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
Thanks in advance
 A: I can't explain everything in your quotations, but in general logs are used to turn additive effects into multiplicative effects. See lognormal.
Lognormal data has a long right tail -- i.e. most values are lower but some values are very high. Think contract values, incomes, house prices, etc. So if the log'd data is normalish (unimodal, not too peaked, symmetrical, etc, etc), it's easier to work in log space. For example, a z-score is the centered data (mean subtracted) over the standard deviation. Both of these concepts make sense with normal data and not so much with non-normal data. (OLS regression requires normally-distributed error terms.)
The log'd data is thus hopefully normal-shaped and thus symmetrical, so the control limits -- and chopping 10% symmetrically off of both tails -- all make sense, along with mean, standard deviation, etc. They exponentiate (reversing the log) back into the data's actual space, and the control limits (calculated in log space) will no longer be symmetrical. The upper bound will be further right.
