Hi,

I'm investigating changes in gene expression after a body weight loss intervention. The data includes baseline measurements and two follow-up measurements. The 40 participants have varying body weights at baseline, and they lose varying amounts of body weight during the study. My main model (see m1 below) has the standard structure used in this scenario. However, because the participants start with different body weights and lose varying amounts of body weight, I would additionally wish to model the intervention "effect" using the percentage of lost body weight from baseline to the specific visit as the explanatory variable. To achieve this aim, I ended up with a model (see m2 below), but I'm unsure whether it is applicable to answer my question.

I would greatly appreciate any help and/or suggestions.

Best, Jari

# covariate data
participant <- factor(rep(1:4, each = 3))
visit <- factor(rep(c("bl", "fup1", "fup2"), times = 4), levels = c("bl", "fup1", "fup2"))
wlp <- c(0, -7, -15, 0, -12, -24, 0, -6, -13, 0, -9, -18)

# model 1, standard time effect (using contrast to compare fup1 and fup2 afterwards)
m1 <- model.matrix(~ 0 + participant + visit)
colnames(m1)

# model 2, "intervention effect" by body weight loss percentage
m2 <- model.matrix(~ 0 + participant + visit:wlp)
m2 <- m2[,-5] # remove "visitbl:wlp" column (redundant)
colnames(m2) <- gsub(":", "_", colnames(m2))
colnames(m2)

Adding wlp into the model will be of limited value because, from the data you show, the weight losses are very consistent between participants and wlp is almost entirely confounded with visit.

You don't explain the reasoning by which you ended up with model m2, but it has too many terms in it and it does not test the hypothesis you want. [Edit later: I see from your comment below that model matrix m2 has the same number of columns as m1 once a column is manually removed, but it still doesn't seem a logical model to me. I don't see any motivation for an interaction model in this scientific context.]

You can try the two alternative models:

m1 <- model.matrix(~ participant + visit)
m2 <- model.matrix(~ participant + wlp)

If the second model gives just as much DE as the first, then that is evidence that expression changes between visits are largely explained by the weight loss.

If the participants vary a lot in terms of weight loss (more than in the toy data that you show), then you could also try

m3 <- model.matrix(~ participant + visit + wlp)

in order to check whether there are visit effects that are not explained by weight loss. Beware though that you need to be very careful in interpeting this model because wlp is almost entirely confounded with visit. This model can only be used to test the hypothesis that I mentioned. It is not suitable for general assessment of differential expression because the two predictors visit and wlp will interfere with each other and mask each other's effects.