I dispute none of this, but so far as I can tell or guess, the main thing powering the superior statistical strength of PatientsLikeMe is the fact that medical researchers have learned to game the system and use complicated ad-hoc frequentist statistics to get whatever answer they want or think they ought to get, and PatientsLikeMe has some standard statistical techniques that they use every time.

1) I'd like to see independent evidence of their "superior statistical strength".

2) On the face of it, the main difference between these guys and a proper clinical trial is an assumption that you can trust self-reports. Placebo effect be damned.

In particular, I'd really, really like to see the results for some homeopathic "remedy" (a real one, not one of those that silently include real active compounds).