Functions & Formulae

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

Cost-effectiveness acceptability function

a(lambda,C_ij,E_ij) = CEAC_j

Maps the simulated costs and health effects of mutually exclusive options from a probabilistic sensitivity analysis, together with a threshold, to the probability that each option has the highest net monetary benefit at that threshold. Evaluated across a range of thresholds, it traces the cost-effectiveness acceptability curve.

  • Two-option CEAC at one threshold

    CEAC = (1/N) * sum_(i=1)^N [1(lambda * Delta_E_i - Delta_C_i > 0)]

    Counts the probabilistic simulations in which the intervention has positive incremental net monetary benefit at threshold lambda and divides the count by the number of simulations. The indicator 1(condition) equals 1 when the condition holds and 0 otherwise. Apart from exact ties, the comparator's value is the complement.

  • Multi-option CEAC for option j

    CEAC_j = (1/N) * sum_(i=1)^N [1(NMB_ij >= NMBmax_i)]

    Counts the simulations in which option j has the highest net monetary benefit among all included options at threshold lambda, and divides the count by the number of simulations. Each option's net monetary benefit in a draw is lambda times its simulated effect minus its simulated cost. With mutually exclusive options and consistent tie handling, the values for all options sum to 1 at each threshold. Because no option can exceed the maximum, the indicator 1(NMB_ij >= NMBmax_i) equals 1 exactly when option j attains the highest net monetary benefit in draw i.

  • Acceptability frontier and error probability

    CEAF = CEAC_(j*), where j* = argmax_j ENB_j; P_err = 1 - CEAC_(j*)

    Selects the option with the highest expected net monetary benefit, the mean across simulations, and takes that option's CEAC value as the cost-effectiveness acceptability frontier at threshold lambda. The error probability is the complement, the share of simulations in which the chosen option does not have the highest net monetary benefit.