Signature
P_error_p = p_two / 2
| Inputs | Definition | Unit |
|---|---|---|
p_two | Two-sided p-value for the test that incremental net benefit, or the treatment coefficient of a net benefit regression, is zero at the stated threshold | proportion |
P_error_p | Probability that the option chosen on the sign of the incremental net benefit estimate is not the option with the higher net benefit | proportion |
|---|
Function
Decision uncertainty function giving the probability that the expected-value choice is wrong
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.
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Implementations
Excel
Error probability from a two-sided p-value in one cell
With the two-sided p-value of incremental net benefit, or of the treatment coefficient in a net benefit regression, in a cell named PValueTwoSided, this formula in a cell named ErrProbPValue returns the error probability.
=PValueTwoSided/2
Assumptions
Symmetric test statistic for halving the two-sided p-value
The p-value comes from a symmetric z or t test at the same threshold as the decision, so the one-sided tail is half the two-sided value. Hoch and colleagues note that the p-value of a parametric analysis rests on a distributional assumption and that bootstrapping may be preferred when the data do not appear normal. HEMA Report 2 notes that near the ICER the two-option error probability can be higher or lower than 50% when the distribution of incremental net health benefit is markedly skewed.
Two options and a probability reading of the p-value
There are two options and the one-sided p-value is read as the probability that the chosen option is not the better one, the reading Hoch and colleagues give for the acceptability curve from net benefit regression. With three or more options the error probability is read from the draws (HE-FM-CEAC-003).
Worked examples
Error probability from the p-value at GBP 30,000 per QALY
At the illustrative GBP 30,000 per QALY of HE-EX-AN-008, incremental net benefit of GBP 1,000 with a standard error of about GBP 1,342 has a two-sided z test p-value of about 0.45606, so the error probability of adopting is about 0.22803, one minus the 0.772 probability that net benefit is positive.
p_two = 0.45606; P_error_p = 0.22803
Error probability from the p-value at a threshold equal to the ICER
At a threshold equal to the ICER the estimate is zero, the two-sided p-value is 1 and the error probability is 0.5, a limiting case that checks the implementation.
p_two = 1; P_error_p = 0.5
Common errors
Two-sided p-value reported as the error probability
Reporting the two-sided p-value of about 0.456 at GBP 30,000 per QALY as the error probability doubles it, since the choice is wrong only when net benefit lies on the other side of zero, a probability of about 0.228.
Sign of the estimate ignored when reading the p-value
Taking one minus the one-sided p-value as the error probability gives about 0.772 at GBP 30,000 per QALY, the probability that adopting is right. When the estimate is negative the new option is rejected and the error probability is still the one-sided p-value, the probability that the new option is cost-effective.
One-sample p-value of probabilistic draws read as the decision uncertainty error probability
Halving the p-value of a one-sample test of the mean of 1,000 probabilistic draws, with an illustrative mean incremental net benefit of GBP 1,000 and standard deviation of GBP 2,000, uses the standard error of the mean, about GBP 63.25, so z is about 15.81 and the error probability comes out at about 0. The spread of the draws gives about 0.30854, the upper normal tail at 1,000 divided by 2,000 (HE-FM-AN-004 read through HE-FM-CEAC-003, computed here for illustration). The p-value measures the Monte Carlo precision of the mean and falls as more draws are run, while the decision uncertainty stays the same. The halved p-value applies to a test whose standard error describes the uncertainty about incremental net benefit itself, such as a trial-based net benefit regression.
Sources
Hoch and colleagues on halving the two-sided p-value of net benefit regression
Hoch JS, Rockx MA, Krahn AD. Using the net benefit regression framework to construct cost-effectiveness acceptability curves, an example using data from a trial of external loop recorders versus Holter monitoring for ambulatory monitoring of community acquired syncope. BMC Health Services Research. 2006;6:68. Methods section, which states that regression programs report a two-sided p-value while a one-sided probability is needed, that it is converted by dividing by two, and that the probability that the new treatment is cost-effective is the one-sided p-value when the coefficient is negative and one minus it when the coefficient is positive. The same section states that the p-value of a parametric analysis is derived from a distributional assumption and that non-parametric methods like bootstrapping may offer better alternatives, and the Discussion states that a CEAC indicates a 50% chance of cost-effectiveness when the threshold equals the sample estimate of the ICER. That the error probability is the one-sided p-value in both cases, and 0.5 at the ICER, is derived from these statements.
NICE manual on reporting decision uncertainty and the error probability
National Institute for Health and Care Excellence. NICE technology appraisal and highly specialised technologies guidance: the manual (PMG36). Published 31 January 2022, last updated 13 October 2026. Chapter 4 Economic evaluation, section 4.7.2 (the model should quantify the decision uncertainty, the probability that a different decision would be reached if the true cost effectiveness of each technology could be ascertained before making the decision) and section 4.7.15 (present the probability that the treatment is cost effective at maximum acceptable ICERs of GBP 25,000 to GBP 35,000 per QALY gained and the error probability, that the treatment is not cost effective, particularly if there are more than 2 alternatives).
HEMA Report 2 on the two-option error probability near the ICER and under skew
Steuten L, Thavorn K, Cipriano LE, Guertin JR, McQueen B, Schmidler G, Sullivan S, Wailoo A, Sculpher M. Methods to analyze and present uncertainty in economic evaluation to support HTA decisions. HEMA Report 2. Health Economics Methods Advisory, 2026. Table 5.2, footnote to the row on the probability of a wrong decision given current evidence (printed page 43), which defines it as the probability that the option with the highest expected net health benefit is in fact incorrect, notes that for a choice between two options it typically reaches around 50% where the ICER is close to the threshold, and that it can be higher or lower than 50% where the distribution of incremental net health benefit is markedly skewed or more than two options are compared.
Canonical Identity
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