Absolute and relative measures – what’s the difference?

I’m re-working a paper on risk relativism in response to some reviewer comments, and also preparing a talk on the topic for Friday’s meeting at KCL, “Prediction in Epidemiology and Healthcare”. The paper originates in Chapter 8 of my book, where I identify some possible explanations for “risk relativism” and settle on the one I think is best. Briefly, I suggest that there isn’t really a principled way of distinguishing “absolute” and “relative” measures, and instead explain the popularity of relative risk by its superficial similarity to a law of physics, and its apparent independence of any given population. These appearances are misleading, I suggest.

In the paper I am trying to develop the suggestion a bit into an argument. Two remarks by reviewers point me in the direction of further work I need to do. One is the question as to what, exactly, the relation between RR and law of nature is supposed to be. Exactly what character am I supposing that laws have, or that epidemiologists think laws have, such that RR is more similar to a law-like statement than, say, risk difference, or population attributable fraction?

The other is a reference to a literature I don’t know but certainly should, concerning statistical modelling in the social sciences. I am referred to a monograph by Achen in 1982, and a paper by Jan Vandebroucke in 1987, both of which suggest – I gather – a deep scepticism about statistical modelling in the social sciences. Particularly thought-provoking is the idea that all such models are “qualitative descriptions of data”. If there is any truth in that, then it is extremely significant, and deserves unearthing in the age of big data, Google Analytics, Nate Silver, and generally the increasing confidence in the possibility of accurately modelling real world situations, and – crucially – generating predictions out of them.

A third question concerns the relation between these two thoughts: (i) the apparent law-likeness of certain measures contrasted with the apparently population-specific, non-general nature of others; and (ii) the limitations claimed for statistical modelling in some quarters contrasted with confidence in others. I wonder whether degree of confidence has anything to do with perceived law-likeness. One’s initial reaction would be to doubt this: when Nate Silver adjusts his odds on a baseball outcome, he surely does not take himself to be basing his prediction on a law-like generalisation. Yet on reflection, he must be basing it on some generalisation, since the move from observed to unobserved is a kind of generalising. What more, then, is there to the notion of a law, than generalisability on the basis of instances? It is surprising how quickly the waters deepen.

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