## Abstract

Twenty years ago, the “Panel on Cost-effectiveness in Health and Medicine” published a landmark text setting out appropriate methods for conducting cost-effectiveness analyses of health technologies. In the two decades since, the methods used for economic evaluations have advanced substantially. Recently, a “second panel” (hereafter “the panel”) was convened to update the text and its recommendations were published in November 2016. The purpose of this paper is to critique the panel’s updated guidance regarding the discounting of costs and health effects. The advances in discounting methodology since the first panel include greater theoretical clarity regarding the specification of discount rates, how these rates vary with the analytical perspective chosen, and whether the healthcare budget is constrained. More specifically, there has been an important resolution of the debate regarding the conditions under which differential discounting of costs and health effects is appropriate. We show that the panel’s recommendations are inconsistent with this recent literature. Importantly, the panel’s departures from previously published findings do not arise from an alternative interpretation of theory; rather, we demonstrate that this is due to fundamental errors in methodology and logic. The panel also failed to conduct a formal review of relevant empirical evidence. We provide a number of suggestions for how the panel’s recommendations could be improved in future.

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The authors have no relevant conflicts of interest.

## Additional information

This work was conducted at the School of Public Health, University of Alberta, the Department of Emergency Medicine, University of Alberta, and at the Centre for Health Policy and Management, School of Medicine, Trinity College Dublin.

## Appendices

### Appendix 1: ‘Welfarist’ (‘Societal’) Perspective

We will now propose several modifications that could be made to the panel’s methods under a welfarist perspective that would address the problems noted in our critique. Our proposed modifications lead to conclusions that are identical to those of Claxton et al. [6].

To resolve the issue with the decision rule in Eq. 3, the LHS must be expressed entirely in utility terms. The LHS is currently expressed in terms of the *consumption* value of the incremental health effects. Since \(\lambda_{t}\) represents the inverse of the marginal utility of consumption, it follows that dividing each term on the LHS of Eq. 3 by \(\lambda_{t}\) would yield the associated *utility* gain. A modified decision rule expressed entirely in terms of utility is:

Next, we will address the issues with Eqs. 4 and 5. A more appropriate specification of Eq. 4 is:

where \(g_{v}\) denotes growth in the consumption value of health. This is the same specification and notation as that used in the Claxton paper. Note that the negative \(g_{c}\) term from the panel’s Eq. 4 has been replaced with a positive \(g_{v}\) term in the modified Eq. 13.

To correct Eq. 5, each of the \(\lambda_{t}\) terms must be inverted:

which simplifies to

Note that \(\lambda_{1}\) was multiplied by \(1 + g_{c}\) in the panel’s Eq. 5, while \(\lambda_{1}\) is divided by \(1 + g_{c}\) in the modified Eq. 14.

Substituting Eqs. 13 and 14 into the modified decision rule in Eq. 12 yields:

Since \(\lambda_{1}\) appears in the denominator of every term in Eq. 15, it can be cancelled:

Conventionally, decisions are made by comparing the discounted ICER of a technology to a cost-effectiveness threshold, rather than by considering a net benefit decision rule such as that in Eq. 16. To derive the optimal discount rates to apply to future incremental costs (\(\Delta S_{2}\)) and incremental health gains (\(\Delta H_{2}\)), we must therefore rearrange Eq. 16 so that it resembles an ICER decision rule of the form:

where \(d_{c}\) and \(d_{h}\) represent the discount rates applied to incremental costs and incremental health effects, respectively, and \(\psi\) denotes the cost-effectiveness threshold. Note that the cost-effectiveness threshold is conventionally represented by \(\lambda\), but \(\lambda\) has already been defined as the inverse of the marginal utility of consumption so \(\psi\) is used instead.

As noted by Claxton et al. [6], a reasonable threshold to use under a welfarist perspective with no budget constraint is the current consumption value of health (\(V_{1}\)). We therefore rearrange Eq. 16 to resemble Eq. 17, where \(\psi = V_{1}\).

To do this, we first group the \(V_{1}\) terms on the LHS of the equation:

Then we divide by the terms in square brackets and rearrange the equation, so \(V_{1}\) is alone on the RHS:

If \(g_{c}\), \(\rho_{c}\) and \(g_{v}\) are “small”, Eq. 18 can be approximated by:

Comparing Eqs. 17 and 19, it follows that:

That is, the discount rate for incremental costs is approximated by the pure social rate of time preference for consumption (\(\rho_{c}\)) *minus* growth in the marginal utility of consumption (\(g_{c}\)). Incremental health effects should be discounted at a rate approximately equal to the discount rate applied to incremental costs *minus* growth in the consumption value of health (\(g_{v}\)). Under the conventional assumption that \(g_{v}\) is positive, this implies that a lower discount rate should be applied to health effects than costs; however, if \(g_{v}\) is negative then a higher discount rate should be applied to health effects.

### Appendix 2: ‘Extra-Welfarist’ (‘Healthcare Sector’) Perspective

Under an extra-welfarist perspective, the objective of the decision maker is to maximize the present value of health. Since there is a fixed health system budget, incremental costs fall upon the budget and displace health outcomes.

In a two-period model, the present value of the health gained is given by:

Meanwhile, the present value of the health forgone due to incremental costs falling on the health system budget is given by:

where the panel uses \(\Delta E_{t}\) to denote the costs that fall upon the healthcare sector budget in each period *t*.

The next stage in the process of deriving discount rates is to express a net benefit decision rule. The simplest net benefit decision rule is to adopt a technology if the present value of the health gained, as expressed in Eq. 22, is greater than or equal to the present value of the health forgone, as expressed in Eq. 23:

However, the panel does not present the net benefit decision rule specified in Eq. 24. Instead, the following net benefit decision rule is reported:

The panel provides no definition of \(g_{k},\) nor do they explain how Eq. 25 may be used to derive appropriate discount rates. The sub-section ends after specifying this equation, with no further explanation provided.

However, following Claxton et al. [6], Eq. 25 may be rearranged to resemble the ICER decision rule in Eq. 17. If the cost-effectiveness threshold is \(\psi = k_{1}\), then:

Under an extra-welfarist perspective, where the health system budget is fixed, it follows that the discount rate for incremental costs is approximated by the social rate of time preference for health (\(\rho_{H}\)) plus the growth rate of \(k_{t} ,\) while incremental health effects should be discounted at the social rate of time preference for health (\(\rho_{H}\)). Differential discounting is appropriate if, and only if, \(k_{t}\) is changing over time. That is, if the magnitude of the health forgone when marginal costs are imposed on the health system budget differs between time periods.

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Paulden, M., O’Mahony, J.F. & McCabe, C. Discounting the Recommendations of the Second Panel on Cost-Effectiveness in Health and Medicine.
*PharmacoEconomics* **35, **5–13 (2017). https://doi.org/10.1007/s40273-016-0482-0

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### Keywords

- Discount Rate
- Incremental Cost
- Marginal Utility
- Time Preference
- Future Consumption