I haven't read the study, but think your assumptions about the statistics are too hasty.

You say "if the sample estimate for the old is +14%, for the young, -30%, if the difference is noise, the +14% is certainly noise," but this is not necessarily true. For example, what if the standard error for the old is 5% and the standard error for the young is 40%? Then the difference between the groups is statistically insignificant, while the 14% is statistically significantly different from zero.

Such a situation may be more likely than you think. One obvious way to get this is if the sample contains a lot more old than young, which seems unlikely. But remember what we are trying to estimate is the *ratio* between the probabilities of heart disease in the treated and untreated groups, or Pt/Pu.

It seems likely that heart disease is much more prevalent in the older group than in the younger, for both treated and untreated. This means that the ratio estimator Pt/Pu will be estimated more precisely for the old than for the young, even if the sample sizes are the same. (This is so even though both Pt and Pu are estaimated more precisely in an absolute terms for the young, because the Pu in the denominator is closer to zero and so the ratio is more sensitive to errors in Pu.) Do the math and I think you'll agree that I am right.

Therefore the idea that the estimated ratios have the statistical properties claimed by the researchers is actually plausible.