# Analysis of pre-post treatment data with changes over time

I am working on a project that used the following design:

I have gene expression data (>20000 genes) collected at 6 time points in 16 participants during over a certain time period. Next, they underwent some kind of intervention for a few days and then gene expression data was collected again at the same 6 time points. During the intervention period, half of the participants were exposed to a treatment (treatment group), the other half wasn't (control group).

What would be an appropriate statistical approach to analyse these data? I'm interested in the change in the expression levels of each gene over time and how this is affected by the intervention and by the treatment.

I have been thinking about several mixed modelling approaches, but I don't think any of them is optimal:

• Creating a dummy variable "Intervention" with intervention=0 at baseline and intervention=1 after intervention and another variable "treatment" with treatment=0 at baseline in both groups and in the control group after the intervention and treatment=1 in the treatment group after the intervention. The model would be: Expression ~ Intervention*Time+Treatment*Time + (1|Subject) (i.e. subject as random effect)

• Creating a dummy variable "Condition" with Condition = baseline at baseline; Condition=InterventionControl after the intervention in the control group and Condition=InterventionTreatment after the intervention in the treatment group. The model would be: Expression~Condition*Time + (1|Subject)

I have been looking at other PRE-POST question on this website (e.g. Best practice when analysing pre-post treatment-control designs) , but I believe the additional time effect in this experiment makes it more complicated than those examples. Any advice would be very much appreciated.