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The “ Shrinkage ” Debate. In traditional statistics, the observed rate is thought to best represent the truth (n outcomes/k trials) Bayesian statistics considers observed data in the context of prior information Empirical Bayes derives prior information from the data - PowerPoint PPT Presentation
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The “Shrinkage” Debate
• In traditional statistics, the observed rate is thought to best represent the truth (n outcomes/k trials)
• Bayesian statistics considers observed data in the context of prior information
• Empirical Bayes derives prior information from the data
– e.g., the “best” guess is a rate somewhere between the observed rate and the overall rate
• Accomplished using hierarchical modeling
Empirical Bayes Approach: Shrink to the average mortality
0%
20%
Mo
rtal
ity
rate
(%
)
Mortality rates forhigh-risk surgery 10%
Mo
rtal
ity
rate
(%
)
15%
5%
Overall mean mortality rate
Adjusted for reliability
Observed mortality rates
Box size is proportional to the hospital caseload
Traditional approach
• Widely used in performance measurement• CMS Hospital Compare website• Massachusetts Cardiac Surgery Report Card
• Advantages: • Innocent until proven guilty
• Disadvantages:• Assumes small hospitals are average• Ignores the volume-outcome relationship
“The Hospital Compare model [standard shrinkage] underestimates the typically poorer performance of low-volume hospitals”
Described methods for shrinking towards mortality for a hospital’s volume group
Composite Measure Approach: Shrink to the mortality for volume group
0%
20%M
ort
alit
y ra
te (
%)
Mortality rates forhigh-risk surgery 10%
Mo
rtal
ity
rate
(%
)
15%
5%
Observed mortality rates
Low volume
Medium volume
High volume
Mortality rates
Composite mortality
Which approach is better?
• When trying to identify the “best” hospitals, incorporating hospital volume is better • Center of excellence model• e.g., Leapfrog Group’s “Survival Predictor”
• But from a quality improvement perspective, volume is not actionable, so it may make sense to shrink to the mean• MBSC risk- and reliability-adjusted outcomes