Question regarding repeated measures mixed models in R I have set out to do a linear mixed model on a repeated measure data set. Overall patients received a drug at different time points and peaks were measured afterwards. I use the lmer package in R
I've made a linear mixed model allowing for the patients as a random factor:
Outcome~Concentrations+(1|pt_id)

However I have doubts as to how to account for the time aspect. Being a clinical trial, not all sampling times are equal, so I guess I should take that into account as well. So the concentration will be affected by the sampling time.
I was thinking something like this:
Outcome ~ Concentrations + (sampling_time|pt_id)

But, I do not know how to catch the effect of the time in the concentration peaks.
Would something like this catch the effect?
Outcome ~ Concentrations + sampling_time + (Concentrations:sampling_time|pt_id)

And should there perhaps be an interaction between Concentrations and sampling_time in the model? As to something like
Outcome ~ Concentrations*sampling_time + (Concentrations:sampling_time|pt_id)

Any suggestions are welcome!

A few points and comments:
The model:
Outcome ~ Concentrations + (sampling_time|pt_id)

does not make sense because sampling_time is a random slope here, but there is no fixed effect for it. This is very rarely what you want because it implied that the overall (fixed) effect of the variable is zero. Moreover, your research question seems to specifically require sampling_time as a fixed effect.
The model:
Outcome ~ Concentrations + sampling_time + (Concentrations:sampling_time|pt_id)

does not make sense because you are fitting random slopes for the interaction between Concentration and sampling_time, yet you don't include this interaction as a fixed effect, so as per the last comment, this implies that the overall/fixed effect of the interaction is zero. Moreover, I find it hard to understand why it would make sense to specify an interaction as a random slope but not the main effects. This means that you think the interaction varies by patient, but the main effects do not.
The models:
Outcome ~ Concentrations + sampling_time + (Concentrations:sampling_time|pt_id)

and
Outcome ~ Concentrations*sampling_time + (Concentrations:sampling_time|pt_id)

do not make sense for the same reasons as above.
Based on the description, an appropriate model would be:
Outcome ~ Concentrations*sampling_time + (1|pt_id)

