# how can I compare if a drug affects a biological process differently than vehicle treatment

I have an experiment where I am trying to see if a drug has a biological effect that is significantly different from vehicle. Activity is measured before and after treatment.

For treatment, I have vehicle (control treatment), drug 1 and drug 2. Vehicle has a significant effect on activity (post activity is greater than baseline). Drug 1 also has a significant effect on activity (with post activity even greater than it's baseline). Lastly drug 2 has no effect of activity (post activity is no different than baseline) I now want to compare these effects to each other. I.e. say that drug 1 increases activity even more than vehicle and that drug 2 effectively suppresses activity since it did not increase activity as seen with vehicle.

The interaction term in a mixed linear model will tell me that that these drugs have different effects on activity compared to baseline, but I want to specifically compare the change from baseline of drug 1 and drug 2 to vehicle. Do I need to run 2 models? One with drug 1 vs vehicle, and another with drug 2 vs. vehicle? I have the model's estimate of mean difference (baseline to drug or vehicle) and st error. Could I use this to do a T Test? I am using JMP if you have specific suggestions.

• Please explain vehicle treatment Jun 8, 2021 at 4:16
• vehicle treatment is a control. It is the same solution the drug is dissolved in, but without the drug. In this case, a saline solution Jun 8, 2021 at 16:35
• Please explain as an edit to the post. Is this a standard term? Jun 8, 2021 at 16:36
• this is a standard term in any field that uses drugs for a treatment. I will edit the post. Jun 9, 2021 at 15:21

$$Y_{post} = \alpha + \beta_1 Y_{pre} + \beta_2 drug1 + \beta_3 drug2 + \epsilon$$
The coefficients for drug1 and drug2 will represent the difference in $$Y_{post}$$ between that treatment and vehicle, adjusted for baseline $$Y$$.
$$Y_{post} - Y_{pre} = \alpha + \beta_1 Y_{pre} + \beta_2 drug1 + \beta_3 drug2 + \epsilon$$