Methodology| Volume 23, ISSUE 1, P96-103, January 01, 2020

Health Years in Total: A New Health Objective Function for Cost-Effectiveness Analysis

Open ArchivePublished:December 23, 2019

Abstract

Objectives

To find an alternative for quality-adjusted life-year (QALY) and equal value of life (EVL) measures. Despite the importance of QALY in cost-effectiveness analysis (CEA)—because it captures the effects of both life expectancy and health-related quality of life (QOL) and enables comparisons across interventions and disease areas—its potential to be discriminatory towards patients with lower QOL presents a critical challenge that has resulted in the exclusion of its use in some public decision making (eg, US Medicare) on healthcare in the United States. Alternatives to QALY, such as EVL, have not gained traction because EVL fails to recognize the QOL gains during added years of life.

Methods

We present a new metric for effectiveness for CEA, health years in total (HYT), which overcomes both the specific distributional issue raised by QALY and the efficiency challenges of EVL.

Results

The HYT framework separates life expectancy changes and QOL changes on an additive scale. HYT have the same axiomatic foundations as QALY and perform better than both QALY, in terms of the discriminatory implications, and EVL, in terms of capturing QOL gains during added years of life. HYT are straightforward to calculate within a CEA model. We found that thresholds of $34 000/HYT and$89 000/HYT correspond to CEA thresholds of $50 000/QALY and$150 000/QALY, respectively.

Conclusions

The HYT framework may provide a viable alternative to both the QALY and the EVL; its application to diverse healthcare technologies and stakeholder assessments are important next steps in its development and evaluation.

Introduction

Cost-effectiveness analysis (CEA) plays a central role in health technology assessments around the world and has even begun to play an influential role in the United States through value frameworks such as that of the Institute of Clinical and Economic Review (ICER). The quality-adjusted life-year (QALY) has been the primary effectiveness measure for CEA from the very beginning.
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A utility maximization model for evaluation of health care programs.
The construct of the QALY was developed under the premise that it would serve as a health index or “utility” of an individual who spends time in a health state.
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Do people consider financial effects in answering quality of life questions?.
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Is silence golden? A test of the incorporation of the effects of ill-health on income and leisure in health state valuations.
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A quality of life (QOL) weight is assigned to the particular health state and represents the utility of that state as perceived by society. A QALY represents an attempt to capture the well-being of health as a function of both being alive and the quality of health.
QALYs help in comparing the wellbeing from health across patients, across diseases, and across treatments. Nevertheless, the health utility assigned to patients who are endowed with worse health (because of more severe disease, disability, age, etc) raises distributional issues in the use of the QALY for resource allocation decisions. For example, patients who may have co-occurring illnesses or disability have an overall lower QOL weight and, hence, an extension of their lives by reduction of health burden from any disease would not generate as many QALYs as a similar extension of life for otherwise healthy people. This distributional limitation arises because of the multiplicative nature of the QALY: life-years are multiplied by the utility.
This fundamental limitation of QALY has been a subject of criticism in the United States, so much so that it has often undermined the important function of CEA in informing the allocation of limited healthcare resources. In the United States, these concerns originated from 2 key events in the 1990s. The first was the passage of the Americans with Disability Act (ADA) in 1990, which prohibited discrimination on the basis of disability, and the second was the 1992 Oregon Medicaid proposal for rationing services, using cost per QALY as a primary metric, which arguably systematically disadvantaged people with pre-existing disabilities.
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More recently, after strong lobbying efforts, specific language barring the Center for Medicaid and Medicare Services from using the QALY criterion to determine coverage was added to the Affordable Care Act
PPACA
Sec. 6301∖1182 SSA. Page 678.
:(c)(1) The Secretary shall not use evidence or findings from comparative clinical effectiveness research conducted under section 1181 in determining coverage, reimbursement, or incentive programs under title XVIII in a manner that treats extending the life of an elderly, disabled, or terminally ill individual as of lower value than extending the life of an individual who is younger, nondisabled, or not terminally ill.
Other countries, specifically the UK, that use cost per QALY in their health technology assessment (HTA) processes have debated this same issue but did not find this specific distributional concern to be sufficient to preclude the use of QALYs.
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“Wickedness or folly? The ethics of NICE’s decisions”.
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Justice and the NICE approach.
Alternative measures of effectiveness have been proposed to address this concern of the QALY. The most widely discussed is Nord et al’s Equal Value of Life (EVL) framework, in which any extension of life is valued at a QOL weight of 1.
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Recently, ICER has proposed a modified version of EVL as a secondary effectiveness measure to address backlash against the use of QALY.
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EVL, however, has had limited traction among academics and decision-making bodies because it undervalues interventions that both extend life and improve QOL.
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Should we aggregate relative or absolute changes in QALY?.
We propose a solution that can address this specific distributional issue of QALYs without failing to account for the QOL impacts during the added years of life. In this article, we introduce the framework of health years in total (HYT), which separates life expectancy effects from QOL impacts through the use of an additive, rather than multiplicative, approach.

A Conceptual Discussion of Health Years in Total

Let us consider 2 treatments, indexed by 0 and 1. Let the corresponding time-period specific survival probabilities and QOL weights be given as Sjt and Qjt, j =0,1; t = 1,2,..,T. QALYs for each treatment are calculated as:

$Equation 1.$
(1)

Without loss of generality, let’s assume S1t ≥ S0t, ∀ t. One can write the incremental QALYs as:
$Equation 2.$
(2)

Equation (2) splits the incremental QALYs into 2 parts: (1) the survival gain from treatment 1 over 0 weighted by the QOL under treatment 1 during the added years of life, and (2) the QOL gains from treatment 1 over 0 during the years patients are alive under both treatments. This split is illustrated in Figure 1A. The distributional challenge with the QALY comes from the first part where the QOL under treatment 1 is usually lower for patients with unrelated comorbidity or disability than those without it. Consequently, similar extensions of life from treatment 1 for these 2 groups of patients are weighted and thereby valued differently.
Nord et al’s EVL formulation represents an attempt to address this problem by equating Q1t = 1 for the first part in (2) but retaining the actual values of Q1t in the second part of (2) (Figure 1B). Essentially, all extension of life is valued at full health. Although this fix solves the distributional issue of QALY, it creates a new one. Suppose treatment 1 extends life at a much better QOL for the patients, whereas another treatment, say 1A, extends the same amount of life but at a much lower QOL because of adverse effects from the treatment; this difference is not captured by the EVL, which values the life-extension from both treatments equally.
It is also important to note that the incremental EVL approach can be written as:
$Equation 3.$
(3)

which implies that it separates the calculation of incremental life-years (the first part) from the incremental (slightly modified) QALYs (the second part) (Figure 1B). This rationale will serve us well in the development of the health years in total (HYT) framework.

Health Years in Total

Starting from (1), we rewrite the incremental QALYs as follows:
$Equation 4.$
(4)

In contrast to EVL, we assume Q0t = 1 for the second part of (3), but retain the original values of Q0t for the first part, giving us:
$Equation 5.$
(5)

Like the EVL, incremental HYT separate the calculation of incremental life-years (the second part) from the incremental (slightly modified) QALY (Figure 1C). In fact, the HYT framework separates the life-year and QOL scale in the absolute levels, too:

It is important to note that for treatment 1, which produces the longest survival, absolute HYT level is the sum of life expectancy and the traditional QALY.
Thus, the calculation of HYT has 2 main features:
• It is just the sum of life-years (LYs) and a modified version of QALY (described below).
• Unlike a QALY that can range from 0 to 1 in any given year, a HYT can range from 0 to 2.
The incremental HYT, as illustrated in (5) are given as:
$ΔHYT=ΔLYs+ΔModifiedQALYs$

The Modified QALYs for any given intervention is based on calculating QALYs over a time period corresponding to the maximum survival under any given alternative. If one is comparing treatment 1 versus treatment 0, and patient life expectancy under treatment 0 is 2 years and under treatment 1 is 2.5 years, then the Modified QALYs for treatment 0 is calculated over 2.5 years (and not 2 years as in the traditional calculation of QALYs). This requires that one estimate a counterfactual QOL level for treatment 0 during the last 0.5 years, which represents the potential QOL of patients under treatment 0 had they not died. Further details and methods to estimate are discussed in the following section.

Conceptual Illustrations: The Role of Modified QALY in the Calculation of HYT

The differences between QALYs, EVL, and HYT and their respective incremental versions are illustrated in Figure 1 using the stylized example of treatments 1 and 0 from the previous section. Figure 1A represents the traditional QALY framework where the total QALYs under treatment 0 would be QALY0 = 2·Q0 and under treatment 1: QALY1 = 2.5·Q1. Incremental QALYs are then given as: ΔQALYs = 2.5·Q1 – 2 × Q0.
Figure 1B illustrates the EVL framework where the extension of life is valued at the QOL weight of 1, leading to incremental EVL of 2 × (Q1-Q0) + 0.5.
Similar to EVL, under the HYT framework, the scale of life-years and QOL are separated in the additive formula. The life-years scale just measures the traditional life expectancy under both the treatments: ΔLYs = 2.5 – 2 = 0.5 years.
For the QOL scale under the HYT framework, a modified QALY is calculated. For treatment 1, the modified QALY1 = traditional QALY1 = 2.5 × Q1 because treatment 1 produced the longer life expectancy. For treatment 0, we directly measure the QOL level, Q0, for patents until 2 years. For the modified QALYs, however, we have to estimate a counterfactual QOL level for treatment 0 beyond 2 years had the patients remained alive until 2.5 years. This is where the modified QALYs deviate from the traditional QALYs. In this stylized example, this counterfactual QOL level is assumed to continue at Q0. Consequently, as illustrated in Figure 1C, the incremental Modified QALYs would be:

Finally, HYT and incremental HYT are given as:
$HYT1=2.5+2.5×Q1$

$HYT0=2+2.5×Q0$

$ΔHYT=0.5+2.5×(Q1−Q0)$

In summary, when comparing a new intervention that extends life over an old intervention, it is important to answer the counterfactual question: what would the QOL have been among patients getting the old intervention had those patients stochastically remained alive for more years? This is because the “factual” QOL experienced by these patients under the new treatment during the additional years of life must be put in context to the counterfactual estimate under the old treatment to get a precise estimate of what value addition this new treatment is generating in terms of QOL, beyond the life extension. Because of the assumption of a stochastic extension of survival under the old treatment, the counterfactual QOL during this extension can be represented by the observed expected QOL weight under the old intervention. In fact, as illustrated in the Appendix (in Supplemental Materials found at https://doi.org/10.1016/j.jval.2019.10.014), this counterfactual QOL weight can be calculated separately for each time period in a practical decision model. No new information is needed to calculate HYT than what is already available in a traditional CEA model.

Are We Double-Counting?

One immediate reaction to the formulation of HYT may be that we seem to be double-counting benefits of treatment by counting the full added years of life and the QOL gains during those added years of life. This is not the case with HYT, which are built on the notion that life-years gained provide distinct utility to individuals from the QOL gains and that these utilities are separable in nature. It is this separability that solves the distributional issues of QALYs and the efficiency challenges of EVL. Figure 1D illustrates the area-wise comparison on incremental QALY, EVL, and HYT metrics. Although it would seem that under HYT, area B and D are being double counted because their absolute magnitudes are the same, B and D represent different attributes of the utility function. For example, if a new treatment produces a lower QOL than old treatment during life extension, B < 0 and D > 0, thereby canceling that specific life extension area under the new treatment.

Axiomatic Foundation for HYT

The axiomatic foundations of HYT are the same as those for QALY.
• Pliskin J.S.
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• Weinstein M.C.
Utility functions for life-years and health status.
For QALY to represent a multi-attribute utility function over life-years and QOL, it must follow 2 main axioms: utility independence and constant proportional trade-off.
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Quality-adjusted life-years (QALY) utility models under expected utility and rank dependent utility assumptions.
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Characterizing QALY under a general rank dependent utility model.
Utility independence requires that preferences over lotteries on longevity do not depend on fixed health levels and conversely that preference over lotteries on health levels do not depend on fixed longevity. The second axiom is the constant proportional trade-off, which means that the fraction of a person’s remaining life that the person would trade-off for a given improvement in health does not depend on the number of years of life that remain. In fact, Pliskin (1980) already showed that the HYT formulation is an acceptable utility function in his equation 2(c) under these axioms.
• Pliskin J.S.
• Shepard D.S.
• Weinstein M.C.
Utility functions for life-years and health status.
In his formulation, and under risk neutrality (r = 1), the general utility function from which the QALY model was derived was given as:
$U(y,q)=p×y+(1−p)×y×U(q)$

where y = longevity and U(q) is the utility of health status and P a proportional trade-off constant. With P = 0.5, one can clearly see that HYT are directly proportional to that utility function.

Implications for Measurement of Quality of Life Weights

The assumption of constant proportional trade-off allows us to estimate a utility weight for a particular health status through the time trade-off method. For example, in a time trade-off scenario, we seek indifference between 2 bundles of goods: L years of life at less than perfect health (with a weight of q) versus L1 years of life (L1 < L) at perfect health at a utility of 1.
If we express this indifference through a QALY-based utility, then: L1 × 1 = L × q → q = L1/L. If we express this utility using a HYT formulation, however, we will arrive at the same measurement principle for q. Specifically, the HYT comparison in this scenario will be L1+ L × 1 = L + L × q → q = L1/L.

Distributional Issues Under QALY, EVL, and HYT

To illustrate how HYT address the limitations of QALY and EVL regarding distributional and efficiency issues, respectively, we demonstrate a comparison of these metrics across 2 populations (A and B) for different treatments. Table 1 shows the comparisons.
Table 1Comparative performance of QALY, EVL, and HYT.
PopulationTreatmentLYQOL weightsQALYΔQALYEVLΔEVLHYTΔHYT
ANo Trt1.4.4.41 + (2 ×.4) = 1.8
Trt2.61.20.81.61.22 + (2 ×.6) = 3.21.4
BNo Trt1.7.7.71 + (2 ×.7) = 2.4
Trt2.91.81.11.91.22 + (2 ×.9) = 3.81.4
ANo Trt1.1.1.11 + (2 ×.1) = 1.2
Trt2.1.20.11.112 + (2 ×.1) = 2.21
BNo Trt1.1.1.11 + 0.1 = 1.1
Trt1110.910.91 + 1 = 2.00.9
ANo Trt1.4.4.41 + (2 ×.4) = 1.8
Trt2Y1: .4, Y2: .71.10.71.412 + (.4 +.7) = 3.11.3
BNo Trt1.4.4.41 + (2 ×.4) = 1.8
Trt2Y1: .4, Y2: .81.20.81.412 + (.4 +.8) = 3.21.4
ANo Trt1.7.7.71 + (1.5 ×.7) = 2.05
Trt1.5.2.3−0.4.2 +.5= .701.5 + (1.5 ×.2) = 1.8−.25
BNo Trt1.9.9.91 + (1.5 ×.9) = 2.35
Trt1.5.4.6−0.3.4 +.5 = .901.5 + (1.5 ×.4) = 2.1−.25
$EVLj=mink(LYk)×QoLj+{LYj−mink(LYk)};$
$j=Trt,NoTrt;k=Trt,NoTrt;$
EVL indicates equal value of life; HYT, health years in total; QALY, quality-adjusted life-year; QOL, quality of life; Trt, treatment.
In our first comparison, the treatment produces an additional life-year compared with no treatment for both population A and B. Population A has a lower overall QOL (0.4) under no treatment than population B (0.7). In both the populations, the treatment increases QOL by 0.2 units. This situation is the classic case where QALYs discriminate against population A because it has a lower QOL to begin with. Although the absolute value addition by the treatment seems to be the same for both populations, the incremental QALYs are lower for population A versus population B. Both EVL and HYT address this problem and produce the same incremental benefits for populations A and B.
In the next comparison, treatment has very different effects in populations A and B. For population A, treatment extends life by a year over no treatment but produces no QOL gain over the baseline QOL of 0.1. In population B, treatment does not extend life but produces substantial (0.1 to 1) increase in QOL. In this situation, QALYs would deem treatment to be 9 times more effective in population B than in population A mainly because they down-weight life-year gained under low baseline QOL. Both EVL and HYT would deem treatment to be more comparable across the population, although still favoring treatment in population A slightly.
In the third comparison, treatment extends life by a year in both populations but improves QOL to 0.7 during the added year of life in population A and to 0.8 in population B. In this case, EVL fails to capture the differential benefit of treatment in population B over A, as EVL values life extension similarly in both populations. Both QALY and HYT can recognize the extra value-addition in population B.
Finally, in the fourth comparison, the treatment produces a gain in life-years over the control but also produces a decrement in QOL. In both populations A and B, treatment results in 0.5 additional life-years but decreases QOL by 0.5 QOL units; however, baseline QOL under no treatment is 0.7 in population A and 0.9 in population B. In this case, in an analogy to the first comparison, QALYs down-weight the gain due to the increase in life-years from treatment in population A compared with population B because of the lower starting QOL in population A. Although the decrements in QOL in both populations exceed the improvements in life-years, use of QALYs value the treatment less in population A over B. EVL solves the distributional issue and values the new treatment in the same way in both populations; however, EVL also calculates the incremental value of treatment to be zero in either population A or B, although the no treatment option produces 0.5 QOL extra units of life throughout the first year and only loses half a year of life in less than perfect health in either population. HYT solve both the distributional issue by valuing treatment the same across populations and also assigning a negative incremental value of treatment.
These comparisons illustrate how HYT can overcome the limitations of both QALYs and EVL and provide a more consistent metric for evaluation of healthcare intervention. Nevertheless, no metric of health can be fully devoid of any distributional implications. Although the use of HYT may be able to generate fairness in the valuation of health benefits across different populations, HYT would put less value on technologies that generate only QOL gains but no survival gains. This is because in these situations, incremental HYT would be the same as incremental QALY, but now would face a different set of thresholds reflecting the distribution of incremental HYT in the overall population of technologies (see the following section). These implications are discussed in the next sections.
Calculations of HYT within simulation models involve some additional work, but the process is relatively straightforward. A detailed description of these calculations is given in Appendix 1 (in Supplemental Materials found at https://doi.org/10.1016/j.jval.2019.10.014).

Because any new effectiveness metric for CEA would only be useful if we also have some knowledge about the corresponding thresholds for decision making, we attempt to provide some initial, rough estimates for the HYT thresholds. Our goal is to estimate the percentiles of the Δ$/ΔQALY distribution that the standard thresholds of$50K to $150K/QALY correspond to and then identify the Δ$/ΔHYT estimates corresponding to the same percentiles in the distribution of Δ$/ΔHYT. We pursue this percentile approach under the assumption that the corresponding thresholds for QALY versus HYT would identify the same number of technologies to be above or below the thresholds, given a fixed budget constraint, although the ranking of those technologies may change. We use the Tufts Center for the Evaluation of Value and Risk in Health (CEVR) CEA registry of incremental cost-effectiveness ratios. Details of this analysis can be found in Appendix 1 (in Supplemental Materials found at https://doi.org/10.1016/j.jval.2019.10.014). Our main analysis involves the 218 estimates that have complete data on costs, QALYs, and life-years. We approximate ΔHYT = ΔLY + ΔQALY – ΔLY × Q0 = ΔLY + ΔQALY – ΔLY × (QALY0/LY0), recreate the ICER distribution with Δ$/ΔHYT, and compare it to the distribution of Δ$/ΔQALY. Figure 2 illustrates the distribution of log(Δ$/ΔQALY) and log(Δ$/ΔHYT). We find that the commonly used thresholds of$50 000/QALY, $100 000/QALY, and$150 000/QALY correspond to the 53rd, 71st, and 78th percentiles of the log(Δ$/ΔQALY) distribution. The corresponding numbers from the same percentiles of the log(Δ$/ΔHYT) distribution give us threshold values of $34 000/HYT,$74 000/HYT, and $89 000/HYT, respectively. The threshold values were the same as HYT when EVL was considered. Implications for HYT Thresholds for Decision Making We applied the same approximation above to the calculation of the incremental cost-effectiveness ratios in Δ$/ ΔQALY reported by ICER reports over the last 5 years. Among the 109 cost-effectiveness results where both life-years and QALYs were reported, we dropped all ratios that represented dominant or dominated treatments (29) and those rations above $200 000/QALY (39) because converting to HYT did not have any effect on being closer to any of the thresholds. Of the remaining 41 ratios that we used for this illustration, 90% of the technologies were in the cardiovascular space. Figure 3 illustrates the comparison between using Δ$/ ΔQALY versus Δ$/ΔHYT with respect to their corresponding thresholds. In general, Δ$/ΔHYT is lower than Δ$/ΔQALY. Nevertheless, when compared with their respective thresholds, we find that among the 41 technologies studied, only 1 technology falls below the lower threshold for HYT but not for QALYs. Several technologies fall above the upper threshold for HYT but not for QALYs. In general, it appears that HYT alter the relative ranks of technologies. It is important to note that compared with using QALYs, use of HYT will down-weight the value of technologies that only produce QOL gains as seen in the cluster of technologies indicated by red dots in Figure 3B. Most of these technologies generate zero or negative incremental life-years but positive QALYs. Consequently, the corresponding incremental HYT are either close to or slightly lower than incremental QALYs. When compared with the$/HYT based thresholds, they fall in the cost-effectiveness rankings.
To better understand how using HYT shifts valuation of technologies compared with QALYs, it is important to note that the difference between incremental HYT and incremental QALYs can be approximated as:

where L1 and L0 are the life expectancy from new and old treatment (L1 ≥ L0). This difference suggests the following:
• 1.
$/HYT will be the same as$/QALY if a new intervention does not produce life expectancy gains or if the QOL under the old treatment was 1. Because the thresholds for $/HYT are lower than$/QALY, this suggests that these types of new technologies will be valued less than they would have been under $/QALY. • 2. Compared with incremental QALYs, technologies that produce life extension will be valued more, especially if QOL under the old treatment was lower. This is a necessary feature of any metric that overcomes the discriminatory attribute of QALYs. Nevertheless, because the$/HYT is about 70% of that $/QALY thresholds, (ΔHYT – ΔQALY)/ΔQALY) > 0.57 (= 1 – (1/.7)) for a new technology to be cost-effective under HYT that was just above the QALY-threshold. In Figure 3B, the green dot represents a technology with an incremental QALY of 0.3 and an incremental HYT of 0.54, leading to the ratio of (ΔHYT – ΔQALY)/ΔQALY) = 0.79. Thus this technology looks more cost-effective under HYT than under QALY. For the red dots, the average (ΔHYT – ΔQALY)/ΔQALY) = 0.02, and for the blue dots, 0.25. More work is needed to fully understand how the theoretical principles of HYT translate to addressing distributional issues in practice use. This is especially important because the majority of technologies used to illustrate here only represent technologies in the cardiovascular space and therefore do not provide a full representation of all technologies. Moreover, we only used an approximation for HYT using the average QOL weights during the entire time horizon. A more thorough analysis should follow principles laid out in the Appendix to calculate HYT. Discussion We present a framework for valuing health outcomes in CEA that addresses a fundamental limitation of QALYs in the context of a distributional issue across populations. The health years in total (HYT) framework disentangles life expectancy impacts from QOL effects through an additive model, thus enabling patients with lower QOL to fully benefit from interventions that extend life expectancy. HYT are the sum of life expectancy plus modified QALYs. The modified QALYs are calculated over a time frame corresponding to the maximum survival of any given alternative, thus requiring the estimation of a counterfactual QOL during the additional time period. We provide illustrations of the use of the HYT framework, establish a theoretical framework, and assess decision-making thresholds for using HYT. Our work suggests that the HYT framework provides a robust and feasible approach to addressing the specific distributional limitation of QALYs that potentially discriminates against life extension for patients with severe disease. In addition, the HYT framework does not penalize treatments that improve QOL during life extension, which the EVL framework does. We believe that if this framework were to be adopted for CEA in the United States and elsewhere, it is important to carry out both cost per QALY and cost per HYT analyses for the foreseeable future to better understand the performance characteristics of the HYT metric. Nevertheless, we also believe cost per HYT analyses may be sufficient to address both dimensions of efficiency and the specific equity concern highlighted. In fact, the HYT’s formulation is also more flexible than a QALY formulation because it provides an opportunity for a society to explicitly put different weights on QOL gains than LY gains. It can also help distinguish between the gains coming from LY versus QOL, which is not always possible in a multiplicative model such as QALY. Despite the advantages of HYT over QALYs and EVL, there are important limitations and areas for further research. First, although the conceptualization of an additive model is fairly straightforward, use of a counterfactual to calculate a modified QALY is not necessarily intuitive. The calculation of modified QALYs for an intervention depends on the life expectancy of its comparators. Development of communication tools is needed to ensure a common understanding and use of HYT. Second, HYT do not address distributional issues as to whether populations with higher QALY shortfalls or other equity factors should receive more resources. • Cookson R. • Mirelman A.J. • Griffin S. • et al. Using cost-effectiveness analysis to address health equity concerns. It is important to note that HYT do not produce different estimates between elderly and disabled people versus younger and non-disabled people as long as technology produces the same incremental health (in terms of LY and QOL gains) in those groups. QALYs do produce different estimates, a limitation that HYT overcome. Nevertheless, the fact that some people do not face the potential to generate more heath is an equity issue that cannot be addressed by any one health metric and therefore should lead to additional equity considerations around QALY or LY shortfall. Third, further exploration of the integration of the modified QALYs and HYT within complex CEA models is needed; complexities may arise that have not been discussed or foreseen herein. Finally, a clearer understanding of the impact of the HYT framework on technology prioritization and value thresholds is needed. Although we present approximations to the HYT in a limited number of examples, extensive and formal evaluations by multiple investigators are needed. It is evident from our work that the use of HYT may shift the distributional issues in QALYs across populations to distributional issues across types of technologies, although the latter may be more palatable to societal decision making. For example, use of HYT, in contrast to use of QALYs, will certainly put more value on technologies producing life-years gain that those solely producing QOL gains. To what extent such preferences reflect social values and also those of the decision maker remains to be seen. However, what we know from the American Disability Act, a key legislation that is often invoked to criticize QALY, is that extension of life as lower baseline QOL cannot be valued differentially than the same extension of life at a higher baseline QOL. When it comes to national legislation and societal values in the US, HYT do conform more to those values than do QALYs. It should be pointed out that according to existing evidence, such shift in valuation of life expectancy over QOL does not accord with general public views in Europe. • Shah K.K. • Tsuchiya A. • Wailoo A.J. Valuing health at the end of life: an empirical study of public preferences. , • Hansen L.D. • Kjaer T. Disentangling public preferences for health gains at end-of-life: further evidence of no support of an end-of-life premium. More work, both qualitative and quantitative, is needed to understand social preferences. As with any new health metric for CEA, a new threshold must be derived to reflect the health opportunity costs of marginal expenditures. We found that the thresholds corresponding to the$50 000, $100 000, and$150 000 per QALY thresholds would correspond to $34 000,$74 000, and $89 000 per HYT (or$ per EVL) cutoffs. These cutoffs were generated based on the rationale of keeping the same number of technologies under the threshold. Ideally, these cutoffs should have been generated by keeping the same amount of budget expenditures under each cut-off; however, such detailed data on technology-use-specific budget impacts are difficult to find. Nevertheless, more work is needed to identify reliable thresholds for alternative metrics.
In summary, we developed a novel framework for valuing health outcomes in CEA in healthcare. We were motivated by the inherent potential of the QALY framework to produce discriminatory results under certain conditions, despite limited evidence of detrimental impacts on decision making. We showed that this framework has a sound theoretical basis, is feasible to implement, and may have important policy implications. We encourage further critique, development, application, and testing of the HYT framework to assess its potential for moving the field beyond the limitations of the QALY.

Acknowledgments

We would like to thank Peter Neumann and the Center for the Evaluation of Value and Risk in Health at the Institute for Clinical Research and Health Policy Studies at Tufts Medical Center for providing us with the CEA registry data. We thank Devika Gandhay and Taran Paul for excellent research assistance. We also thank the Institute for Clinical and Economic Review (ICER) Health Economic council members and seminar participants at the University of Washington PHEnOM seminar, at the Centre for Health Economics, University of York, at the Office of Health Economics, London and two anonymous reviewers for helpful comments. All errors and opinions are ours. No external funding source was used for this work.

Supplemental Material

• Appendix 1

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