01.12.2013  Technical advance  Ausgabe 1/2013 Open Access
Direct risk standardisation: a new method for comparing casemix adjusted event rates using complex models
 Zeitschrift:
 BMC Medical Research Methodology > Ausgabe 1/2013
Electronic supplementary material
Competing interests
Authors’ contributions
Background
Direct standardisation
Age specific death rate per 100 admissions  Directly standardised rates  

Children  Adults  Elderly  
Hospital 1
 20  10  20  (0.25×20) + (0.5×10) + (0.25×20) = 15 
Hospital 2
 12  24  (0.5×12) + (0.25×24) = 12 
Indirect standardisation
Casemix group  National standard death rate  Hospital A: Death rate  Hospital A: Casemix proportions  Hospital B: Death rate  Hospital B: Casemix proportions 

1.
High risk
 0.9  0.8  0.4  0.8  0.3 
2.
Low risk
 0.1  0.2  0.6  0.2  0.7 
SMR
 O = (0.4×0.8) + (0.6×0.2)  O = (0.3×0.8) + (0.7×0.2)  
E = (0.4×0.9) + (0.6×0.1)  E = (0.3×0.9) + (0.7×0.1)  
SMR = 105  SMR = 112 
Methods
Calculate event rates in risk groups rather than casemix groups
Calculating directly risk standardised rates
Creating categories of risk  Weights for combining risk category specific event rates for each centre 

Equal width: 0.00.1, 0.10.2, 0.20.3, etc.  Equal 
Equal numbers of patients in each  Proportion of all patients in each category 
Equal numbers of observed deaths in each  Proportion of all observed deaths in each category 
Equal numbers of predicted deaths in each  Proportion of all predicted deaths in each category 
Examples
Data and methods
Results
HES data
DAVROS data
Centre  SMR  CMF  

Observed value  SE (theoretical)  SE (bootstrap)  Observed value  SE (theoretical)  SE (bootstrap)  
A
 1.03  0.095  0.076  1.06  0.083  0.077 
B
 1.19  0.084  0.069  1.19  0.076  0.070 
C
 0.92  0.061  0.046  0.90  0.053  0.047 
D
 0.95  0.097  0.083  0.97  0.094  0.089 
E
 0.99  0.109  0.090  1.01  0.099  0.092 
F
 0.84  0.098  0.081  0.84  0.091  0.084 
G
 1.01  0.115  0.101  1.02  0.102  0.101 
H
 0.98  0.131  0.105  0.96  0.114  0.112 
I
 1.08  0.129  0.104  1.08  0.111  0.106 
Discussion

As easy to calculate as the SMR

Creates an index, the CMF which is similar to the SMR, or a standardised rate

Can be calculated using continuous covariates

Unlike the SMR, can be used to compare populations, centres or time periods fairly

Has an easily estimated standard error that is similar to the SMR