Table 1. Simulated Pay-for-Performance Bonus Fractions and 25th Percentile Thresholds, by Bonus Algorithm.
| Parameter | Bonus Algorithm1 | ||||||||
|---|---|---|---|---|---|---|---|---|---|
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| All-or-Nothing | Continuous | Constrained2 | Composite | ||||||
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|
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| Mean | 25th Percentile | Mean | 25th Percentile | Mean | 25th Percentile | Mean | 25th Percentile | ||
|
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| Bonus Fraction | |||||||||
| 1. | Baseline Simulation3 | 0.50 | 0.40 | 0.96 | 0.95 | 0.67 | 0.60 | 1.00 | 0.97 |
| Uncertainty | |||||||||
| 2. | σ(ρ) = 0.051 | 0.50 | 0.40 | 0.98 | 0.98 | 0.75 | 0.70 | 1.00 | 0.99 |
| 3. | σ(ρ) =0.165 | 0.50 | 0.40 | 0.95 | 0.93 | 0.64 | 0.50 | 1.00 | 0.96 |
| Number of Indicators | |||||||||
| 4. | 10 Indicators | 0.51 | 0.40 | 1.00 | 0.95 | 0.68 | 0.60 | 1.00 | 0.98 |
| Weights | |||||||||
| 5. | 1 Indicator @ 50%; 4@12.5% | 0.48 | 0.25 | 0.96 | 0.94 | 0.66 | 0.50 | 1.00 | 0.96 |
| Indicator Correlation | |||||||||
| 6. | 1 pair @ 0.50 correlation | 0.50 | 0.40 | 0.96 | 0.95 | 0.83 | 0.77 | 1.00 | 0.97 |
| 7. | 2 pairs @ 0.50 correlation | 0.50 | 0.40 | 0.96 | 0.95 | 0.67 | 0.60 | 1.00 | 0.97 |
| Target Improvement Over Base (λ/t) | |||||||||
| 8. | 50%/20%{α=E[ρ]} | 0.50 | 0.40 | 0.98 | 0.97 | 0.74 | 0.70 | 1.00 | 0.98 |
| 8a. | 50%/20%{α=1.5E[ρ]} | 0.00 | 0.00 | 0.70 | 0.68 | 0.00 | 0.00 | 0.70 | 0.68 |
| 9. | 75%/70% {α=E[ρ]} | 0.50 | 0.40 | 0.95 | 0.94 | 0.65 | 0.50 | 1.00 | 0.96 |
| 10. | 56.4%/53.3%{α=1.96σε} | 0.50 | 0.40 | 0.95 | 0.94 | 0.65 | 0.50 | 1.00 | 0.96 |
| 10a. | 56.4/53.3%{E[ρ]=1.5(1.96σε)} | 0.59 | 0.40 | 0.97 | 0.95 | 0.73 | 0.60 | 1.00 | 0.96 |
| Expected Intervention Effect(λ/t) | |||||||||
| 11. | α = 1.2E[ρ] | 0.34 | 0.20 | 0.94 | 0.92 | 0.54 | 0.40 | 0.96 | 0.93 |
| 12. | α = 1.33E[ρ] | 0.24 | 0.00 | 0.92 | 0.89 | 0.44 | 0.30 | 0.93 | 0.90 |
| 13. | α = 1.5E[ρ] | 0.15 | 0.00 | 0.89 | 0.86 | 0.33 | 0.20 | 0.90 | 0.87 |
| Relative Growth Rates (ρ/α) | |||||||||
| 14. | α = E[ρ] | 0.50 | 0.40 | 0.81 | 0.73 | 0.54 | 0.40 | 0.99 | 0.84 |
| 15. | α = 1.2E[ρ] | 0.34 | 0.20 | 0.70 | 0.60 | 0.37 | 0.20 | 0.79 | 0.64 |
| 16. | α = 1.33E[ρ] | 0.24 | 0.00 | 0.61 | 0.51 | 0.28 | 0.20 | 0.66 | 0.51 |
| 17. | α = 1.5E[ρ] | 0.15 | 0.00 | 0.50 | 0.39 | 0.18 | 0.00 | 0.49 | 0.34 |
Statistics for 19 simulations of bonus payments are based on 500 random normal trials with specified target growth rate for 5-10 quality indicators. A full explanation of each simulation may be found in the Results section of this article.
Statistics based on 50 percent bonus for 0.90<λ/t<1.0, and 0 or 1.0 at lower/upper limit.
Based on 5 equally weighted, uncorrelated, indicators, α=0.25 target improvement rate, σ(ρ) =0.125, from baseline rate = 53.3 percent.
NOTES: E[ρ], σ(ρ) = the mean and standard deviation of a plan's own expected intervention effectiveness over baseline; 1.96σε = 1.96 standard deviations (95 percent confidence level) above baseline level assuming a 53-percent baseline rate and 1,000 patients.
SOURCE: Statistics based on simulations conducted by Cromwell, J., Drozd, E., Smith, K., and Trisolini, M., RTI International.