Functions & Formulae

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

Decision uncertainty function giving the probability that the expected-value choice is wrong

d(NB_d(theta), lambda) = P_error

Takes the uncertain net benefit of each option at a stated cost-effectiveness threshold and returns P_error, the probability that the option chosen on expected net benefit is not the option with the highest net benefit, the decision uncertainty that PMG36 section 4.7.2 asks a model to quantify. From a table of probabilistic draws P_error is one minus the acceptability of the chosen option, live as HE-FM-CEAC-003 (function HE-FN-CEAC-001), where the share N_d*/N of the article is the multi-option CEAC of HE-FM-CEAC-002 or the two-option CEAC of HE-FM-CEAC-001, and the draws procedure for three options is HE-CF-EVPI-001. With two options and a normal incremental net benefit the acceptability of the chosen option is the standard normal cumulative probability at the absolute mean divided by its standard deviation, the probability of HE-FM-AN-004 read for the chosen option, so P_error is the upper normal tail at that ratio, the same tail that enters the loss term of HE-FM-EVPI-004. That combination of live records is cited, not restated. The split of EVPI into P_error times the mean loss when wrong is HE-FM-EVPI-003, EVPI itself is HE-FM-VOI-001 and HE-FM-EVPI-001, population EVPI is HE-FM-VOI-002, the incremental net monetary benefit of the article's worked example is HE-FM-NMB-002 and the maximum net benefit rule is HE-FM-NMB-003. The Monte Carlo standard error of an error probability estimated from N draws is the binomial standard error of HE-FM-BINOM-004 with N in place of n, and the number of runs belongs to the PSA package, so neither is restated. This package adds the error probability read from the p-value of a test of incremental net benefit. Notation follows the Decision Uncertainty article.

  • Two-option error probability as half the two-sided p-value of incremental net benefit

    P_error_p = p_two / 2

    In a two-option comparison analysed by a test of incremental net benefit at a stated threshold, such as net benefit regression, the expected-value choice follows the sign of the estimate. Hoch and colleagues state that the probability that the new treatment is cost-effective is the one-sided p-value when the estimate is negative and one minus the one-sided p-value when it is positive, so in both cases the probability that the choice is wrong is the one-sided p-value, half the two-sided p-value that statistical software usually reports (derived from those statements). The result needs no normal distribution function. For a z test it equals the upper normal tail at the absolute statistic, which is the two-option normal error probability given by HE-FM-AN-004 read through HE-FM-CEAC-003 (derived). HE-ER-AN-007 covers the related slip of taking one minus the two-sided p-value as the probability that net benefit is positive.

Decision Uncertainty — Functions & Formulae | HealthEconomics.wiki