foolysh - you make some respectable points about statistics. The supposed 'gold standard' of research is the randomised contolled trial - the RCT - which assigns people blindly (ie neither they nor their carers nor the administrators of the trial know what's happening) to one group or another (control or intervention). Problem is, this is not ethical - you cannot order someone not to breastfeed their own baby for the sake of research. It is also not possible - it is very obvious to the mother whether she is or is not breastfeeding
So breastfeeding/formula feeding research cannot go with the RCT....but RCTs are not the only way to go. You can do perfectly respectable retrospective research if the samples are big enough. That means getting many mothers/babies and tracking what they have done, or asking what they have done, vis a vis feeding. There are ways of ensuring the study is 'powered' enough ie has enough recruits, to allow you to control for variables....so you control for socio-economic factors, birthweight, whatever, so they are not allowed to affect your results. This allows you to ensure that what you are looking at is feeding method, not (inadvertently) age/education/poverty/professional status whatever of the parents.
Smoking is an example of how you cannot do an RCT (how can you order someone to smoke for 30 years just so you can check his health out later?) and yet the epidemiological and clinical research is good enough for no one to argue any more that linking it to ill health is spurious - although in the early days, this was certainly done.
I know you prob know all this - just showing you I do too, so you'll accept what I next say
You're wrong in assuming these large studies on feeding are not done. There are many, many studies with hundreds and thousands of subjects. There are a couple of on-going large studies in the UK - one in Dundee, one in Avon - which every time they report on breastfeeding (in peer reviewed journals) add to or confirm our understanding of how infant feeding has a measurable long and short term health impact.
I think the literature on infant feeding is pretty robust, and stands up to scrutiny. There are many types of research available to use - just not the RCT.