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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.

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    $\begingroup$ Please explain vehicle treatment $\endgroup$ – kjetil b halvorsen Jun 8 at 4:16
  • $\begingroup$ 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 $\endgroup$ – Robert C Spencer Jun 8 at 16:35
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    $\begingroup$ Please explain as an edit to the post. Is this a standard term? $\endgroup$ – kjetil b halvorsen Jun 8 at 16:36
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    $\begingroup$ this is a standard term in any field that uses drugs for a treatment. I will edit the post. $\endgroup$ – Robert C Spencer Jun 9 at 15:21
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A simple ANCOVA model should do what you need here. I.e.,

$Y_{post} = \alpha + \beta_1 Y_{pre} + \beta_2 drug1 + \beta_3 drug2 + \epsilon$

The coefficients for drug1 and drug2 will represent the difference in $Y_{post}$ between that treatment and vehicle, adjusted for baseline $Y$.

This model is identical and will tell you the effect of each drug on change in the outcome (relative to vehicle):

$Y_{post} - Y_{pre} = \alpha + \beta_1 Y_{pre} + \beta_2 drug1 + \beta_3 drug2 + \epsilon$

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