## from statistical evidence to evidence of causality

**I** took the opportunity of having to wait at a local administration a long while today (!) to read an arXived paper by Dawid, Musio and Fienberg on the−both philosophical and practical−difficulty to establish the probabilities of the causes of effects. The first interesting thing about the paper is that it relates to the Médiator drug scandal that took place in France in the past year and still is under trial: thanks to the investigations of a local doctor, Irène Frachon, the drug was exposed as an aggravating factor for heart disease. Or maybe the cause. The case-control study of Frachon summarises into a 2×2 table with a corrected odds ratio of 17.1. From there, the authors expose the difficulties of drawing inference about causes of effects, i.e. causality, an aspect of inference that has always puzzled me. (And the paper led me to search for the distinction between odds ratio and risk ratio.)

“And the conceptual and implementational difficulties that we discuss below, that beset even the simplest case of inference about causes of effects, will be hugely magnified when we wish to take additional account of such policy considerations.”

**A** third interesting notion in the paper is the inclusion of counterfactuals. My introduction to counterfactuals dates back to a run in the back-country roads around Ithaca, New York, when George told me about a discussion paper from Phil he was editing for JASA on that notion with his philosopher neighbour Steven Schwartz as a discussant. (It was a great run, presumably in the late Spring. And the best introduction I could dream of!) Now, the paper starts from the counterfactual perspective to conclude that inference is close to impossible in this setting. Within my limited understanding, I would see that as a drawback of using counterfactuals, rather than of drawing inference about causes. If the corresponding statistical model is nonindentifiable, because one of the two responses is always missing, the model seems inappropriate. I am also surprised at the notion of “sufficiency” used in the paper, since it sounds like the background information cancels the need to account for the treatment (e.g., aspirin) decision. The fourth point is the derivation of bounds on the probabilities of causation, despite everything! Quite an interesting read thus!

December 25, 2013 at 7:07 am

Inferring causality through a “statistical” argument is a strange beast. Though counterfactual reasoning is (thanks to Rubin) the standard approach for introducing medical researchers to the notion, I find Judea Pearl’s approach more general/comprehensive (and interestingly enough he was was led it to it from the earlier Bayesian nets days!).

So the next time you are stuck in an administration queue you may want to read his survey: http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf

Or if the (exponentially distributed?) waiting time in French queues is shorter than the Greek ones, a short paper (with historical references!) on odds ratios, relative risks and hazard ratios: http://www.ncbi.nlm.nih.gov/pubmed/12393077

Mary Xmas and a Happy New Year

December 24, 2013 at 2:32 pm

Have you seen Andrew’s paper on Cause of Effects? It may interest you. http://andrewgelman.com/2013/11/11/ask-forward-causal-inference-reverse-causal-questions/

Merry xmas and happy new year!

ps.: Maybe the comment above is by someone who don’t know English well?

December 24, 2013 at 3:00 am

Well for Causality that is a huge thing in Demographics and Geography, what off about it is that it takes qualitative factors and convert them as best as they can to Quantitative. A lot of time though it goes exactly into the way you have described it. As a ratio, a lot of times I would use ratios to compare the models. Ratio’s have helped me simulate certain events. In my opinion, Causality is an odd way of doing stats but u have to. For philosophy, they use causality all the time like if A+B=C then C-B=A. This is true but I’m trying to show an example to what your referring to. It’s interesting you talk about this because my colleague from the Congo had talked about a mathematics vs chemistry paradox, like we all know 2+2 =4 and we all know Blue and Yellow make Green. These qualitative factors are a lot more like the chemical side to statistics.

December 24, 2013 at 9:21 am

What is this about?! Sounds like spam but with enough connections to the topic to make me wonder. If so those robots are getting much better!