Functions & Formulae

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

Expected net benefit function

e(lambda,C_j(theta),E_j(theta)) = ENB_j

Maps the joint distribution of an option's uncertain costs and health effects, and a threshold, to the mean of its net benefit. The option with the highest expected net benefit is the one to adopt on current evidence, and the same quantity is the baseline for value of information analysis.

  • Expected net monetary benefit from probabilistic simulations

    ENB_j = sum_(n=1)^N [lambda * E_jn - C_jn] / N

    Averages option j's net monetary benefit over N probabilistic simulations, each valuing the simulated health effect at threshold lambda and subtracting the simulated cost. Because net benefit is linear in cost and effect, the result equals lambda times the mean effect minus the mean cost from the same simulations. The option-level formula on the net monetary benefit page is the deterministic counterpart.

  • Expected net health benefit from probabilistic simulations

    ENHB_j = sum_(n=1)^N [E_jn - C_jn / lambda] / N

    Averages option j's net health benefit, its simulated health effect minus its simulated cost divided by lambda, over N simulations. The result equals the expected net monetary benefit divided by lambda, so both forms rank options identically at any positive threshold. NICE asks for expected net health benefits alongside ICERs, using £25,000 and £35,000 per QALY.