The adjusted outcomes were estimated using indirect standardisation. The observed number of events for a trust or hospital was divided by the number expected on the basis of the multivariable regression model. The adjusted rate was then estimated by multiplying this ratio by the average rate in all patients included in the analysis.
A worked example is given below:
Observed events = number of patients at the Trust with the event of interest.
Expected events = sum of predicted risks over all patients at the Trust, not just those with the event (from multivariable prediction model).
Adjusted rate = Overall national rate x (Observed events / Expected events)
In a rather artificial example, a Trust operates on 10 patients, 1 of whom dies within 90 days, and so their observed mortality is 10%. These patients are predicted to die with the following predicted risks (from the prediction model):
0.02, 0.05, 0.05, 0.10, 0.10, 0.10, 0.20, 0.25, 0.30, 0.35.
Observed deaths = 1
Expected deaths = 0.02 + 0.08 + 0.05 + 0.10 + 0.10 + 0.10 + 0.10 + 0.15 + 0.20 + 0.25 = 1.15
The overall 90-day mortality across England and Wales is 3.8%
The hospital’s risk-adjusted mortality is therefore 3.8x(1/1.15) = 3.3%.
This Trust was operating on particularly high-risk patients. The number of deaths observed at this hospital was a little less than the number of deaths expected for patients with these characteristics and therefore their risk-adjusted mortality is a little lower than the overall national rate, and much lower than their observed rate.