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