## Friday, June 5, 2015

### Florida Hospital Deaths May Not Be Systematic

This afternoon I was confronted with two news stories regarding a hospital that has what is being reported as a disproportionately high mortality rate during infant heart surgery.  Obviously this is a sad story, but because it's about a statistical anomaly, it is interesting to me.

## BACKGROUND

Specifically, 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

## METHOD

From 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:

## CONCLUSION

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.