The bottom-line: The major justification for my substantiated (or at least so I think) rant against the use of shrinkage in this case is the elephant in the room that no-one wants to talk about: the substantially limited information (avg number of complications per individual < 50) for otherwise infrequent events (avg complication rate <5%). In such a situation, shrinkage will make everyone look like everyone else, limiting the ability to draw meaningful complications by looking at the values of the random effects. In fact, PP had to rely on post hock classifications of the good, the bad and the ugly to overcome the unavoidable shrinkage towards the mean and overcome the lack of information that could distinguish one surgeon from another. Similar points (with more examples from the actual score card) were made by Ewen Harrison.
(You may stop reading now – or you may read past the rant in the next paragraph)
Rant Mode On: Another criticism that I received, is that I fail to understand random effects modeling, which I personally thought it was funny because one of my recent papers actually says one should scrap the Cox survival model for generalized additive models (which are just generalized linear mixed models in disguise). In any case, assuming that my understanding of mixed models is poor, maybe my conclusion that these models are to be preferred for such applications is also problematic?
Since one may consider my vote-of-confidence-to-the-almighty-mix-model v.s. my criticism of their application in the Scorecard project, subtle evidence for paranoid schizophrenia let me sum up how one can simultaneously hold these beliefs:
Even though mixed models are to be preferred especially as more data accumulate(a point I make clear in the 3 blog posts I wrote), no modeling could overcome the severe lack of events in the scorecard database.
There are other technical issues that one could “rant” about e.g. how were the hospital and surgeon effects were combined, but I will not digress any further.
Rant mode off
Back to criticism: In my opinion a major reason that mixed models were used is the potentially large number of surgeons with zero complications in their limited observation records*. The use of shrinkage models allow one to report performance for such surgeons, and generate nice colorful graphs (with one and possibly two decimal points) about their performance instead of reporting a NaN (Not A Number). Incidentally, the shrinkage of the individual surgeon effects all the way towards the population mean is the mixed model’s way of telling you the same thing: since it could not estimate how these people actually performed, it might as well give back the only answer consistent with the model applied, i.e. everybody is (almost) like everybody else and thus everyone is average.
*Curiously this information, i.e. the number of surgeons without any complication in the source database is not provided, although I’d have thought it would be important to report this number in the shake of transparency.
Word of caution: For surgeons without any complications in the database, the actual information comes not from their complications but from the number of uncomplicated surgeries they performed. This raises the question of inclusion effects (a point Andrew Gelman thoroughly address in his book) and the associated selection biases inherent in comparing surgeons who accept v.s. those who do not accept Medicare (or accept too little of it) and the corresponding social determinants of health outcomes (beautifully explained here).
A non-statistical criticism: As a nephrologist, I find it amusingly insulting that Acute Kidney Injury (coded as Acute Renal Failure) was not considered a surgical complication, even though it certainly complicates surgeries. Surgery is in fact the leading cause of “hospital-acquired” AKI (40% of cases are preceded by a surgical procedure). But maybe, as Benjamin Davies pointed out, the real end-points are not really measured by the Scorecard. Or I could be just delusional when I point out to surgical colleagues that the selection of analgesia, fluid management and pre as well as post perioperative care DO play a role for some complications. Or it could be just the anesthesiologists’s fault :)