*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.

Also, we don't know the demographics of the cohort served by the hospital. If the hospital serves a generally poorer demographic with high levels of drug and alcohol abuse then its high mortality rate could have nothing to do with the doctors.

ReplyDeleteCompletely agree. The only thing I saw in media that looked for an underlying cause was a reference to this hospital conducting fewer of these surgeries, thus this being a "training" issue. Obviously if I had more prolific cross-hospital data, we could test several hypotheses.

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