Sensitivity Analysis 

 Observational studies, however well done, remain exposed to the problem of unobserved confounding. In response, methods of formal sensitivity analysis are growing in popularity these days (see Jens's post on a related issue  here .) 
  
Rosenbaum and Rubin's basic idea  is to hypothesize the existence of an unobserved covariate, U, and then to recompute point-estimates and p-values for a range of associations between this unobserved covariate and, in turn, the treatment T and the outcome Y.  If moderate associations (= moderate confounding) change the inference about the effect of the treatment on the outcome we question the robustness of our conclusions.  

 But how to assess whether the critical association between U, T, and Y that would invalidate the standard results is large in substantive terms?  


 One popular strategy compares this critical association to the strength of the association between T, Y, and an important known (and observed) confounder. For example, one might say that the amount of unobserved confounding it would take to invalidate the conclusions of a study on the effect of sibship size on educational achievement would have to be at least as large as the amount of confounding generated by omitting parental education from the model.  

 This is indeed the strategy used in a few studies.  But what if U should be taken to stand not for a single but for a whole collection of unobserved confounders? Clearly, it then is no longer credible to compare the critical association of U with the amount of confounding created by a single known covariate.  Better to compare it to a larger set of observed confounders. But with larger sets of included variables, we have the problem of interactions between them, and of surpressing and amplifying relationships.  In short, gauging the critical association of U with T and Y in substantive terms will become a whole lot less intuitive. 

 (FYI, Robins and his colleagues in epi have proposed an alternative method of sensitivity analysis, which hasn’t found followers in the social sciences yet, to my knowledge.  I’m currently working on implementing their method in one of my projects.)