A direct method for measuring discounting and QALYs more easily and reliably

Societal costs of sepsis in the Netherlands

BACKGROUND

Sepsis is a life-threatening syndrome characterized by acute loss of organ function due to infection. Sepsis survivors are at risk for long-term comorbidities, have a reduced Quality of Life (QoL), and are prone to increased long-term mortality. The societal impact of sepsis includes its disease burden and indirect economic costs. However, these societal costs of sepsis are not fully understood. This study assessed sepsis's disease-related and indirect economic costs in the Netherlands.

METHODS

Sepsis prevalence, incidence, sepsis-related mortality, hospitalizations, life expectancy, QoL population norms, QoL reduction after sepsis, and healthcare use post-sepsis were obtained from previous literature and Statistics Netherlands. We used these data to estimate annual Quality-adjusted Life Years (QALYs), productivity loss, and increase in healthcare use post-sepsis. A sensitivity analysis was performed to analyze the burden and indirect economic costs of sepsis under alternative assumptions, resulting in a baseline, low, and high estimated burden. The results are presented as a baseline (low-high burden) estimate.

RESULTS

The annual disease burden of sepsis is approximately 57,304 (24,398-96,244; low-high burden) QALYs. Of this, mortality accounts for 26,898 (23,166-31,577) QALYs, QoL decrease post-sepsis accounts for 30,406 (1232-64,667) QALYs. The indirect economic burden, attributed to lost productivity and increased healthcare expenditure, is estimated at €416.1 (147.1-610.7) million utilizing the friction cost approach and €3.1 (0.4-5.7) billion using the human capital method. Cumulatively, the combined disease and indirect economic burdens range from €3.8 billion (friction method) to €6.5 billion (human capital method) annually within the Netherlands.

CONCLUSIONS

Sepsis and its complications pose a substantial disease and indirect economic burden to the Netherlands, with an indirect economic burden due to production loss that is potentially larger than the burden due to coronary heart disease or stroke. Our results emphasize the need for future studies to prevent sepsis, saving downstream costs and decreasing the economic burden.

Testing Nonmonotonicity in Health Preferences

OBJECTIVE

The main aim of this article is to test monotonicity in life duration. Previous findings suggest that, for poor health states, longer durations are preferred to shorter durations up to some threshold or maximum endurable time (MET), and shorter durations are preferred to longer ones after that threshold.

METHODS

Monotonicity in duration is tested through 2 ordinal tasks: choices and rankings. A convenience sample (n = 90) was recruited in a series of experimental sessions in which participants had to rank-order health episodes and to choose between them, presented in pairs. Health episodes result from the combination of 7 EQ-5D-3L health states and 5 durations. Monotonicity is tested comparing the percentage rate of participants whose preferences were monotonic with the percentage of participants with nonmonotonic preferences for each health state. In addition, to test the existence of preference reversals, we analyze the fraction of people who switch their preference from rankings to choices.

RESULTS

Monotonicity is frequently violated across the 7 EQ-5D health states. Preference patterns for individuals describe violations ranging from almost 49% with choices to about 71% with rankings. Analysis performed by separate states shows that the mean rates of violations with choices and ranking are about 22% and 34%, respectively. We also find new evidence of preference reversals and some evidence-though scarce-of transitivity violations in choices.

CONCLUSIONS

Our results show that there is a medium range of health states for which preferences are nonmonotonic. These findings support previous evidence on MET preferences and introduce a new "choice-ranking" preference reversal. It seems that the use of 2 tasks with a similar response scale may make preference reversals less substantial, although it remains important and systematic.

HIGHLIGHTS

Two procedures based on ordinal comparisons are used to elicit preferences: direct choices and rankings. Our study reports significant rates of nonmonotonic preferences (or maximum endurable time [MET]-type preferences) for different combinations of durations and EQ-5D health states.Analysis for separate health states shows that the mean rates of nonmonotonicity range from 22% (choices) to 34% (rankings), but within-subject analysis shows that nonmonotonicity is even higher, ranging from 49% (choices) to 71% (rankings). These violations challenge the validity of multiplicative QALY models.We find that the MET phenomenon may affect particularly those EQ-5D health states that are in the middle of the severity scale and not so much the extreme health states (i.e., very mild and very severe states).We find new evidence of preference reversals even using 2 procedures of a similar (ordinal) nature. Percentage rates of preference reversals range from 1.5% to 33%. We also find some (although scarce) evidence on violations of transitivity.

What if 0 is not equal to 0? Inter-personal health utilities anchoring using the largest health gains

Prioritizing health technologies requires comparisons of improvements in longevity or quality of life (QoL), or both. For this purpose, value sets are constructed that contain weights assigned to health states based on societal preferences. I show that how this is typically done may distort the results by giving unjustifiably larger impact to individuals who prioritize improvements in QoL over longevity. The problem results from equating the utility differences between being dead and full health across people, ignoring the fact that interpersonal utility comparisons are forbidden (or at least problematic) in economics. I propose another approach: the numerical value of maximal health gain (either in longevity or QoL) is assumed to be equal across individuals, to remove the impact of the range of utilities differing between people. I test this approach using EQ-5D-5L and EQ-5D-3L utilities elicited in Poland for two modeling techniques: a simple econometric model and a Bayesian one that accounts for censoring. The proposed approach increases the utilities of the worst health state: from [Formula: see text] to [Formula: see text] in EQ-5D-5L and from about [Formula: see text] to [Formula: see text] in EQ-5D-3L. In the Bayesian approach, the impact is greater: from [Formula: see text] to [Formula: see text] for EQ-5D-5L and from [Formula: see text] to [Formula: see text] for EQ-5D-3L. I discuss some normative arguments why the proposed approach may be more justifiable for aggregating individual preferences for health outcomes.

Reducing socioeconomic health inequalities? A questionnaire study of majorization and invariance conditions

We study the appeal of basic preference conditions that underpin health inequality indices, including the widely used concentration index. We did a lab experiment in which 349 respondents had to choose repeatedly between two policies that generated a distribution of income and health among five groups in society. We found stronger support for preference conditions that focus on inequality in the marginal distribution of health (and income) than for preference conditions that favor reduced correlation between both dimensions. Respondents' choices were more in line with the principle of income related health transfers when policies did not affect the ranking of groups in terms of health. Respondents also expressed more concern about the correlation between income and health when health was expressed as a shortfall rather than an attainment. Support for the preference conditions was unaffected when all groups in society experienced the same absolute or relative health change.

Time and lexicographic preferences in the valuation of EQ-5D-Y with time trade-off methodology

In the valuation of EQ-5D-Y-3L, adult respondents are asked to complete composite time trade-off (cTTO) tasks for a 10-year-old child. Earlier work has shown that cTTO utilities elicited in such a child perspective are generally higher than when adults take their own perspective. We explore how differences in time preference in child and adult perspectives could explain this effect. Furthermore, as cTTO valuation in a child perspective involves explicit consideration of immediate death for a child, we also consider how cTTO utilities could be affected by decision-makers lexicographically avoiding death in children. We report the results of an experiment in which 219 respondents valued 5 health states in both adult and child perspectives with either a standard cTTO or a lead-time TTO only approach, in which immediate death is less focal. Time preferences were measured in both perspectives. Our results suggest that utilities were lower when lead-time TTO, rather than cTTO, was used. We find large heterogeneity in time preference in both perspectives, with predominantly negative time preference. The influence of time preferences on utilities, however, was small, and correcting for time preferences did not reduce differences between utilities elicited in both perspectives. Surprisingly, we found more evidence for differences in utilities between adult and child perspectives when lead-time TTO was used. Overall, these results suggest that time and lexicographic preferences affect time trade-off valuation in child and adult perspectives, but are not the explanation for differences between these perspectives. We discuss the implications of our findings for EQ-5D-Y-3L valuation.

Time and lexicographic preferences in the valuation of EQ-5D-Y with time trade-off methodology

In the valuation of EQ-5D-Y-3L, adult respondents are asked to complete composite time trade-off (cTTO) tasks for a 10-year-old child. Earlier work has shown that cTTO utilities elicited in such a child perspective are generally higher than when adults take their own perspective. We explore how differences in time preference in child and adult perspectives could explain this effect. Furthermore, as cTTO valuation in a child perspective involves explicit consideration of immediate death for a child, we also consider how cTTO utilities could be affected by decision-makers lexicographically avoiding death in children. We report the results of an experiment in which 219 respondents valued 5 health states in both adult and child perspectives with either a standard cTTO or a lead-time TTO only approach, in which immediate death is less focal. Time preferences were measured in both perspectives. Our results suggest that utilities were lower when lead-time TTO, rather than cTTO, was used. We find large heterogeneity in time preference in both perspectives, with predominantly negative time preference. The influence of time preferences on utilities, however, was small, and correcting for time preferences did not reduce differences between utilities elicited in both perspectives. Surprisingly, we found more evidence for differences in utilities between adult and child perspectives when lead-time TTO was used. Overall, these results suggest that time and lexicographic preferences affect time trade-off valuation in child and adult perspectives, but are not the explanation for differences between these perspectives. We discuss the implications of our findings for EQ-5D-Y-3L valuation.

Correcting for discounting and loss aversion in composite time trade-off

Time trade-off utilities have been suggested to be biased upwards. This bias is a result of the method being applied assuming linear utility of life duration, which is violated when individuals discount future life years or are loss averse for health. Applying a "corrective approach", that is, measuring individuals' discount function and loss aversion and correcting time trade-off utilities for these individual characteristics, may reduce this bias in utilities. Earlier work has developed this approach for time trade-off in a student sample. In this study, the corrective approach was extended to composite time trade-off (cTTO) methodology, which enabled correcting utilities for health states worse than dead. In digital interviews a sample of 150 members of the general public completed cTTO tasks for six health states, and afterward they completed measurements of loss aversion and discounting. cTTO utilities were corrected using these measurements under multiple specifications. Respondents were also asked to reflect on and adjust their cTTO utilities directly. Our results show considerable loss aversion and both positive and negative discounting were prevalent. As predicted, correction generally resulted in lower utilities. This was in accordance with the direction of adjustments made by respondents themselves.

Multivariate risk preferences in the quality-adjusted life year model

The interest in multivariate and higher-order risk preferences has increased. A growing body of literature has demonstrated the relevance and impact of these preferences, but for health the evidence is lacking. We measure multivariate and higher-order risk preferences for quality of life (QoL) and longevity, the two attributes of the Quality-Adjusted Life Year (QALY) model. We observe preferences for a positive correlation between these attributes and for pooling together a fixed loss in one of the attributes and a mean-zero risk in the other, and for pooling together mean-zero risks in QoL and longevity. The findings indicate that higher-order risk preferences are stronger for health than for money. Furthermore, we test if preferences for a risky treatment for a disease affecting only QoL, depend on life expectancy. We find no such a relation, but there is a positive relation between riskiness of a comorbidity affecting life expectancy and risk aversion for a QoL treatment. We therefore observe no definitive deviation from the QALY model, although the model is more robust when expected longevity is high. Our findings suggest that the current practice of cost-effectiveness analysis should be generalized to account for risk aversion in QoL and longevity, and higher-order preferences.

Simplified Mathematical Modelling of Uncertainty: Cost-Effectiveness of COVID-19 Vaccines in Spain

When exceptional situations, such as the COVID-19 pandemic, arise and reliable data is not available at decision-making times, estimation using mathematical models can provide a reasonable reckoning for health planning. We present a simplified model (static but with two-time references) for estimating the cost-effectiveness of the COVID-19 vaccine. A simplified model provides a quick assessment of the upper bound of cost-effectiveness, as we illustrate with data from Spain, and allows for easy comparisons between countries. It may also provide useful comparisons among different vaccines at the marketplace, from the perspective of the buyer. From the analysis of this information, key epidemiological figures, and costs of the disease for Spain have been estimated, based on mortality. The fatality rate is robust data that can alternatively be obtained from death registers, funeral homes, cemeteries, and crematoria. Our model estimates the incremental cost-effectiveness ratio (ICER) to be 5132 € (4926–5276) as of 17 February 2021, based on the following assumptions/inputs: An estimated cost of 30 euros per dose (plus transport, storing, and administration), two doses per person, efficacy of 70% and coverage of 70% of the population. Even considering the possibility of some bias, this simplified model provides confirmation that vaccination against COVID-19 is highly cost-effective.

Living up to expectations: Experimental tests of subjective life expectancy as reference point in time trade-off and standard gamble

Earlier work suggested that subjective life expectancy (SLE) functions as reference point in time trade-off (TTO), but has not tested or modelled this explicitly. In this paper we construct a model based on prospect theory to investigate these predictions more thoroughly. We report the first experimental test of reference-dependence with respect to SLE for TTO and extend this approach to standard gamble (SG). In two experiments, subjects' SLEs were used to construct different versions of 10-year TTO and SG tasks, with the gauge duration either described as occurring above or below life expectation. Our analyses suggest that both TTO and SG weights were affected by SLE as predicted by prospect theory with SLE as reference point. Subjects gave up fewer years in TTO and were less risk-tolerant in SG below SLE, implying that weights derived from these health state valuation methods for durations below SLE will be biased upwards.

The Corrective Approach: Policy Implications of Recent Developments in QALY Measurement Based on Prospect Theory

BACKGROUND AND OBJECTIVES

Common health state valuation methodology, such as time tradeoff (TTO) and standard gamble (SG), is typically applied under several descriptively invalid assumptions, for example, related to linear quality-adjusted life years (QALYs) or expected utility (EU) theory. Hence, the current use of results from health state valuation exercises may lead to biased QALY weights, which may in turn affect decisions based on economic evaluations using such weights. Methods have been proposed to correct responses for the biases associated with different health state valuation techniques. In this article we outline the relevance of prospect theory (PT), which has become the dominant descriptive alternative to EU, for health state valuations and economic evaluations.

METHODS AND RESULTS

We provide an overview of work in this field, which aims to remove biases from QALY weights. We label this "the corrective approach." By quantifying PT parameters, such as loss aversion, probability weighting, and nonlinear utility, it may be possible to correct TTO and SG responses for biases in an attempt to produce more valid estimates of preferences for health states. Through straightforward examples, this article illustrates the effects of this corrective approach and discusses several unresolved issues that currently limit the relevance of corrected weights for policy.

CONCLUSIONS

Suggestions for research addressing these issues are provided. Nonetheless, if validly corrected health state valuations become available, we argue in favor of using these in economic evaluations.

Do time trade-off values fully capture attitudes that are relevant to health-related choices?

Previous research has shown that demographics, beliefs, and self-reported own health influence TTO values. Our hypothesis is that attitudes towards length and quality of life influence TTO values, but should no longer affect a set of related choices that are based on respondents' own TTO scores. A representative sample of 1339 respondents was asked their level of agreement to four statements relating to the importance of quality and length of life. Respondents then went on to value 4 EQ-5D 5L states using an online interactive survey and a related set of 6 pairwise health-related choice questions, set up, so that respondents should be indifferent between choice options. We explored the impact of attitudes using regression analysis for TTO values and a logit model for choices. TTO values were correlated with the attitudes and were found to have a residual impact on the choices. In particular, those respondents who preferred quality of life over length of life gave less weight to the differences in years and more weight to differences in quality of life in these choice. We conclude that although the TTO responses reflect attitudes, these attitudes continue to affect health-related choices.

New findings from the time trade-off for income approach to elicit willingness to pay for a quality adjusted life year

In this paper we empirically investigate how to appropriately model utility of wealth and health. We use a recently proposed alternative approach to value willingness to pay (WTP) for health, making use of trade-offs between income and life years or quality of life, which we extend to allow for a more realistic multiplicative utility function over health and money. Moreover, we show how reference-dependency can be incorporated into this model and derive its predictions for WTP elicitation. We propose three experimental elicitation procedures and test these in a feasibility study, analysing the responses under different assumptions about the discount rate. Several interesting results are reported: first, the data are highly skewed, but if we trim the 5% lowest and highest values, we obtain plausible WTP estimates. Second, the results differ considerably between procedures, indicating that WTP estimates are sensitive to the assumed utility function. Third, respondents appear to be loss averse for both health and money, which is consistent with assumptions from prospect theory. Finally, our results also indicate that respondents are more willing to trade quality of life than life years.

Discounting health and money: New evidence using a more robust method

This study compares discounting for money and health in a field study. We applied the direct method, which measures discounting independent of utility, in a representative French sample, interviewed at home by professional interviewers. We found more discounting for money than for health. The median discount rates (6.5% for money and 2.2% for health) were close to market interest rates, suggesting that at the aggregate level the direct method solves the puzzle of unrealistically high discount rates typically observed in applied economics. Constant discounting fitted the data better than the hyperbolic discounting models that we considered. The substantial individual heterogeneity in discounting was correlated with age and occupation.

Deriving time discounting correction factors for TTO tariffs

The Time Trade-off (TTO) method is a popular method for valuing health state utilities and is frequently used in economic evaluations. However, this method produces utilities that are distorted by several biases. One important bias entails the failure to incorporate time discounting. This paper aims to measure time discounting for health outcomes in a sample representative for the general population. In particular, we estimate TTO scores alongside time discounting in order to derive a set of correction factors that can be employed to correct raw TTO scores for the downward bias caused by time discounting. We find substantial positive correction factors, which are increasing with the severity of the health state. Furthermore, higher discounting is found when using more severe health states in the discounting elicitation task. More research is needed to further develop discount rate elicitation procedures and test their validity, especially in general public samples. Moreover, future research should investigate the correction of TTO values for other biases as well, such as loss aversion, and to develop a criterion to test the external validity of TTO scores.

Methods for Performing Survival Curve Quality-of-Life Assessments

BACKGROUND

Many medical decisions involve an implied choice between alternative survival curves, typically with differing quality of life. Common preference assessment methods neglect this structure, creating some risk of distortions.

METHODS

Survival curve quality-of-life assessments (SQLA) were developed from Gompertz survival curves fitting the general population's survival. An algorithm was developed to generate relative discount rate-utility (DRU) functions from a standard survival curve and health state and an equally attractive alternative curve and state. A least means squared distance algorithm was developed to describe how nearly 3 or more DRU functions intersect. These techniques were implemented in a program called X-Trade and tested.

RESULTS

SQLA scenarios can portray realistic treatment choices. A side effect scenario portrays one prototypical choice, to extend life while experiencing some loss, such as an amputation. A risky treatment scenario portrays procedures with an initial mortality risk. A time trade scenario mimics conventional time tradeoffs. Each SQLA scenario yields DRU functions with distinctive shapes, such as sigmoid curves or vertical lines. One SQLA can imply a discount rate or utility if the other value is known and both values are temporally stable. Two SQLA exercises imply a unique discount rate and utility if the inferred DRU functions intersect. Three or more SQLA results can quantify uncertainty or inconsistency in discount rate and utility estimates. Pilot studies suggested that many subjects could learn to interpret survival curves and do SQLA.

LIMITATIONS

SQLA confuse some people. Compared with SQLA, standard gambles quantify very low utilities more easily, and time tradeoffs are simpler for high utilities. When discount rates approach zero, time tradeoffs are as informative and easier to do than SQLA.

CONCLUSIONS

SQLA may complement conventional utility assessment methods.

Would you rather be ill now, or later?

The time tradeoff (TTO) method is frequently used to calculate the quality adjustment of the quality adjusted life year and is therefore an important element in the calculation of the benefits of medical interventions. New specifications of TTO, known as 'lead time' TTO and 'lag time' TTO, have been developed to overcome methodological issues of the 'classic' TTO. In the lead time TTO, ill-health is explicitly placed in the future, after a period of good health, whereas in lag time TTO, a health state starts immediately and is followed by a 'lag time' of good health. In this study, we take advantage of these timing properties of lead and lag time TTO. In particular, we use data from a previous study that employed lead and lag time TTO to estimate their implied discounting parameters. We show that individuals prefer being ill later, rather than now, with larger per-period discount rates for longer durations of the health states.

Prospect theory in the health domain: a quantitative assessment

It is well-known that expected utility (EU) has empirical deficiencies. Cumulative prospect theory (CPT) has developed as an alternative with more descriptive validity. However, CPT's full function had not yet been quantified in the health domain. This paper is therefore the first to simultaneously measure utility of life duration, probability weighting, and loss aversion in this domain. We observe loss aversion and risk aversion for gains and losses, which for gains can be explained by probabilistic pessimism. Utility for gains is almost linear. For losses, we find less weighting of probability 1/2 and concave utility. This contrasts with the common finding of convex utility for monetary losses. However, CPT was proposed to explain choices among lotteries involving monetary outcomes. Life years are arguably very different from monetary outcomes and need not generate convex utility for losses. Moreover, utility of life duration reflects discounting, causing concave utility.

The way that you do it? An elaborate test of procedural invariance of TTO, using a choice-based design

The time tradeoff (TTO) method is often used to derive Quality-Adjusted Life Year health state valuations. An important problem with this method is that results have been found to be responsive to the procedure used to elicit preferences. In particular, fixing the duration in the health state to be valued and inferring the duration in full health that renders an individual indifferent, causes valuations to be higher than when the duration in full health is fixed and the duration in the health state to be valued is elicited. This paper presents a new test of procedural invariance for a broad range of time horizons, while using a choice-based design and adjusting for discounting. As one of the known problems with the conventional procedure is the violation of constant proportional tradeoffs (CPTO), we also investigate CPTO for the alternative TTO procedure. Our findings concerning procedural invariance are rather supportive for the TTO procedure. We find no violations of procedural invariance except for the shortest gauge duration. The results for CPTO are more troublesome: TTO scores depend on gauge duration, reinforcing the evidence reported when using the conventional procedure.

Looking at Patients’ Choices through the Lens of Expected Utility

The expected utility framework underlies much research in medical decision making. Because the framework requires decisions to be decomposed into probabilities of states and the values of those states, researchers have investigated the two components separately from each other and from patients’ actual decisions. The authors propose that it would be productive to focus more research on the relationships among risk perceptions, outcome valuations, and choices in the same decision makers. They outline exploratory analyses based on two existing national surveys, the Medical Expenditure Panel Survey and the Joint Canada/United States Survey of Health.

Constantly proving the opposite? A test of CPTO using a broad time horizon and correcting for discounting

Purpose

An important assumption underlying the quality-adjusted life year (QALY) model is that people trade off life years against health in the same proportion irrespective of the number of remaining life years. This is known as the constant proportional trade-offs (CPTO) condition. Previous studies have produced mixed empirical evidence about the validity of CPTO. This paper is the first to test CPTO using the time trade-off (TTO) method for a broad time horizon.

Methods

In a sample of 83 students, we use a choice based TTO protocol to elicit TTO scores for back pain, using ten different gauge durations ranging between 1 and 46 years. The TTO scores are corrected for discounting, which is elicited by means of the direct method.

Results

We find average TTO scores varying between 0.72 and 0.81. Although the scores do not differ much for different durations in absolute terms, some differences are significant, rejecting CPTO, with and without correcting for discounting. No clear relationship between TTO scores and gauge duration is found. An anchoring and rounding heuristic to some extent explains our results.

Conclusions

Our findings highlight the importance of elicitation methods and context dependencies in QALY measurement and warrant detailed investigation of their influence.

On the (not so) constant proportional trade-off in TTO

Purpose

The linear and power QALY models require that people in Time Trade-off (TTO) exercises sacrifice the same proportion of lifetime to obtain a health improvement, irrespective of the absolute amount. However, evidence on these constant proportional trade-offs (CPTOs) is mixed, indicating that these versions of the QALY model do not represent preferences. Still, it may be the case that a more general version of the QALY model represents preferences. This version has the property that people want to sacrifice the same proportion of utilities of lifetime for a health improvement, irrespective of the amount of this lifetime.

Methods

We use a new method to correct TTO scores for utility of life duration and test whether decision makers trade off utility of duration and quality at the same rate irrespective of duration.

Results

We find a robust violation of CPTO for both uncorrected and corrected TTO scores. Remarkably, we find higher values for longer durations, contrary to most previous studies. This represents the only study correcting for utility of life duration to find such a violation.

Conclusions

It seems that the trade-off of life years is indeed not so constantly proportional and, therefore, that health state valuations depend on durations.