BACKGROUNDSpecifically, I wanted to know is this a case of something systematic occurring (doctors bad at surgery, something nefarious, etc) or is it possible that this is just a "statistical anomaly" .. in essence.. is this just an outlier hospital?
Here are two news stories for background (the feds are investigating this now):
Story 1 and Story 2
METHODFrom a statistical standpoint I can't prove that something systematic isn't occurring, but I can speak to the likelihood of this hospital's death rate a random outlier, effectively due to "sampling error". Here is the data I was able to glean from the articles:
- The national average death rate for these surgeries is 3.3%
- The average at this hospital is 12.5%. They cited 8 deaths, so I can calculate that our "n" is 64.
The question here is: Is the St. Mary's hospital death rate significantly different than the national average? Because this is just testing one sample proportion against the population, I used the binomial exact test. Here's my R output:
The important piece here is the p-value which is approximately 0.0012. That means about a 1.2 in 1000 chance of this difference being due to random chance. So this is obviously unexpected... but is it really?
The problem with this logic is that there may be a few thousand hospitals that perform this type of surgery. And if each has a 1.2 in 1000 chance of having a mortality rate of 12.5% or greater, then it is likely that one could?
In short summary, we know this is an instance of a very unlikely data point. However, given the number of hospitals that perform this type of surgery, it is possible that this is due to statistical sampling.