Signature
pi_bar = R - sum_(k=1)^K [m_k * EC_k]; Pi = N * pi_bar
| Inputs | Definition | Unit |
|---|---|---|
R | Payment per member of the payment cell, the same for every member | £ per member per year |
m_k | Share of the plan's members in the payment cell who belong to risk group k; the shares sum to 1 | proportion |
EC_k | Expected annual cost of care per member of risk group k | £ per member per year |
N | Number of members the plan enrols in the payment cell | people |
pi_bar | Expected profit per enrolled member of the payment cell | £ per member per year |
|---|---|---|
Pi | Total expected profit of the plan in the payment cell | £ 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).
Try this function
Implementations
Excel
Expected profit per member and in total from a risk mix in two Excel cells
With the payment in Payment, the plan's shares by risk group in MixShare, the expected cost of each group in GroupCost and the number of members in Members, the first formula returns the profit per member and the second the total.
=Payment-SUMPRODUCT(MixShare,GroupCost); =Members*(Payment-SUMPRODUCT(MixShare,GroupCost))
Assumptions
Same payment for every member of the payment cell
The payment formula does not distinguish the risk groups in the sum, for example because it adjusts for age but not for chronic disease. Groups that the formula does distinguish are treated as separate payment cells.
Expected cost of each risk group unchanged by selection
Enrolling a different mix of members changes the plan's average cost but not the expected cost of a member of any given group, so the profit measures the effect of the mix alone.
Costs of attracting the risk mix not deducted
Advertising, benefit design and other screening costs are not subtracted, so the result is an upper bound on the net gain from selection.
Worked examples
Plan enrolling 80% healthy 70-year-olds
In the article's example a plan whose 1,000 members aged 70 are 80% healthy and 20% chronically ill has an expected cost per member of £2,800 plus £1,700, or £4,500. Against the £5,000 payment it expects £500 per member and £500,000 in total.
R = 5000; m_k = [0.8,0.2]; EC_k = [3500,8500]; N = 1000; pi_bar = 500; Pi = 500000
Plan enrolling the payment cell's own risk mix
With the population mix of 70% healthy and 30% chronically ill, the average expected cost equals the £5,000 payment and the plan expects to break even, as the article's payment was set to match the age group's average.
R = 5000; m_k = [0.7,0.3]; EC_k = [3500,8500]; N = 1000; pi_bar = 0; Pi = 0
Plan enrolling only healthy 70-year-olds
A plan that enrolled only members without a chronic condition would expect £1,500 per member and £1,500,000 in total for 1,000 members, the largest gain available in this payment cell, computed here for illustration.
R = 5000; m_k = [1,0]; EC_k = [3500,8500]; N = 1000; pi_bar = 1500; Pi = 1500000
Common errors
Crediting the risk-mix profit to efficiency
In the article's example the plan's £500 per member comes entirely from enrolling fewer chronically ill members; it treats each type of member at the same expected cost as any other plan. Comparing average costs across plans without adjusting for the mix credits the plan with savings it did not make.
Treating the risk-mix profit as the net gain from selection
The £500,000 is an upper bound. Attracting a healthier mix has costs, and Brown and colleagues note that money spent on screening, such as targeted advertising, may not benefit members.
Sources
Medicare Advantage enrolment of lower-cost members given their risk scores
Brown J, Duggan M, Kuziemko I, Woolston W. How does risk selection respond to risk adjustment? New evidence from the Medicare Advantage program. American Economic Review. 2014;104(10):3335-3364. Model and results sections, which show plans enrolling people with lower costs given their risk score, so that payments exceed the expected cost of the members enrolled, and which treat screening costs such as targeted advertising as a cost of selection.
Group over- and undercompensation as the incentive to select a risk mix
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, which explains that a plan paid too little for a group has an incentive to discourage membership from that group, and too much an incentive to attract it.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0