A simple question I hope.
I have an experimental design where I measure some response (let's say blood pressure) from two groups: a control group and an affected group, where both are given three treatments: t1, t2, t3. The data are not paired in any sense.
Here is an example data:
set.seed(1) df <- data.frame(response = c(rnorm(5,10,1),rnorm(5,10,1),rnorm(5,10,1), rnorm(5,7,1),rnorm(5,5,1),rnorm(5,10,1)), group = as.factor(c(rep("control",15),rep("affected",15))), treatment = as.factor(rep(c(rep("t1",5),rep("t2",5),rep("t3",5)),2)))
What I am interested in is quantifying the effect that each treatment has on the affected group relative to the control group. How would I model this, say using an linear model (for example lm in R)?
Am I wrong thinking that:
lm(response ~ 0 + treatment * group, data = df)
which is equivalent to:
lm(response ~ 0 + treatment + group + treatment:group, data = df)
is not what I need? I think that in this model the treatment:group interaction terms are relative to the mean over all baseline group and baseline treatment measurements.
I therefore thought that this model:
lm(response ~ 0 + treatment:group, data = df)
is what I need but it's quantifying each combination of treatment and group interaction terms: treatmentt1:groupcontrol treatmentt1:groupaffected treatmentt2:groupcontrol treatmentt2:groupaffected treatmentt3:groupcontrol treatmentt3:groupaffected
So perhaps this model:
lm(response ~ 0 + treatment + treatment:group, data = df)
is the correct one?
Although in addition to quantifying each combination of treatment and groupaffected interaction term it's also quantifying the effect of each treatment. I'm not sure what is the baseline each of the treatment and groupaffected interaction terms are compared to in this model.
Help would be appreciated.
Also, let's say I ran a fourth treatment which is actually the combination of two treatments, say t1+t3, where I don't know what the expectation of their combined effect is: additive/subtractive or synergistic. Is there any way this can be combined?