Usedto,
Can you give me an estimate of what you mean by 'far, far more'?
10x more? So 9 not reported for every 1 reported?
100x more? So 99 not reported for every 1?
1000 x more? 999 not for every one reported?
10,000 x more? 9,999 not for every 1 reported?
I did explain why even quite dramatic under-reporting / under-acknowledgement (even 1000 x more than reported) may not actually sway the argument for / against vaccination.
So if the difference between 2 different risks is e.g. 1 in 2 vs 1 in 3, under-reporting even of 1 case in 3 has a dramatic effect on the conclusion as to which risk is greater.
If Risk A is 1 in 10, and risk B is 1 in 100, risk B has to be much more under-reported for it to actually be the greater risk.
If the 'official statistics' give risk of significant harm for measles + mumps + rubella to be 1 in 50, and risk of significant harm from the MMR vaccine to be 1 in 20,000 (both figures plucked out of the air, as they are just to illustrate my point), then if every case of harm from the diseases is accurately reported, there have to be 399 unreported cases of vaccine harm for every one reported in order for the risks to be equal.
So rather than saying 'I can't do any analysis because I believe that 1 of the statistics has an error in it [this is of course not the case - all the figures will have errors - the point is that you believe one to have a much larger error than the others]', you can do the anslysis as if you believe them to have no errors, and then compare the result with what you believe the error to be.
If the magnitude of the error would have to be unfeasibly large to make vaccination the riskier option (so if you believe that under-reporting is perhaps 100 cases unreported per reported case, but the difference between the probabilities is 10,000x) then vaccinate.
If the magnitude of the error required to reverse the conclusion s sufficiently small, based on your hunch about under-reporting (so e.g. 100 cases unreported per reported case and the difference between the probabilities is 100x, or even 1000x) then it is reasonable to say that the two risks are comparable (or that not vaccinating is safer) and to decide to take the risk of not vaccinating.