A multi-criteria decision analysis perspective on the health economic evaluation of medical interventions

Abstract

A standard practice in health economic evaluation is to monetize health effects by assuming a certain societal willingness-to-pay per unit of health gain. Although the resulting net monetary benefit (NMB) is easy to compute, the use of a single willingness-to-pay threshold assumes expressibility of the health effects on a single non-monetary scale. To relax this assumption, this article proves that the NMB framework is a special case of the more general stochastic multi-criteria acceptability analysis (SMAA) method. Specifically, as SMAA does not restrict the number of criteria to two and also does not require the marginal rates of substitution to be constant, there are problem instances for which the use of this more general method may result in a better understanding of the trade-offs underlying the reimbursement decision-making problem. This is illustrated by applying both methods in a case study related to infertility treatment.

Appendix

Define V ₁(e) = λ e and V ₂(c) =  − c, and consider the NMB function

$$ \hbox{NMB}(c^{i},e^{i},\lambda) = \lambda e^{i} - c^{i} = V_{1}(e^{i}) + V_{2}(c^{i}). $$

(11)

Let $\underline{c}$ and $\overline{c}$ denote the worst and best possible value of the cost criterion, and let $\underline{e}$ and $\overline{e}$ denote the worst and best possible value of the effectiveness criterion. This allows us to express V ₁(e) and V ₂(c) as the following positive affine transformations of the linear partial value functions $v_{1}(e)=\frac{e - \underline{e}}{\overline{e} - \underline{e}}$ and $v_{2}(c)=\frac{\underline{c} - c}{\underline{c} - \overline{c}}$:

$$ V_{1}(e) = \frac{\lambda \overline{e} - \lambda \underline{e}}{\lambda \overline{e} - \lambda \underline{e}} (\lambda e - \lambda \underline{e}) + \lambda \underline{e} = (\lambda \overline{e} - \lambda \underline{e}) v_{1}(e) + \lambda \underline{e}, $$

(12)

$$ V_{2}(c) = \frac{\underline{c} - \overline{c}}{\underline{c} - \overline{c}} (\underline{c} - c) - \underline{c} = (\underline{c} - \overline{c}) v_{2}(c) - \underline{c}. $$

(13)

Now, by substituting (12) and (13) in (11), it follows after rewriting that

$$ \hbox{NMB}(c,e,\lambda) = (\lambda \overline{e} - \lambda \underline{e}) v_{1}(e) + (\underline{c} - \overline{c}) v_{2}(c) + \lambda \underline{e} - \underline{c}. $$

(14)

Finally, by normalizing the scaling factors, we obtain the following expression for the NMB function:

$$ \hbox{NMB}(c,e,\lambda) = (\lambda \overline{e} - \lambda \underline{e} + \underline{c} - \overline{c}) (w_{1} v_{1}(e) + w_{2} v_{2}(c)) + \lambda \underline{e} - \underline{c}, $$

(15)

with w ₁ and w ₂ defined as

$$ w_{1}=\frac{(\lambda \overline{e} - \lambda \underline{e})}{\lambda \overline{e} - \lambda \underline{e} + \underline{c} - \overline{c}}, $$

(16)

$$ w_{2}=\frac{\underline{c} - \overline{c}}{\lambda \overline{e} - \lambda \underline{e} + \underline{c} - \overline{c}}. $$

(17)