Wilhelm et. al. 2016 is a meta-analysis of 23 placebo controlled beta-blocker studies. The attempt of the study was to indicate what fraction of the beta-blocker's effect was due to the placebo effect.
In a discussion with another person, a few issues have come up. First, he feels uncomfortable with the variability of the study designs for the 23 studies used. I see that as being a necessary component of the analysis, as it is seeing if different methodologies yield different results.
He claims the studies are not randomized, but they do seem to be randomly selected, just controlled for certain requirements in order to perform the moderator analysis.
The conclusion also seems reasonable: if study quality improvement yields stronger results, the logical conclusion is that the effect is real and not due to some kind of statistical noise.
Am I accidentally ignoring the flaws, or are they simply not there?