# Control for over-dispersion. Why do this: take natural log of metric, exponentiate, rank, remove top and bottom 10%

I'm looking at some NHS healthcare data on the number of deaths in England

The measure i'm looking at is called the SHMI - it's simply:

The number of observed deaths at a hospital / The expected number of deaths

To get the expected number of deaths, 140 statistical models are used, and there is overdispersion naturally, since deaths can be influenced by factors not included in the models for expected deaths - road accidents etc. So we have greater variability in the expected deaths than would be accounted for in the models

I understand this concept

The hospitals are examined as whether their SHMI scores are within the expected control limits:

"The 95 per cent control limits are calculated using an additive random-effects model with a 10 per cent trim for over-dispersion"

additive affects model is used because the models use groups of patients to get expected deaths, but these groups' composition may skew the expected results, so we want to account for the variability

Following on we get to this, which is where i'm lost:

Why are they taking the natural log of the SHMI score? Why do you need to know how multiples of e gets you the SHMI score?

Can someone say in plain English what they're ranking and excluding the top and bottom 10% of