Cost-Effectiveness Acceptability Curves

• Cost-Effectiveness Acceptability Curves (CEACs) are probabilistic decision tools that map the likelihood an intervention is cost-effective at various willingness-to-pay levels.
• They utilize the net monetary benefit framework and probabilistic sensitivity analysis to integrate uncertainty from cost, effectiveness, and epidemiological parameters.
• CEACs inform policy decisions by visually representing trade-offs and optimal strategy thresholds, supporting transparent resource allocation in health economics.

A Cost-Effectiveness Acceptability Curve (CEAC) is a probabilistic decision-analytic tool widely utilized in health economics to @@@@1@@@@ and communicate the uncertainty surrounding the cost-effectiveness of competing interventions across a range of willingness-to-pay (WTP) thresholds. For each candidate intervention or regime, the CEAC traces the estimated probability that the strategy is optimal according to the net monetary benefit (NMB) criterion, conditional on sampled model, epidemiological, and economic uncertainty. The function provides actionable guidance for policymakers by mapping the probability of cost-effectiveness as the WTP per unit health gain varies, facilitating decision-making under uncertainty and assisting resource allocation (Green et al., 2022, Spieker et al., 2019, Lim et al., 20 Jan 2026, Fernández-Morales et al., 19 Jan 2026).

1. Net Monetary Benefit Framework and Mathematical Formulation

The CEAC is founded on the Net Monetary Benefit formalism, which enables integration of costs ($C$), health effectiveness measures ($E$, e.g., QALYs or DALYs), and a WTP threshold ($\lambda$) into a single summary statistic. For any intervention indexed by $i$, the net benefit in simulation or posterior draw $k$ is defined as: $$\mathrm{NMB}_i^{(k)}(\lambda) = \lambda\, E_i^{(k)} - C_i^{(k)}$$ Alternatively, for incremental analyses (comparing candidate versus baseline/no-treatment),

$$\mathrm{NMB}_i(\lambda) = \lambda\, \Delta E_i - \Delta C_i$$

where $\Delta E_i$ is the incremental effectiveness and $\Delta C_i$ is the incremental cost (Lim et al., 20 Jan 2026).

In Bayesian frameworks, the NMB is computed for each posterior parameter draw and each regime or strategy (Fernández-Morales et al., 19 Jan 2026). For population-averaged analyses, NMB may be written as $$\mathrm{NMB}(\lambda) = E[\mathrm{NMB}_i(\lambda) | A_i=1] - E[\mathrm{NMB}_i(\lambda) | A_i=0]$$ (Spieker et al., 2019). The CEAC leverages this quantity as the principal decision metric.

2. Probabilistic Sensitivity Analysis and CEAC Estimation Algorithms

Probabilistic Sensitivity Analysis (PSA) constitutes the standard computational vehicle for CEAC construction. PSA propagates uncertainty in all input parameters—costs, clinical outcomes, epidemiological variables, discount rates, and more—by simulating large samples (typically $N=10,000$) from their prescribed probability distributions (Lim et al., 20 Jan 2026, Green et al., 2022).

The CEAC is then defined as the proportion (frequentist) or posterior probability (Bayesian) that a given intervention’s NMB exceeds zero or, in comparative settings, exceeds all other alternatives: $$\mathrm{CEAC}_i(\lambda) = \Pr\bigl(\mathrm{NMB}_i(\lambda) = \max_j \mathrm{NMB}_j(\lambda)\bigr)$$

The stepwise algorithm for CEAC calculation is as follows (Lim et al., 20 Jan 2026, Fernández-Morales et al., 19 Jan 2026, Green et al., 2022):

1. Define a grid of WTP thresholds, $\lambda_1,\ldots,\lambda_K$.
2. For each PSA iteration $k$, compute $\mathrm{NMB}_i^{(k)}(\lambda)$ for all strategies $i$ and WTP values.
3. For each $\lambda$, tally the proportion of samples where $i$ attains maximal NMB.
4. Plot $\mathrm{CEAC}_i(\lambda)$ versus $\lambda$ for all interventions.

In Bayesian analyses (see Algorithm 1 and code in (Fernández-Morales et al., 19 Jan 2026)), CEACs are computed pointwise across posterior draws: $$\mathrm{CEAC}_k(\lambda) \approx \frac{1}{M}\sum_{m=1}^M \mathbf{1}\!\Bigl\{\arg\max_{j}\psi_{j}^{(m)}(\lambda)=k\Bigr\}$$ where $\psi_{j}^{(m)}(\lambda)$ is the mean NMB for regime $j$ in posterior sample $m$ at WTP $\lambda$.

3. Theoretical Properties and Asymptotic Behavior

CEACs exhibit well-characterized asymptotic behavior under standard regularity conditions. As sample size and the number of PSA draws ($N,K$) grow large, the CEAC for a candidate strategy approaches a step function at its incremental cost-effectiveness ratio (ICER): $$\mathrm{CEAC}(\lambda) \longrightarrow \begin{cases} 1, & \lambda > \mathrm{ICER}\ 0.5, & \lambda = \mathrm{ICER}\ 0, & \lambda < \mathrm{ICER} \end{cases}$$ This formalizes the decision rule: above a given WTP, one strategy is almost surely optimal; below, its probability of being cost-effective vanishes (Spieker et al., 2019).

Limitations of CEACs include:

• Sensitivity to the mean NMB only (“strength of evidence” regarding optimality), and not distributional features.
• Lack of symmetry near values 0 and 1 (distinguishing “strong evidence for control” from mere absence of evidence).
• Overlap and crossing points that elucidate classical trade-offs between low-cost/low-effect and high-cost/high-effect strategies (Lim et al., 20 Jan 2026).

4. Practical Computation and Software Workflows

The CEAC construction pipeline is standardized in several analytic ecosystems. The R package BCEA (Green et al., 2022) implements:

• compute_CEAC(): computes CEACs for all comparator arms and WTP thresholds.
• ceac.plot(): visualization in base R, ggplot2, or plotly formats.
• Additional routines for comparing simultaneously across multiple interventions, reporting the Cost-Effectiveness Acceptability Frontier (CEAF), and integrating advanced decision rules (risk aversion, mixed strategies).

The following R code (from (Green et al., 2022)) simulates a two-arm PSA, computes NMBs, and plots the CEAC:

bcea_obj <- bcea(e = effects, c = costs, ref = 1, interventions = labels, Kmax = 50000) ceac.plot(bcea_obj, comparison = 2, col = "blue", lty = 1, lwd = 2)

Python and R pseudocode provided in (Fernández-Morales et al., 19 Jan 2026) operationalize the "which–max" approach for multi-regime Bayesian CEACs.

5. Interpretation, Policy Application, and Methodological Extensions

CEACs are interpreted as the probability that a given intervention is cost-effective at WTP $\lambda$. The x-axis represents $\lambda$ (valuing health relative to cost); the y-axis displays the probability of cost-effectiveness. For multi-intervention problems, the curve visually demonstrates trade-offs and dominance relationships (Lim et al., 20 Jan 2026, Green et al., 2022). Crossing points between curves signal threshold values where strategic preference shifts.

Policy relevance is illustrated in vaccination prioritization (Lim et al., 20 Jan 2026): CEAC curves for three Hepatitis A vaccination strategies (S1: 20–39y, S2: 40–59y, S3: 20–59y) in Korea confirm S2 as robustly optimal across nearly all WTP values. S1 briefly overtakes S3 within a narrow WTP band, reflecting a low-cost/low-effect versus high-cost/high-effect trade-off. The stability of dominance for S2 supports its adoption under resource constraints. Such CEAC-based analyses inform allocation when explicit WTP thresholds are not specified.

Recent methodological advances include complementary statistics such as Net Benefit Separation (NBS) and the Cost-Effectiveness Determination Curve (CED), which address limitations of CEACs by quantifying the probability at the individual level of one treatment providing higher net benefit than another (Spieker et al., 2019). These extensions accommodate confounding and censoring via semiparametric standardization, inverse probability of censoring weighting, and bootstrap variance estimation.

6. Limitations, Critiques, and Complementary Approaches

While CEACs have become ubiquitous in health economic evaluation, their limitations are documented:

• The CEAC portrays only the likelihood that mean NMB exceeds zero or that one regime is optimal, without quantifying the magnitude or probability of patient-level improvement.
• Distributional nuances, e.g., heavy-tailed cost outcomes, can cause discordance between CEAC-based and NBS-based rankings (Spieker et al., 2019).
• For some decision environments, the CEAC may not provide sufficient justification for choosing among strategies with competing effect and cost profiles.

Complementary measures such as the determination curve (CED) and simulation-based methods for evaluating stochastic dominance among individual outcomes provide additional insight and may be used in tandem with CEACs.

7. Empirical Evaluation and Simulation Evidence

Simulation studies confirm the finite-sample performance and robustness of CEAC estimation techniques across a spectrum of data-generating processes, sample sizes, covariate structures, and censoring rates (Spieker et al., 2019, Fernández-Morales et al., 19 Jan 2026). For instance, in simulated endometrial cancer data, CEAC and CED estimators exhibit negligible bias and accurate coverage of bootstrap intervals even under administrative censoring. In applied settings, such as SEER-Medicare database analysis or age-stratified vaccination modeling, CEACs resolve complex resource prioritization problems and distill large uncertainty clouds into easily interpretable probabilistic decision summaries (Lim et al., 20 Jan 2026, Fernández-Morales et al., 19 Jan 2026).

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In summation, Cost-Effectiveness Acceptability Curves are pivotal for quantifying and conveying uncertainty in health economic evaluation. Rooted in probabilistic sensitivity analysis and the net monetary benefit framework, CEACs enable rigorous comparison of competing strategies across WTP thresholds, support transparent policy allocation, and facilitate communication of evidential strength to decision-makers. Contemporaneous developments in Bayesian computation, complementary distributional metrics, and programmatic software have expanded their utility and applicability (Lim et al., 20 Jan 2026, Fernández-Morales et al., 19 Jan 2026, Green et al., 2022, Spieker et al., 2019).