The “ Shrinkage ” Debate

1. 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

2. Observed mortality rates Adjusted for reliability 20% 15% Overall mean mortality rate Mortality rates for high-risk surgery Mortality rate (%) Mortality rate (%) 10% 5% Box size is proportional to the hospital caseload 0% Empirical Bayes Approach: Shrink to the average mortality

3. 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

4. “The Hospital Compare model [standard shrinkage] underestimates the typically poorer performance of low-volume hospitals”

5. Described methods for shrinking towards mortality for a hospital’s volume group

6. Observed mortality rates Composite mortality 20% Mortality rates Low volume 15% Medium volume Mortality rates for high-risk surgery High volume Mortality rate (%) Mortality rate (%) 10% 5% 0% Composite Measure Approach: Shrink to the mortality for volume group

7. 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