Overview

CEACT implements cost-effectiveness analyses for two-arm clinical trials: observed incremental summaries, non-parametric bootstrap uncertainty, cost-effectiveness planes, cost-effectiveness acceptability curves (CEACs), net monetary benefit, and deterministic sensitivity analysis.

The package follows standard practice in trial-based economic evaluation, where patient-level costs and effects are observed alongside treatment allocation (Glick et al. 2014; Drummond et al. 2015).

Let \(C_i\) denote cost, \(E_i\) denote effect, and \(A_i \in \{0,1\}\) denote treatment assignment, with \(A_i=0\) for the reference group and \(A_i=1\) for treatment.

Core Quantities

Mean costs and effects by arm are

\[ \bar{C}_a = \frac{1}{n_a}\sum_{i:A_i=a} C_i, \qquad \bar{E}_a = \frac{1}{n_a}\sum_{i:A_i=a} E_i. \]

Incremental cost and incremental effect are

\[ \Delta C = \bar{C}_1 - \bar{C}_0, \qquad \Delta E = \bar{E}_1 - \bar{E}_0. \]

When \(\Delta E \ne 0\), the incremental cost-effectiveness ratio is

\[ ICER = \frac{\Delta C}{\Delta E}. \]

Because ratios can be unstable when \(\Delta E\) is near zero, CEACT also uses net monetary benefit at willingness-to-pay threshold \(k\) (Stinnett and Mullahy 1998):

\[ INMB(k) = k\Delta E - \Delta C. \]

Treatment is cost-effective at threshold \(k\) when \(INMB(k)>0\). The CEAC is the probability of this event over an uncertainty distribution:

\[ CEAC(k) = Pr\{k\Delta E - \Delta C > 0\}. \]

CEACT estimates this probability from non-parametric bootstrap replicates (Efron and Tibshirani 1993), preserving treatment-arm sample sizes by stratified resampling. CEACs and planes are widely used to communicate decision uncertainty in cost-effectiveness studies (Fenwick et al. 2001; Briggs et al. 2002).

Real Trial-Based CEA Example

The example below first uses the trial_cea dataset included with CEACT package. This patient-level dataset contains treatment assignment, total costs, and QALYs for 500 trial participants and is suitable for demonstrating the package workflow.

data("trial_cea")
trial <- trial_cea

head(trial)
#>   id treat cost    qaly dissev race    blcost    blqaly male     group
#> 1  1     1 2439 0.76059  0.335    1 2113.3491 0.9943529    0 treatment
#> 2  2     0 2598 0.70727  0.302    1  508.5120 0.8351629    1   control
#> 3  3     0 6315 0.68618  0.405    0 2271.8215 0.7526733    0   control
#> 4  4     0 1332 0.44657  0.199    1  653.7864 0.8441091    1   control
#> 5  5     1 2972 0.66752  0.302    0 1438.7561 0.8653243    1 treatment
#> 6  6     0 3699 0.59028  0.447    0 1773.7224 1.0000000    0   control

observed <- cea(cost + qaly ~ group, data = trial, ref = "control")
summary(observed)
#> Cost-Effectiveness Summary
#> Formula: cost + qaly ~ group
#> Reference group: control
#> Treatment group: treatment
#> Incremental cost: 25
#> Incremental effect: 0.042
#> ICER: 588.802
#> 
#>              Outcome          Reference          Treatment Difference
#> delta_cost      Cost 3015 (SD 1582.802) 3040 (SD 1168.737)     25.000
#> delta_effect  Effect   0.573 (SD 0.217)   0.615 (SD 0.205)      0.042
#>                             CI p.value
#> delta_cost   [-219.54; 269.54]  0.8409
#> delta_effect     [0.005; 0.08]  0.0251

The observed treatment arm produces more QALYs with a small increase in mean cost. The ICER is the additional cost per additional QALY.

Bootstrap Uncertainty

set.seed(42)
boot_res <- boot_icer(cost + qaly ~ group, data = trial, ref = "control",
                      R = 1000, ci.type = "perc")
summary(boot_res)
#>                   Metric Observed BootstrapMean  StdError    Bias
#> DeltaCost     Delta Cost   25.000        22.690   122.813  -2.310
#> DeltaEffect Delta Effect    0.042         0.044     0.018   0.002
#> ICER                ICER  588.802       729.717 10682.651 140.915
#>                                CI
#> DeltaCost      [-221.62; 259.395]
#> DeltaEffect        [0.007; 0.079]
#> ICER        [-7579.75; 11119.446]

The bootstrap distribution summarizes sampling uncertainty in \(\Delta C\), \(\Delta E\), and the ICER. For publication-quality analyses, the number of replications should generally be increased beyond this vignette if computation time allows (Willan and Briggs 2006).

plot_ceplane(boot_res, k = 20000)

Cost-effectiveness plane from stratified non-parametric bootstrap replicates. The red line is the willingness-to-pay threshold.

Most simulated replicates lie in the north-east quadrant, indicating higher cost and higher effect for treatment. Replicates below the threshold line are cost-effective at that threshold.

Net Monetary Benefit and CEAC

ceac_tbl <- compute_nmb_ceac(
  boot_res,
  wtp_range = seq(0, 50000, 5000)
)

ceac_tbl
#>      WTP      ENMB Prob_CE
#> 1      0  -25.0000   0.419
#> 2   5000  187.2954   0.882
#> 3  10000  399.5908   0.964
#> 4  15000  611.8862   0.979
#> 5  20000  824.1816   0.983
#> 6  25000 1036.4770   0.984
#> 7  30000 1248.7724   0.986
#> 8  35000 1461.0678   0.988
#> 9  40000 1673.3632   0.988
#> 10 45000 1885.6586   0.989
#> 11 50000 2097.9540   0.989

plot_ceac(ceac_tbl)

Cost-effectiveness acceptability curve. The curve gives the bootstrap probability that treatment is cost-effective at each willingness-to-pay threshold.

The CEAC rises as the willingness-to-pay threshold increases because the treatment’s positive incremental effect receives more decision value. The curve should be interpreted as decision uncertainty, not as the expected size of the health benefit.

Deterministic Sensitivity Analysis

dsa_effect <- dsa_icer(
  cost + qaly ~ group,
  data = trial,
  param = "qaly",
  range = seq(0.50, 0.70, 0.025),
  ref = "control",
  metric = "INMB",
  k = 20000
)

dsa_effect
#>   Parameter        INMB
#> 1     0.500 -1483.71762
#> 2     0.525  -983.71762
#> 3     0.550  -483.71762
#> 4     0.575    16.28238
#> 5     0.600   516.28238
#> 6     0.625  1016.28238
#> 7     0.650  1516.28238
#> 8     0.675  2016.28238
#> 9     0.700  2516.28238

plot_dsa(dsa_effect, metric = "INMB")

One-way deterministic sensitivity analysis varying treatment-arm effect.

This one-way analysis shows how the incremental net monetary benefit changes as the assumed treatment-arm effect changes. Such analyses are useful for checking which assumptions drive conclusions, but they do not replace probabilistic uncertainty analysis.

Reproducibility Checklist

Define the reference and treatment arms before analysis.
Report \(\Delta C\), \(\Delta E\), ICER, and INMB at relevant thresholds.
Use bootstrap or model-based uncertainty methods for CEACs.
Interpret ICERs alongside the cost-effectiveness plane and net benefit.
Report the willingness-to-pay thresholds used for decision interpretation.

References

Briggs, Andrew H., Bernie J. O’Brien, and Gordon Blackhouse. 2002. “Thinking Outside the Box: Recent Advances in the Analysis and Presentation of Uncertainty in Cost-Effectiveness Studies.” Annual Review of Public Health 23: 377–401.

Drummond, Michael F., Mark J. Sculpher, Karl Claxton, Greg L. Stoddart, and George W. Torrance. 2015. Methods for the Economic Evaluation of Health Care Programmes. 4th ed. Oxford University Press.

Efron, Bradley, and Robert J. Tibshirani. 1993. An Introduction to the Bootstrap. Chapman; Hall/CRC.

Fenwick, Elisabeth, Karl Claxton, and Mark Sculpher. 2001. “Representing Uncertainty: The Role of Cost-Effectiveness Acceptability Curves.” Health Economics 10 (8): 779–87.

Glick, Henry A, Jalpa A Doshi, Seema S Sonnad, and Daniel Polsky. 2014. Economic Evaluation in Clinical Trials. OUP Oxford.

Stinnett, Aaron A., and John Mullahy. 1998. “Net Health Benefits: A New Framework for the Analysis of Uncertainty in Cost-Effectiveness Analysis.” Medical Decision Making 18 (2 Suppl): S68–80.

Willan, Andrew R, and Andrew H Briggs. 2006. Statistical Analysis of Cost-Effectiveness Data. John Wiley & Sons.

Cost-Effectiveness Analysis for Clinical Trials with CEACT