Functions & Formulae

Each applied formula has its own function page, with a signature, implementations, and tests.

Actuarial value calculation function for health plan cost sharing

S = f(X, D, c, M); P = X - S; AV = g(P, X)

Maps a health plan's cost-sharing rules and the allowed costs of a standard population over one benefit year to the share of those costs that the plan pays. Each person's allowed cost is split into the cost sharing paid by the member and the remainder paid by the plan, and the plan's total is divided by the total allowed cost. The records follow the notation of the Actuarial Value article, where X is allowed cost, S is cost sharing and P is the plan payment. Premiums appear in neither term.

  • Actuarial value as the plan-paid share of total allowed cost

    AV = sum_(g=1)^G [n_g * P_g] / sum_(g=1)^G [n_g * X_g]

    Divides the plan's total payment for covered care by the total allowed cost of that care, both summed over a standard population for one benefit year. The population is held as G spending groups of n_g people with the same allowed cost per person, the layout of the article's worked example and of a continuance table. With one person in every group the formula is the article's ratio of summed plan payments to summed allowed costs over N people, and it equals 1 minus the members' share of total allowed cost.

  • Member cost sharing under a deductible, coinsurance and out-of-pocket maximum

    S = min(M, min(X, D) + c * max(0, X - D)); P = X - S

    Gives the cost sharing paid by a member with annual allowed cost X under a simple plan with one deductible, one coinsurance rate and an annual out-of-pocket maximum. The member pays all allowed cost up to the deductible and the coinsurance share of the cost above it, but no more than the out-of-pocket maximum in total, and the plan pays the remainder P. The functions min and max return the smaller and the larger of their arguments.

  • Allowed cost at which the out-of-pocket maximum is reached

    X_star = D + (M - D) / c

    Gives the annual allowed cost at which the deductible plus coinsurance on the excess equals the out-of-pocket maximum, the point at which the member cost sharing in HE-FM-AV-002 stops rising. Above it every extra unit of allowed cost is paid in full by the plan.