Censoring or Truncation Due to ``Death":  What’s the Question? 

 A few weeks ago, Felix Elwert gave a bang-up presentation at the Wednesday seminar series on the effect of cohabitation on divorce rates (see  here ).  One of the most interesting points I took away from the discussion was the following:  in some social science situations in which a treatment is followed by an intermediate outcome, then by a final outcome, we might be interested in different causal questions.  One causal question is the effect of the treatment on the final outcome; this is commonly called the intention-to-treat effect (ITT).  The name comes from, I believe, an encouragement design context; the treatment is an encouragement to, say, get a vaccine, the intermediate outcome is whether a test subject gets a vaccine, the final outcome is whether the test subject gets a disease, and the ITT is the effect of encouragement on disease rates. 


 A second causal question different from the ITT is the effect of the intermediate outcome on the final outcome; in the vaccine example above, the question here would be the effect of the vaccine on disease rates. 

 Felix’s point was that if we think of cohabitation as the treatment, marriage as the intermediate outcome, and divorce as the final outcome, there are different causal questions we might want to ask.  Those of us steeped in a principal stratification and a truncation due to ``death" way of looking things might jump to the conclusion that the idea of divorce makes no sense for people who don’t get married.  Thus, the only ``right" way to look at this situation, we might say, is to isolate the set of people who would get married regardless of cohabitation (the treatment).  Not so.  If what we’re really interested in is avoiding divorce  per se  (maybe because divorce is stigmatizing, more stigmatizing than not ever having been married), then perhaps we don’t care whether people avoid divorce by not getting married or avoid divorce by getting married and staying that way.  In that case, what we’re after is the ITT.  If, however, what we want is stable marriages, then we need to do the principal stratification and truncation due to death bit. 

 I think Felix’s insight has some applicability to the legal context.  More on that in a subsequent post.