I finally found out what they're about: a guy who got pancreatic cancer. Well, he died this January (9 months ago). I have a feeling a lot of people will take those stickers off without even reflecting on their effect...that is, their lack thereof.
In one of my posts at Debunking Christianity, I looked at the question of whether or not there really is any scientific evidence that "prayer works" or a correlation between faith and health. Unsurprisingly, I found none.
The core methodology of such studies is flawed for three reasons:
1) Some studies examine how frequent churchgoing relates to health. The problem with this methodology is that the same correlation would appear between frequent football game attendance as well; anyone healthy enough to frequently attend anything that they enjoy will do so, and the more unhealthy you get, the less you will be able to attend...and so church attendance is not special.
2) Another big problem with studies designed to measure the "prayer effect" is that the people are often receiving medical care while being studied, and it is impossible to say that the prayer had an effect compared to their treatment. If you could study only patients who have exactly the same disease at exactly the same stage and receive exactly the same treatments, then you could truly control these other variables. However, it is basically impossible to control the other variables that will affect the prognosis.
3) The final problem is that it is impossible to separate people into "prayed for" and "not prayed for" groups by virtue of the fact that you'd have to ask each person and their extended families and their entire churches not to pray...and do you think that is going to work? If someone has a serious condition and is religious, they're going to stop praying for a few weeks or months? No. And so many of the people in the "not prayed for" group whose situation turns bad are lumped in as "evidence" that those who don't receive prayer are worse off...even though the people themselves as well as their families and church members were praying for them, especially if the health condition is serious, like cancer or heart disease.
And those are just the core methodology problems. In other studies, the ones cited as "evidence prayer works", the sample sizes are very small (n<20), and therefore the probability values are unimpressive: p>0.05. Whether or not you agree that the standard for statistical significance should be p<0.05, when p values approach 0.2, you have very little statistical evidence to back up a claim of a significant impact from whatever variable you're studying. But people conveniently ignore this when touting these meager studies.
In the only double blind, multi-year, multi-thousand-patient study ever conducted on the effect of prayer on health, God failed the test. Big time. Every empirical study has shown the same thing -- that nothing fails like prayer. Don't believe me? Find one documented amputee whose limb grew back from prayer. One. Ever.
Some studies purporting to support the idea that prayer works have been literally written by criminals and frauds.
Dr. Richard Sloan (M.D., not Ph.D.) has done a lot of work in examining these sorts of issues and wrote a book recently summarizing the facts -- there is no valid study supporting the idea that prayer changes anything (valid in the sense that they used a competent methodology and a large sample size and got a good p value).
On the logical side of things:
Does prayer move God to act? If yes, then God is callous/cruel, and God is not totally sovereign. If no, then God will act regardless of whether you pray or not.
If the desired goal does not happen after you pray, would you admit that God wanted things to turn out the way that they did, or do you believe that God wanted things to turn out differently? If God wanted things to turn out the way that they did, then your prayers don't matter, because God is sovereign. If God wanted things to turn out differently, then your God is weak or stupid or both.
See, God gets the credit when the desired goal occurs, but none of the blame when it doesn't.
So both from the logical and evidential sides, you really have an uphill climb in trying to show that praying for someone even makes sense.
