Net benefit separation and the determination curve: A probabilistic framework for cost-effectiveness estimation

Abstract

Considerations regarding clinical effectiveness and cost are essential in comparing the overall value of two treatments. There has been growing interest in methodology to integrate cost and effectiveness measures in order to inform policy and promote adequate resource allocation. The net monetary benefit aggregates information on differences in mean cost and clinical outcomes; the cost-effectiveness acceptability curve was developed to characterize the extent to which the strength of evidence regarding net monetary benefit changes with fluctuations in the willingness-to-pay threshold. Methods to derive insights from characteristics of the cost/clinical outcomes besides mean differences remain undeveloped but may also be informative. We propose a novel probabilistic measure of cost-effectiveness based on the stochastic ordering of the individual net benefit distribution under each treatment. Our approach is able to accommodate features frequently encountered in observational data including confounding and censoring, and complements the net monetary benefit in the insights it provides. We conduct a range of simulations to evaluate finite-sample performance and illustrate our proposed approach using simulated data based on a study of endometrial cancer patients.

Keywords: Censoring; confounding; cost-effectiveness; observational; policy.

Figure 1.

Illustration of the limiting behavior of the cost-effectiveness acceptability curve. Here, the experimental treatment is more costly on average, but also yields greater mean clinical benefit (a prototypical setting in which a cost-effectiveness analysis would be warranted). Note that the step from zero to one in the limit of the CEA occurs precisely at the value of the ICER.

Figure 2.

Illustration of NBS under four scenarios. In the first (upper left), treatment A = 1 dominates A = 0; the reverse is true in the second scenario (upper right). In the third scenario (lower left), the treatments are comparably cost-effective, and the the fourth scenario (lower right), treatment A = 1 is moderately more cost-effective as compared to A = 0.

Figure 3.

Illustration of non-redundancy of the NMB and NBS under the simple characterization described in Section 3.1. The solid and dashed curves denote the density function for B(λ) in the control and treated group, respectively. In all cases, $c_a^1=-1$ in order to produce the left-skewed individual net benefits (often encountered in practice). In the left panel, α₀ = 5, β₀ = 1/3, and $c_0^2=-8$; α₁ = 5/4, β₁ = 5, and $c_1^2=-6.47$. In this setting, the NBS is null but the NMB is not. The setup of the right panel differs only in that $c_1^2=-8$, producing a discrepancy between the NBS and NMB that is the reverse of the left panel.

Figure 4.

Cost-effectiveness determination curve for RT (left) and CT (right) vs. control over the willingness-to-pay range of interest (bold). Corresponding point-wise confidence intervals are included for the willingness-to-pay values of primary interest. For the purposes of illustrating the scope of curve behavior, we extend the range of λ beyond the range of interest (shown in lighter gray).

Figure 5.

Plot of the NMB ($ × 1000) for RT (left) and CT (right) vs. control over the willingness-to-pay range of interest (bold). For the purposes of illustrating the scope of curve behavior, we extend the range of λ beyond the range of interest (shown in lighter gray).

Figure 6.

Cost-effectiveness acceptability curve for RT (left) and CT (right) vs. control over the willingness-to-pay range of interest (bold). For the purposes of illustrating the scope of curve behavior, we extend the range of λ beyond the range of interest (shown in lighter gray).