In a paper on cluster investigations, the authors make this interesting comment on what we usually call 'chance':

True randomness probably does exist in the sub-atomic world of quantum
physics; however, for the problems that epidemiologists
address, chance is more a reflection of the limits
of human knowledge. [...] chance is a
pragmatic way of describing the accumulation of many small variations
for
which it is either economically feasible nor
worthwhile to uncover the causes.

Well said!

The authors point out that you need to look for a mechanism - a plausible exposure - to link the cases.That's how genuine clusters were uncovered - angiosarcoma of the liver, vaginal adenocarcinoma and so on.

This chimes with a point made in Nate Silver's book 'The Signal and the Noise' (which incidentally would make an excellent holiday read when you have time. The whole book is brilliant but it's worth it just for the story about Gary Kasparov versus the computer in chapter 9.)

Silver points out that you can find statistical correlations for all sorts of weird and wonderful things. But they are only useful for predicting the future, only reveals an underlying truth, if you can see how the correlation works, why the one drives the other. From 1967 - 1997, which team won the Superbowl predicted whether the stock market would rise or fall, with a P value of 0.000005. But there's no logic to that, and after 1997 the correlation fell apart. House prices, on the other hand, do have a logical link to the stock market and so give a more reliable indication.

I guess we call this 'triangulation' - bringing other information or knowledge to bear when trying to interpret a statistic. It's also relevant when trying to decide whether a hospital with a high mortality rate really is a poor performer - you need more than just the statistics.

A couple of other things:

1. This paper comes from the point / counter point series of the International Journal of Epidemiology so there are some interesting responses.

2. This is quite a sophisticated line of argument. In an exam, first state accepted wisdom and only then, if you feel like it, go on to describe Coory and Jordan's suggestions.