You realize that the authors think that the ascorbate molecule is their active ingredient, right?

Not really relevant. Let’s say the authors modify the study as you suggest and use sodium chloride as the active ingredient. Now let’s say no difference is observed between the placebo group and the test group. Does that mean sodium is effective or ineffective? You can’t say without having a true control group to compare against. You’re basically saying “I would be more ok with this study if it was totally useless.”

> Does that mean sodium is effective or ineffective?

This comment misidentifies what the authors see as the active ingredient. They are not trying to study sodium. They are trying to study ascorbate. If you want to study ascorbate, then also giving sodium to one group and not the other will confound your interpretation of the results, as it does here.

> Let’s say the authors modify the study as you suggest and use sodium chloride as the active ingredient

That is not, at all, my suggestion. The authors have identified the active ingredient they want to test. Their test, however, was imbalanced in other ways. I am pointing out that imbalance.

In a placebo trial, it’s very important that the placebo be statistically independent from the treatment group. You’re basically saying you would change the study so the placebo and control were not independent distributions. That would make the study worthless. I don’t know what else to say other than that you have no idea what you’re talking about. No where did the authors say they’re only studying ascorbate. They explicitly say they’re studying a treatment regime of sodium ascorbate. If you want to study only sodium, then run a RCT with only sodium chloride. Comparing sodium chloride to sodium ascorbate is not the way to study the effect of sodium.

> In a placebo trial, it’s very important that the placebo be statistically independent from the treatment group.

Statistical independence has nothing to do with our conversation, which is about designing an appropriate set of comparator groups to enable valid inference about the hypothesis.

I’m afraid I don’t have time to continue a discussion where we have to pretend that the authors - who have identified sodium as a confounder for their hypothesis - actually wanted to study sodium.

Statistic independence has everything to do with it. If your control and treatment groups are not independent, you can’t differentiate a case where both groups experience an effect vs. both groups experiencing no effect. Please explain how that would work in your experiment.