It's an interesting idea that research and statistics will change behaviour, or that hard hitting adverts will make people think twice. In the UK at least many many people deeply distrust the government and public health as a result of the way that the BSE/vCJD was communicated/managed and the MMR/Wakefield affair. That means that no matter how much information is given, it may well be ignored because it isn't trusted. Even when there is a very direct link between the adverse effect of something (smoking being the best example) it doesn't mean that when you know something is good/bad that your behaviour will change - think of how many mothers smoke when pregnant, or who manage to give up when pregnant and then start again.
Public campaigns are very crude tools, and they have to be carefully applied. Also given that many of the mothers having babies were not breastfed themselves and that most of them are in good health, it really isn't that intuitive that ff is bad, and I think ramming it down people's throats would be really ineffective. Except perhaps for HVs.
Providing research evidence more generally to more people is an excellent idea, but it would also mean teaching critical appraisal skills to everyone, as the way that research is presented can be very difficult to decipher. I studied critical appraisal as part of my Masters in Public Health, and it was one of the hardest course I've ever taken. Well worthwhile though.
So looking at the leukemia study (you can read the whole paper, which is excellent) the first thing to bear in mind is that whilst there may be a protective effect (longer breastfeeding having a stronger effect is a good indicator), in terms of absolute numbers that effect is fairly tiny. So from the US Leukemia & Lymphoma Society, there is an estimate that in 2009, 3,509 children under the age of 15 will be diagnosed with leukemia throughout the United States, the equivalent number for the UK is about 500 a year (from the Children with Leukemia website). So a 21% reduction in risk when the risk is 0.00005 (46.1 cases in every million) is on an individual basis somewhat meaningless. That's not to say it might not be an important finding, and help to understand more about leukemia (which given that the cause is unknown is particularly important).
Thinking about Brahms point this is an observational study, the mothers were asked a large number of retrospective questions by telephone, and the controls were only matched for age on diagnosis, race (white/non-white) and geography (all participants were from the US/Canada). All parents had to be English speaking and have a home phone, so that would have some equalising effect. They did however adjust their analysis for education, race and family income. The other thing that struck me is that the numbers of ever breastfed in each group were not that dissimilar (% of ever breastfed in the control group 55%:48% never breastfed) although in statistical terms 7% is not to be sniffed at (and obviously significant). It looks like a fairly decent study, and the authors do discuss recall bias, selection bias, chance findings etc) and there is also an interesting discussion as to why breastfeeding might be protective.
However, there is a more recent meta-analysis goliath.ecnext.com/coms2/gi_0199-3465797/Breastfeeding-and-the-risk-of.html which includes a couple of large cohort studies (these are more reliable as they are longitudinal studies and suffer from less bias, although again observational) and these show no correlation. The conclusion drawn this time is that the relationship is probably very complicated. It's a good piece if anyone is interested, quite readable. For me the trouble is that what tends to get reported from research is a few cherry picked figures rarely presented in proportion, and data complications are rarely mentioned at all.
I do think that breastfeeding brings many benefits for both mother and child, but threatening people with cancer if they don't isn't a good approach (especially when it's really not true).