This is always an interesting thing to me. First, I have experience with this stuff, on both sides of the 12-step fence.
To dispel one myth though: as there's no one in charge in 12 step programs, no one to answer to, the idea that one has to do anything to be a "member", including belief in some "higher power" or any variation on that theme is demonstrably false. There's plenty of atheists in AA, and plenty of atheist and agnostic meetings listed in the meeting directories for reference. The prayers are not at all meetings, not any more than traditional, and when people opt out of such, no one even blinks an eye. Just sayin'.
As for efficacy...
It's difficult to get hard data in a program that's anonymous. That's always one problem with the "data" that's shown. As there's no membership list, no one in charge (as aforementioned), it would be difficult to organize any cooperation in this way. Also don't know anyone that's actually been polled/interviewed about such information.
What I think is more relevant though, is that we want to measure it's efficacy- and this needs to be defined. Is it defined as "permanent abstinence from ETOH"? From drugs and alchohol? Prescriptions? How about psych meds? How about periods of abstinence? How about those that switch to activity addictions (gambling, sex, food...)?
Let's say simply that we've defined "recovery" as permanent abstinence from all "illicit" drugs and alcohol. The prescription for this in 12-step programs... is the 12-steps. So, anyone polled/interviewed would have to have completed the 12-steps no? We wouldn't determine the efficacy of the latest and greatest non-SSRI if the patient was non-compliant with the regime, no?
Where I'm going with this last thing is that I see a huge (well, total, that I'm aware of by personal experience... FWIW) efficacy of "recovery" for those that have completed the 12-steps. This is anecdotal of course, but no one I know ignores their own experience. Not advocating that this is the only way by any stretch, but that in terms of it's efficacy what I believe is overlooked is whether or not the treatment has truly been tried. Have seen people maintain this narrow definition of recovery thru individual therapy, churches, a couple other places. That though (simply defining recovery as permanent abstinence from _____, I have some concerns about, but that's another thread.