Signature
pi_i = R_i - EC_i
| Inputs | Definition | Unit |
|---|---|---|
R_i | Premium, capitation or risk-adjusted payment received for member i | £ per member per year |
EC_i | Expected cost of care for member i, written E[C_i] in the article, given what the plan knows about the member | £ per member per year |
pi_i | Expected profit on member i; a negative value is an expected loss | £ per member per year |
|---|
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
Expected profit per member from payment and expected cost in one Excel cell
With the payment in a cell named Payment and the member's expected cost in a cell named ExpectedCost, Excel returns the expected profit; a negative result is an expected loss.
=Payment-ExpectedCost
Assumptions
Payment fixed in advance of the member's actual costs
R_i does not rise with the costs the member actually incurs. If part of the payment follows actual costs, as in risk sharing, the gain from selection is smaller.
Plan information on expected cost beyond the payment formula
The plan can predict EC_i from information the payment does not use, such as chronic disease when the formula adjusts only for age. Without such information every member of a payment cell has the same expected profit and selection has nothing to act on.
Worked examples
Expected profit on a 70-year-old without a chronic condition
In the article's illustrative example the risk-adjusted payment for a 70-year-old is £5,000 and a member without a chronic condition is expected to cost £3,500, so the expected profit is 5,000 − 3,500 = 1,500, or £1,500.
R_i = 5000; EC_i = 3500; pi_i = 1500
Expected loss on a 70-year-old with a chronic condition
A member with a chronic condition is expected to cost £8,500, so the plan expects a loss of £3,500 on each such member.
R_i = 5000; EC_i = 8500; pi_i = -3500
Expected profit on a low-risk member under community rating
In the Community Rating article's pool the premium is £2,000 and a low-risk member is expected to cost £1,000, so an insurer expects a profit of £1,000 on that member, the same figure as the cross-subsidy in HE-FM-CRAT-002.
R_i = 2000; EC_i = 1000; pi_i = 1000
Expected profit when the payment also adjusts for chronic disease
If the formula paid £8,500 for a chronically ill member, the member would be expected to break even and the gain from selection would disappear, as the article notes.
R_i = 8500; EC_i = 8500; pi_i = 0
Common errors
Reading a concentration of healthy members as proof of cream skimming
A positive average expected profit shows that a plan has healthier members than its payment assumes, not that the plan selected them, since healthier people may choose some plans for their own reasons. Evidence of selection by the plan needs a design that separates insurer behaviour from consumer choice, such as an audit study.
Using realised instead of expected costs in the cream-skimming profit
A member who happens to have a costly year is not thereby unprofitable in expectation. Selection acts on predictable differences, so the profit is computed with expected costs given what the plan can observe, not with costs realised after the event.
Sources
Equal profitability of members under risk adjustment in selection markets
Geruso M, Layton TJ. Selection in health insurance markets and its policy remedies. Journal of Economic Perspectives. 2017;31(4):23-50. Sections on premium rating restrictions, which generally exacerbate adverse selection because insurers must ignore information on expected costs when setting prices, and on risk adjustment, which can in principle make all members equally profitable to the insurer on net.
Payment minus cost read as plan profit in payment system evaluation
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. Section 5.3.1 and its footnote 15, which defines over- and undercompensation as predicted payment minus actual cost so that positive values correspond to profits when the predictions are treated as revenue. Read in the authors' working-paper version.
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