Unobservable Quantities in Competing Risks 

 As I remarked in an earlier entry, some researchers are troubled by the potential outcomes framework of causality because it makes explicit reference to unobservable quantities. The implication, of course, is that science should stick to what’s observable.   

 This position strikes me as needlessly restrictive. In any case, unobservble quantities are by no means exclusive to the potential outcomes framework of causal inference.  


 I hasten to add, of course, that I’m a stranger to the philosophical discourse on the issue.  Interestingly, A.P Dawid has advanced the argument that many results from the potential outcomes framework of causality can be obtained without reference to unobservable quantities by sticking to conditional probabilities.  Doing that, however, the math gets quite bit uglier than in the standard potential-outcomes way of presenting these results. Not coincidentally, I suppose, this is why some statisticians like Jamie Robins stress the pedagogic and heuristic value of thinking in potential outcomes, which appears to be uncontested even among those with philosophical objections to causal inference.  

 Heuristics aside, I’m a bit at a loss over the steadfast opposition to dealing with unobservable quantities in certain quarters.  Didn’t we ditch the insistence on (and belief in) direct observation with the Wiener Kreis? And don’t references to unobservable quantities suffuse the way we think? Take, for example, the irrealis, or hypothetical subjunctive mood in English (If my wife were queen of Thebes…). Or, even more glaringly, the Konjunktiv II mood in German.  Is the notion of potential outcomes really such a stretch? 

 Interestingly, unobservable quantities also pop up in other areas of statistics, not just in causal inference. Competing risk analysis, a branch of survival analysis, has been dealing in unobservables more or less since its inception in the 1960s. Within the first two or three pages of any treatment of competing risk analysis, the authors will discuss the interpretation of risk specific failure times, hazards, and survival functions. The most popular interpretation of risk specific survival times is “the time a case would fail due to this risk, if it hadn’t failed due to some other risk before.?  An unobservable eventuality if I’ve ever seen one. 

 This is not to say that everybody is happy with this interpretation. Kalbfleisch and Prentice (2002), for example, in what’s easily the most authoritative text on survival analysis, ban this interpretation to a supplementary section because they want to “consider primarily statistical models for observable quantities only and avoid reference to hypothetical and unobserved times to failure? (p.249). Too bad. But even they seem to consider the interpretation a helpful heuristic.