When looking at ALL hospitals simultaneously, what does it mean if any of the hospitals have a survival rate outside their predicted range?

If we were looking at only one hospital, we’d expect its survival rate to fall outside its predicted range rarely if chances of survival at the hospital match the formula: only 1 time in 20 just by chance. But, if we are looking at all 13 hospitals at once, we’d actually expect that at least one hospital will fall outside its range just by chance about 9 times in 20.

This is similar to the situation where you hear a friend won a good prize in a raffle. This may be surprising, but it becomes a lot less surprising when you hear they bought 100 tickets. Just as this gave them more chances of winning, the more hospitals we look at, the more likely it becomes that at least one will fall outside its range, even if survival at all the hospitals matches the formula.

So, on average, we’d anticipate about half of NCHDA’s annual reports to have at least one hospital outside its range, either above or below, by chance alone.

See what happens if a hospital falls below its predicted or extended predicted range.

Considering now the extended predicted range, if we look at all 13 hospitals at once, we’d only expect any one of them to be outside their extended range very rarely, just 1 time in 40. This is why a hospital’s survival rate being outside the extended predicted range is considered strong evidence that the chances of a patient surviving at that hospital are different to what is expected.