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In my current research (randomised, placebo control trial) I'm investigating an effect of two interventions (Intervention 1 - low dose of dietary supplement, Intervention 2 - high dose of dietary supplement) on cardio-metabolic characteristic (DV) measured on two occasions 12 weeks apart. In addition, I have a covariate - say some gut bacterial abundance, which is measured on the same two occasions which can be treated as both time-invariant (only baseline abundance) or time-varying covariate.

One of the hypothesis is whether bacterial abundance modulates an effect of the intervention on DV. To this end I'm planning the following

Model1
mod0 <- lme(DV ~ Intervention * Time + Abundance_baseline + 
            (1 | subject), REML = F, data)
mod1 <- lme(DV ~ Intervention * Time * Abundance_baseline + 
            (1 | subject), REML = F, data)
lrtest(mod0, mod1)

and

Model2 
mod0 <- lme(DV ~ Intervention * Time + Abundance + 
            (1 | subject), REML = F, data)
mod1 <- lme(DV ~ Intervention * Time * Abundance + 
            (1 | subject), REML = F, data)
lrtest(mod0, mod1)

Question 1: Are those models correct regarding my hypothesis?

Question 2: My intention is to capture an effect of the change in bacterial abundance on Intervention*Time interaction by using the time-varying covariate. Does it make sense?

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