it from subject A. Another subject within the same group (say subject A2) will have their response measured at timepoint 2, and so forth.

The interest here is that we would like to quantify the trend of response change between every timepoint when controlling for group (disease versus control). One justification for that is pooling all of the responses and regressing over the 4 time points to run a trend analysis may result in the loss of response varaible changes that occur between timepoints since these timepoints are not equally spread, and also act as a proxy for disease state. The consequence of this is that there are some biological considerations assigned to each timepoint, and so understanding how the response changes between every sequential pairwise timepoint comparison may be of interest.

With that said, there are statistical issues that arise; one is multiple comparisons since I would be running a statistical test between every pairwise timepoint, and another is that every combination of timepoint and group (e.g. timepoint 3 with disease) consists of subjects unique to that class.

One rudimentary solution is to run a linear mixed effect model where the dataset has been partitioned to contain data between two timepoints across both disease and control. That way I can evaluate the effect of disease on the responses between two timepoints. However, this doesn't address whether this is valid, and the fact that multiple comparisons will occur as I would do this 3 times (i.e. t4-t3, t3-t2, t2-t1).

Answer 1

With only 1 observation per individual, this should be handled OK by a simple interaction model:

lm(response ~ timepoint * disease)

That allows for a separate association with outcome for each combination of timepoint and disease; there's no need to evaluate an overall linear trend if you think that's unreasonable. You then use post-modeling analysis tools to evaluate the model overall and to make specific comparisons of interest.

With that said, there are statistical issues that arise; one is multiple comparisons since I would be running a statistical test between every pairwise timepoint

You don't necessarily need to do all pairwise comparisons. It sounds like what you care about are the differences between sequential timepoint values. In the emmeans package you can do that with "consec" contrasts. That can cut down on the multiple comparisons.

and another is that every combination of timepoint and group (e.g. timepoint 3 with disease) consists of subjects unique to that class.

That's not a problem. Many designs in experimental biology involve sacrifice of animals at fixed points in time; that's conceptually the same as what you have, one observation per individual. The lack of repeated measures might give you lower power than what you would have otherwise, but there's nothing inherently wrong with that.