I wouldn't worry much about the effects on statistical power. In multi-level models looking at a level 2 (in your situation, person) intervention effect, the power is much more sensitive to the number of people than the number of observations per person. Also, you are not actually eliminating observations the way you have been doing it: you still have a separate observation for each of the 8 baseline days--you just don't distinguish among them in the modeling. So the real issue is a modeling issue. By treating days -7 through 0 as being equivalent in the modeling, you are positing model in which "nothing happens" during those baseline days. So the question is whether or not that is a reasonably realistic assumption. Presumably the patients know they are in a study and so there may be some "anticipation effects" whereby they change relevant behaviors in advance of starting their intervention. But maybe those truly are negligible. Or perhaps in your design they don't actually know ahead of time when the intervention will start. The issue is whether the modeling assumption is a reasonable reflection of real-world circumstances.
That said, if you want to use autoregressive residuals, I think you can have your cake and eat it too. As far as I know, there is nothing that requires that the variable specified for grouping residuals also be a covariate in the model. So you can still have rx_time be the variable in the equations of the regression, but use -residuals(ar1, t(days))-. Well, that is, you could were it not for the fact that the -t()- variable must be non-negative. But that has an easy fix: -gen d7 = days + 7- and then use -residuals(ar1, t(d7))-.
I have never actually done this myself, and I don't have a handy data set in which to try it out to make sure this works, but my understanding of the -melogit- command and how its options works lead me to believe this will work.
That said, if you want to use autoregressive residuals, I think you can have your cake and eat it too. As far as I know, there is nothing that requires that the variable specified for grouping residuals also be a covariate in the model. So you can still have rx_time be the variable in the equations of the regression, but use -residuals(ar1, t(days))-. Well, that is, you could were it not for the fact that the -t()- variable must be non-negative. But that has an easy fix: -gen d7 = days + 7- and then use -residuals(ar1, t(d7))-.
I have never actually done this myself, and I don't have a handy data set in which to try it out to make sure this works, but my understanding of the -melogit- command and how its options works lead me to believe this will work.
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