I'm co-investigator on a clinical trial where the we are studying the effect of an intervention. The study is powered to detect a clinically meaningful change for some primary endpoint. My questions are around the planned secondary endpoints.
There are two secondary endpoints: 1) whether or not individuals randomized in the trial were prescribed medications (in this case statins) and 2) among those who were prescribed medications, whether or not individuals adhered to those medications. The first secondary endpoint is the main one and we have decided to use a regression model to estimate the intervention effect. The latter secondary endpoint hinges on the results of the first one. The PI wants to look at whether the intervention had an effect on statin adherence among those who were prescribed. Specifically, he wants to use a regression model to do this.
My concerns are 1) by subsetting to this group, we no longer have the randomization with respect to the intervention, so that the "effect of intervention on adherence" is meaningless, and 2) in line with the first point, the underlying mechanisms may vary between the main secondary outcome and the adherence outcome. In other words, we may have many unmeasured factors. My suggestion was to keep the analysis descriptive: tabulate the binary adherence outcome by the binary intervention, and restricting the analysis to those who were prescribed medications. However, a reviewer (non-statistician) insists that we can still use regression.
Are there things that I can add in order to make a convincing case for keeping it descriptive?