Signature
OC_g = R_g - C_g; PR_g = R_g / C_g
| Inputs | Definition | Unit |
|---|---|---|
R_g | Average payment for the members of group g | £ per member per year |
C_g | Average cost for the members of group g; in the article's illustration, the group's expected cost | £ per member per year |
OC_g | Average payment minus average cost for group g; negative values are undercompensation | £ per member per year |
|---|---|---|
PR_g | Average payment divided by average cost for group g | none |
Function
Selection incentive function for payments that do not match expected cost
Maps the payment an insurer or provider receives for a member and the member's expected cost of care to the expected profit or loss on that member, the expected profit per member from the mix of risks a plan enrols, and the group-level over- or undercompensation and predictive ratio that evaluators of payment systems use to find groups likely to be targets of selection. Cream skimming is profitable where these measures differ predictably between groups that a plan can identify and influence. Community rating creates such differences through the premium, as the cross-subsidies on the Community Rating page show (HE-FM-CRAT-002), and the risk equalisation transfers that offset them are on that page (HE-FM-CRAT-003).
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Implementations
Excel
Over- or undercompensation and predictive ratio from member records in two Excel cells
With the payments for the group's members in a range named GroupPayment and their costs in a range named GroupCost, the first formula returns over- or undercompensation and the second the predictive ratio.
=AVERAGE(GroupPayment)-AVERAGE(GroupCost); =SUM(GroupPayment)/SUM(GroupCost)
Assumptions
Groups defined by the actions plans can take
The groups are those a plan can affect through its own actions in the market concerned, for example through its network or benefit design, as Layton and colleagues recommend. A group no plan action can reach says little about selection incentives.
Payments and costs for the same members and period
Both measures compare the payments generated by the payment formula with the costs of the same members over the same period, so the difference and the ratio describe the same group.
Positive average cost for the predictive ratio
The ratio is undefined when the group's average cost is zero; the difference measure remains defined.
Worked examples
Overcompensation for 70-year-olds without a chronic condition
In the article's example the £5,000 payment against an expected cost of £3,500 gives overcompensation of £1,500 and a predictive ratio of 5,000 ÷ 3,500 = 1.43.
R_g = 5000; C_g = 3500; OC_g = 1500; PR_g = 1.43
Undercompensation for 70-year-olds with a chronic condition
Against an expected cost of £8,500 the same payment gives undercompensation of £3,500, shown as minus £3,500, and a predictive ratio of 5,000 ÷ 8,500 = 0.59, the article's figures.
R_g = 5000; C_g = 8500; OC_g = -3500; PR_g = 0.59
Compensation measures for all 70-year-olds together
For the age group as a whole the payment equals the average cost of £5,000, so the difference is zero and the ratio is 1, computed here for illustration, although the two subgroups differ by £5,000 per member.
R_g = 5000; C_g = 5000; OC_g = 0; PR_g = 1
Common errors
Judging selection incentives from a broad group only
The article's 70-year-olds as a whole show a ratio of 1 while the subgroups without and with a chronic condition show 1.43 and 0.59. A measure for a broad group can hide the incentive within it, which is why Layton and colleagues recommend defining groups by the actions plans can take.
Comparing a predictive ratio with a compensation difference from another study
A ratio of 0.59 and a difference of minus £3,500 describe the same group in the article but are on different scales. The same undercompensation of £3,500 against an average cost of £5,000 would give a ratio of 0.30, computed here for illustration, so results are converted to one measure before they are compared.
Sources
Over- and undercompensation and predictive ratio formulas for payment systems
Layton TJ, Ellis RP, McGuire TG, van Kleef RC. Evaluating the performance of health plan payment systems. In: McGuire TG, van Kleef RC, eds. Risk Adjustment, Risk Sharing and Premium Regulation in Health Insurance Markets: Theory and Practice. London: Academic Press; 2018:133-167. Introduction, which notes that US researchers tend to use predictive ratios and European researchers over- and undercompensation, and section 5.3.1, equations 5.3 (the group average of predicted payment minus actual cost) and 5.4 (the sum of predicted payments divided by the sum of actual costs), with positive values or ratios above 1.0 indicating overcompensation; section 5.3.2 recommends defining groups as those that may be affected by a plan action. Read in the authors' working-paper version.
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