I want to use a multiple logistic regression to model the relationship between two experimental groups (test and control) and accuracy of a procedure, controlling for the experience (in years) of the participants.
outcome ~ group + experience
The design I am using is paired in the sense that every participant is tested twice, so there are no differences in baseline characteristics between groups (since they are the same individuals). If I was only testing for differences in time, a paired t-test would suffice, but I need to control for experience, hence a regression model is being built.
Time is measured in seconds until the procedure is completed, and accuracy is defined as completing it within a pre-specified threshold (the outcome is 1 if less than or equal to 6 minutes and 0 otherwise). It is expected that time and experience are negatively correlated or, experience practitioners are expected to take less time to complete the procedure.
I would like to test for interactions in this model, but I don't think it makes much sense to interact the group with experience.
outcome ~ group * experience
I am considering including time in the model and test for interaction with experience.
outcome ~ group + experience*time
Since time is used in the definition of the response of the logistic model I expect it to be significant even with a small sample size. However it seems to me that including time in this model would be circular reasoning.
outcome ~ group*time + experience
Q1: Is this a correct interpretation?
Q2: If I try interactions between time and the group instead, would that tell me that time is modifying the effect attributed to the group?
Q3: Does it make sense to test for interactions between experience and group in this setting?
EDIT: I understand Douglas Altman's point of that, while unnecessary dichotomization of a continuous variable is prevalent in medical research, it leads to loss of estimate precision (at the very least). I was able to make the case for a linear model of
time ~ group + experience for this experiment as a secondary endpoint, but the main goal needs to remain being accuracy, which is why the outcome is a dichotomization of time. This practice is prevalent for a reason :)