Towards a better QALY model

A Feasible Estimation of a "Corrected" EQ-5D Social Tariff

OBJECTIVES

To demonstrate the feasibility of estimating a social tariff free of utility curvature and probability weighting biases and to test transferability between riskless and risky contexts.

METHODS

Valuations for a selection of EQ-5D-3L health states were collected from a large and representative sample (N = 1676) of the Spanish general population through computer-assisted personal interviewing. Two elicitation methods were used: the traditional time trade-off (TTO) and a novel risky-TTO procedure. Both methods are equivalent for better than death states, which allowed us to test transferability of utilities across riskless and risky contexts. Corrective procedures applied are based on rank-dependent utility theory, identifying parameter estimates at the individual level. All corrections are health-state specific, which is a unique feature of our corrective approach.

RESULTS

Two corrected value sets for the EQ-5D-3L system are estimated, highlighting the feasibility of developing national tariffs under nonexpected utility theories, such as rank-dependent utility. Furthermore, transferability was not supported for at least half of the health states valued by our sample.

CONCLUSIONS

It is feasible to estimate a social tariff by using interviewing techniques, sample sizes, and sample representativeness equivalent to prior studies designed to generate national value sets for the EQ-5D. Utilities obtained in distinct contexts may not be interchangeable. Our findings caution against routinely taking transferability of utility for granted.

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.

How Much Better is Faster? Value Adjustments for Health-Improvement Sequences

While the quality-adjusted life-year construct has advantages of simplicity and consistency, simplicity requires strong assumptions. In particular, standard assumptions result in health-state utility functions that are unrealistically linear and separable in risk and duration. Consequently, sequencing of a series of health improvements has no effect on the total value of the sequence because each increment is assessed independently of previous increments. Utility functions in nearly all other areas of applied economics are assumed to be nonlinear with diminishing marginal utility so it matters where an improvement occurs in a sequence. We construct a conceptual framework that that demonstrates how diminishing marginal utility for health improvements could affect preferences for different sequence patterns. Using this framework, we derive conditions for which the sum of conventional health-state utilities understates, overstates, or approximates the sequence-sensitive value of health improvements. These patterns suggest the direction and magnitude of possible adjustments to conventional value calculations. We provide numerical examples and identify recent studies whose results are consistent with the conceptual model.

Cost‑Effectiveness Risk‑Aversion Curves: Comparison of Risk-Adjusted Performance Measures and Expected-Utility Approaches

Accounting for risk attitudes in medical decision making under uncertainty has attracted little research. A recent proposal recommended using the results of a cost-effectiveness analysis to construct a cost-effectiveness risk-aversion curve (CERAC) to inform risk-averse decision makers choosing among healthcare programs with uncertain costs and effects. The CERAC is based on a risk-adjusted performance measure widely used in financial economics called the Sortino ratio. This paper evaluates the CERAC based on the Sortino ratio, derives its various properties, discusses the implications of using it to inform decision making under uncertainty, and compares it with the expected-utility approach. Analytic formulae for the CERAC, relating it to the means and standard deviations of costs and effects of a healthcare program, are derived for both approaches. Compared with the expected-utility approach, the CERAC based on the Sortino ratio implicitly assumes that the decision maker is highly risk averse.

A Head-to-Head Comparison of the Standard Quality-Adjusted Life Year Model With the Annual Profile Model

OBJECTIVES

The standard quality-adjusted life year (QALY) model (SQM) assumes time-utility independence within constant health states and additive independence when health varies over time. The validity of SQM has been challenged through reported violations of these assumptions. An alternative approach that relaxes these assumptions is to assign a single valuation to an entire health profile: an integral assessment of disease severity over time. Here, we compare SQM with the annual profile model (APM) and test SQM for additive independence.

METHODS

Eighty-two respondents valued 6 episodic conditions, including 4 of short duration, with SQM and APM, using the time trade-off method. Inter-rater reliability was assessed using intraclass correlation coefficients. Face validity was tested by asking respondents how well they were able to imagine the health states under SQM and APM. We calculated SQM QALY values for a 1-year time period, allowing for a direct comparison with APM values. For the short-term conditions we expected higher QALY values for SQM, violating additive independence.

RESULTS

APM showed higher interrater reliability (intraclass correlation coefficient of 0.53 vs 0.18, respectively) and better face validity than SQM, with 6% (APM) vs 21% (SQM) of all respondents reporting difficulties. Additive independence of SQM was violated in 5 of the 6 conditions (including the 4 short duration health states), with higher QALY values under SQM (mean difference 0.04).

CONCLUSION

The impact of short-term conditions is systematically underestimated under SQM when compared to a health profile model. APM is a less restrictive model and demonstrates better validity.

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 societal monetary value of a QALY associated with EQ-5D-3L health gains

There is an extensive body of empirical research that focuses on the societal monetary value of a quality-adjusted life year (MVQALY). Many of these studies have found the estimates to be inversely associated with the size of the health gain, and thus not conforming to the linearity assumption imposed in the QALY model. In this study, we explore the extent to which the MVQALY varies when it is associated with different types and magnitudes of quality of life (QoL) improvements. To allow for a comprehensive assessment, we derive the MVQALY corresponding to the full spectrum of health gains defined by the EQ-5D-3L instrument. The analysis was based on a large and representative sample of the population in Spain. A discrete choice experiment and a time trade-off exercise were used to derive a value set for utilities, followed by a willingness to pay questionnaire. The data were jointly analysed using regression analyses and bootstrapping techniques. Our findings indicate that societal values for a QALY corresponding to different EQ-5D-3L health gains vary approximately between 10,000€ and 30,000€. MVQALY associated with larger improvements on QoL was found to be lower than that associated with moderate QoL gains. The potential sources of the observed non-constant MVQALY are discussed.

A comparison of individual and collective decision making for standard gamble and time trade-off

Quality-Adjusted Life-Years (QALYs) are typically derived from individual preferences over health episodes. This paper reports the first experimental investigation into the effects of collective decision making on health valuations, using both time trade-off (TTO) and standard gamble (SG) tasks. We investigated collective decision making in dyads, by means of a mixed-subjects design where we control for learning effects. Our data suggest that collective decision making has little effect on decision quality, as no effects were observed on decision consistency and monotonicity for both methods. Furthermore, QALY weights remained similar between individual and collective decisions, and the typical difference in elicited weights between TTO and SG was not affected. These findings suggest that consulting with others has little effect on health state valuation, although learning may have. Additionally, our findings add to the literature of the effect of collective decision making, suggesting that no such effect occurs for TTO and SG.

QALYs without bias? Nonparametric correction of time trade-off and standard gamble weights based on prospect theory

Common health state valuation methodologies, such as standard gamble (SG) and time trade-off (TTO), typically produce different weights for identical health states. We attempt to alleviate these differences by correcting the confounding influences modeled in prospect theory: loss aversion and probability weighting. Furthermore, we correct for nonlinear utility of life duration. In contrast to earlier attempts at correcting TTO and SG weights, we measure and correct all these tenets simultaneously, using newly developed nonparametric methodology. These corrections were applied to three less-than-perfect health states, measured with TTO and SG. We found considerable loss aversion and probability weighting for both gains and losses in life years, and we observe concave utility for gains and convex utility for losses in life years. After correction, the initially significant differences in weights between TTO and SG disappeared for all health states. Our findings suggest new opportunities to account for bias in health state valuations but also the need for further validation of resulting weights.

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.

Quality-adjusted life year weights and treatment bias: Theory and evidence from cognitive interviews

Objectives:

The purpose of this research is to understand the thought processes that underpin responses to stated preference approaches for eliciting quality of life, in particular the standard gamble.

Methods:

We utilize standard gamble preference elicitation survey techniques to elicit quality-adjusted life year weights for two reduced health states: chronic severe depression and total blindness. After the survey, we conduct open-ended qualitative interviews with respondents to determine their thought processes while taking the surveys and to shed light on what their quality-adjusted life year weight is capturing. Survey responses were coded and analyzed for themes in NVivo, the results of which were then formalized in the terminology of decision sciences.

Results:

The qualitative results of the cognitive interviews present systematic evidence for a type of cognitive bias present in standard gamble quality-adjusted life year weight elicitation, which has not been previously highlighted and which we call treatment bias. We define this treatment bias as the consideration of salient treatment alternatives correlated with a reduced health state, when these alternatives are not explicitly posed in the question. Our formalization of this cognitive behavior demonstrates that treatment bias will always bias the elicited health state utility of treating the illness in question downward.

Conclusion:

The treatment bias highlighted in this study has implications for economic evaluation when comparing treatment for illnesses where alternative treatments are widely publicized versus those that are not. For example, comparing the effectiveness of treating depression versus arthritis may be biased against depression if advertisements for anti-depressants are more widely viewed by survey respondents than advertisements for arthritis treatments. We propose a statement to be imbedded in all questionnaires regarding stated preference elicitation of quality-adjusted life year weights in order to correct for this bias in future stated preference surveys.

Additive Multicriteria Decision Analysis Models: Misleading Aids for Life-Critical Shared Decision Making

Background. There is growing interest in multicriteria decision analysis (MCDA) for shared decision making (SDM). A distinguishing feature is that a preferred treatment should extend years of life and/or improve health-related quality of life (HRQL). Additive MCDA models are inadequate for the task. A plethora of MCDA models exist, each claiming that it can correctly solve real-world problems. However, most were developed in nonhealth fields and rely on additive models. This makes the problem of choosing an MCDA model as an aid for SDM a challenging and urgent one. Methods. A published 2017 MCDA of a hypothetical prostate cancer patient is used as a case in point of how not to do and how to do MCDA for SDM. We critically review it and analyze it using several additive linear MCDA models with years of life and HRQL as attributes and the linear quality-adjusted life-year (QALY) model. The following simple reasonableness test is presented for applicability of a method as an aid for SDM: Can a treatment that causes premature death trump a treatment that causes acceptable adverse effects? Results. Additive MCDA models and the linear QALY recommend significantly different alternatives. Additive MCDA models fail the proposed reasonableness test; the linear QALY model passes. Conclusions. MCDA possesses a strong craft element in addition to its technical aspects. MCDA practitioners and clinicians need to understand model limitations to choose models appropriate to the context. Additive MCDA models are inadequate for life-critical SDM. We advocate QALY models with additional research for increased realism as a tool for SDM.

A QALY loss is a QALY loss is a QALY loss: a note on independence of loss aversion from health states

Evidence has accumulated documenting loss aversion for monetary and, recently, for health outcomes-meaning that, generally, losses carry more weight than equally sized gains. In the conventional Quality-Adjusted Life Year (QALY) models, which comprise utility for quality and length of life, loss aversion is not taken into account. When measuring elements of the QALY model, commonly, the (implicit) assumption is that utility for length and quality of life are independent. First attempts to quantify loss aversion for QALYs typically measured loss aversion in the context of life duration, keeping quality of life constant (or vice versa). However, given that QALYs are multi-attribute utilities, it may be possible that the degree of loss aversion is dependent on, or inseparable from, quality of life and non-constant. We test this assumption using non-parametric methodology to quantify loss aversion, under different levels of quality of life. We measure utility of life duration for four health states within subjects, and present the results of a robustness test of loss aversion within the QALY model. We find loss aversion coefficients to be stable at the aggregate level, albeit with considerable heterogeneity at the individual level. Implications for applied work on prospect theory within health economics are discussed.

Preference-Sensitive Management of Post-Mammography Decisions in Breast Cancer Diagnosis

Decision models representing the clinical situations where treatment options entail a significant risk of morbidity or mortality should consider the variations in risk preferences of individuals. In this study, we develop a stochastic modeling framework that optimizes risk-sensitive diagnostic decisions after a mammography exam. For a given patient, our objective is to find the utility maximizing diagnostic decisions where we define the utility over quality-adjusted survival duration. We use real data from a private mammography database to numerically solve our model for various utility functions. Our choice of utility functions for the numerical analysis is driven by actual patient behavior encountered in clinical practice. We find that invasive diagnostic procedures such as biopsies are more aggressively used than what the optimal risk-neutral policy would suggest, implying a far-sighted (or equivalently risk-seeking) behavior. When risk preferences are incorporated into the clinical practice, policy makers should bear in mind that a welfare loss in terms of survival duration is inevitable as evidenced by our structural and empirical results.

Quality-Adjusted Life-Years without Constant Proportionality

BACKGROUND

A quality-adjusted life-year is a common unit of measurement in health valuation. Under its constant proportionality assumption, the value of a quality-adjusted life span is defined as the product of preference weight and life span.

OBJECTIVES

To empirically identify an alternative functional relationship between life span and value by relaxing the constant proportionality assumption.

METHODS

Using an online survey, 5367 respondents completed 30 to 40 paired comparisons where each involved a choice between two health outcomes: one with a longer life span and health problems (five-level EuroQol five-dimensional questionnaire) and the other with a shorter life span and no problems (time trade-off pair). Using 2670 pairs, a saturated model with indicator variables for 27 life spans and 90 health problems of varying duration and severity was estimated by maximum likelihood. Its coefficients empirically illustrate the relationship between life span and value on a quality-adjusted life-year scale.

RESULTS

The results reject constant proportionality (P < 0.01) and support the use of a power function to describe the relationship between life span and value, namely, value = preference weight × life span^β. The estimate of power (β = 0.415; 95% confidence interval 0.41-0.42) appears to depend on whether life span was expressed in a temporal unit of days (0.403), weeks (0.509), months (0.541), or years (0.654).

CONCLUSIONS

Raising life span to a power less than 1 implies decreasing marginal value of life span and greatly improved model fit, and confirms previous violations of proportionality. This power function may replace conventional assumptions in health valuation studies. Nevertheless, governmental agencies may favor a longer time horizon than that of the general population.

Estimating a constant WTP for a QALY-a mission impossible?

Economic evaluations are an important input to decision-making and priority-setting in the health care sector. Measuring preferences for health improvements, as the demand-side value (willingness to pay) of gaining a quality-adjusted life year (QALY), is one relevant component in the interpretation of the results from health economic evaluations. Our article addresses whether willingness to pay for a QALY (WTP-Q) is sensitive to the size of the health differences and the probability for improvement. We use data from a contingent valuation survey based on 1400 respondents conducted in the spring of 2014. The results show that the expectation of sensitivity to scope, or higher WTP to the larger expected quality of life improvement, is not supported. We find WTP-Q values that conform reasonably well to previous studies in Sweden.

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.

Are preferences over health states informed?

Background

The use of preference-elicitation tasks for valuing health states is well established, but little is known about whether these preferences are informed. Preferences may not be informed because individuals with little experience of ill health are asked to value health states. The use of uninformed preferences in cost-effectiveness can result in sub-optimal resource allocation. The aim of this study was to pilot a novel method to assess whether members of the public are informed about health states they value in preference-elicitation tasks.

Methods

The general public was said to be informed if the expectations of the public about the effect of ill health on people’s lives were in agreement with the experience of patients. Sixty-two members of the public provided their expectations of the consequences of ill health on five life domains (activities, enjoyment, independence, relationships, and avoiding being a burden). A secondary dataset was used to measure patient experience on those five consequences.

Results

There were differences between the expectations of the public and the experience of patients. For example, for all five life consequences the public underestimated the effects of problems in usual activities compared to problems in mobility. They also underestimated the effect of ‘anxiety or depression’ compared to physical problems on enjoyment of life and on the quality of personal relationships.

Conclusions

This proof-of-concept study showed that it is possible to test whether preferences are informed. This study should be replicated using a larger sample. The findings suggest that preferences over health states in this sample are not fully informed because the participants do not have accurate expectations about the consequences of ill health. These uninformed preferences may not be adequate for allocation of public resources, and research is needed into methods to make them better informed.

Altruistic Preferences in Time Tradeoff

Whether respondents incorporate altruistic preferences in time tradeoff (TTO) exercises remains understudied. We present an extended quality-adjusted life-year model incorporating altruism. We derive that altruism may affect TTO values in 2 directions. First, “longevity altruists” may wish to prolong life for the sake of their loved ones (to avoid being missed). Second, “quality-of-life altruists” may have a preference to avoid bad health states resulting in being a burden to loved ones. The existence and influence of these preferences in a TTO were empirically confirmed in a sample of 1690 respondents from the general public. We classified respondents as “longevity altruists” or “quality-of-life altruists” based on their reasoning behind inclusion of loved ones in their TTO responses. In line with expectations, longevity altruists traded fewer years than quality-of-life altruists. Nonaltruists gave intermediate values.

A Simulation Framework for Evaluating the Effectiveness of Chronic Disease Management Interventions

The treatment and management of chronic diseases currently comprise a major fraction of the United States' healthcare expenditures. These expenses are projected to increase as the US population ages. Utilization of the ambulatory healthcare system stemming from chronic conditions has been seen as contributory factor in the rising expenditures. Efforts to better manage chronic conditions ought to result in better health outcomes and, by extension, savings through lower utilization of ambulatory services. The longer-term financial consequences of such interventions, however, are more uncertain. This study offers a System Dynamics simulation framework that identifies and models the critical relationships associated with health outcomes and longer-term financial consequences. This framework is demonstrated through a comparison between groups with a similar generic chronic condition, but one group is subjected to a management intervention and the other group is not. The framework provides constructive insights into how the initial intervention cost estimates, the resulting savings, and the health status may change depending on uncertainties, feedback effects, and cost structures.

Willingness to pay for a quality-adjusted life year: an evaluation of attitudes towards risk and preferences

Background

This paper examines the Willingness to Pay (WTP) for a quality-adjusted life year (QALY) expressed by people who attended the healthcare system as well as the association of attitude towards risk and other personal characteristics with their response.

Methods

Health-state preferences, measured by EuroQol (EQ-5D-3L), were combined with WTP for recovering a perfect health state. WTP was assessed using close-ended, iterative bidding, contingent valuation method. Data on demographic and socioeconomic characteristics, as well as usage of health services by the subjects were collected. The attitude towards risk was evaluated by collecting risky behaviors data, by the subject’s self-evaluation, and through lottery games.

Results

Six hundred and sixty two subjects participated and 449 stated a utility inferior to 1. WTP/QALY ratios varied significantly when payments with personal money (mean €10,119; median €673) or through taxes (mean €28,187; median €915) were suggested. Family income, area income, higher education level, greater use of healthcare services, and the number of co-inhabitants were associated with greater WTP/QALY ratios. Age and female gender were associated with lower WTP/QALY ratios. Risk inclination was independently associated with a greater WTP/QALY when “out of pocket” payments were suggested. Clear discrepancies were demonstrated between linearity and neutrality towards risk assumptions and experimental results.

Conclusions

WTP/QALY ratios vary noticeably based on demographic and socioeconomic characteristics of the subject, but also on their attitude towards risk. Knowing the expression of preferences by patients from this outcome measurement can be of interest for health service planning.

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.

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.

Critical limb ischemia and its impact on patient health preferences and quality of life-an international study

Critical limb ischemia (CLI) has a significant impact on patients' quality of life (QoL). Despite cost utility evaluations being required by different authorities, data on patient health preferences and utilities for CLI are scarce. Hence, the objective of this study was to assess the impact of CLI on health preferences and health status of affected patients, and to generate health state utilities. In the International Study, 200 patients with CLI (stages III and IV according to Fontaine scale) were interviewed by trained interviewers with a discrete choice instrument, a standard gamble (SG), and the EuroQol-five dimension (EQ-5D) questionnaires (Marten Meesweg, Rotterdam, Netherland). Conjoint analysis showed that a planned amputation (33%) was the most relevant health attribute followed by ambulatory function (25%) and chronic pain (15%). Non-dependence on caregiver impacted on patient health state preference considerably, whereas healing of ulcer/skin lesions had less impact. Preference values obtained from the SG were 0.84, for an amputation subpopulation arriving at 0.70. The EQ-5D index values as well as the EQ-5D visual analog scale for patients with CLI were 0.56. The QoL data of patients with CLI result in decreased QoL and preference values with a planned amputation.

Estimating a WTP-based value of a QALY: the 'chained' approach

A major issue in health economic evaluation is that of the value to place on a quality adjusted life year (QALY), commonly used as a measure of health care effectiveness across Europe. This critical policy issue is reflected in the growing interest across Europe in development of more sound methods to elicit such a value. EuroVaQ was a collaboration of researchers from 9 European countries, the main aim being to develop more robust methods to determine the monetary value of a QALY based on surveys of the general public. The 'chained' approach of deriving a societal willingness-to-pay (WTP) based monetary value of a QALY used the following basic procedure. First, utility values were elicited for health states using the standard gamble (SG) and time trade off (TTO) methods. Second, a monetary value to avoid some risk/duration of that health state was elicited and the implied WTP per QALY estimated. We developed within EuroVaQ an adaptation to the 'chained approach' that attempts to overcome problems documented previously (in particular the tendency to arrive at exceedingly high WTP per QALY values). The survey was administered via Internet panels in each participating country and almost 22,000 responses achieved. Estimates of the value of a QALY varied across question and were, if anything, on the low side with the (trimmed) 'all country' mean WTP per QALY ranging from $18,247 to $34,097. Untrimmed means were considerably higher and medians considerably lower in each case. We conclude that the adaptation to the chained approach described here is a potentially useful technique for estimating WTP per QALY. A number of methodological challenges do still exist, however, and there is scope for further refinement.

The impact of patients' subjective life expectancy on time tradeoff valuations

BACKGROUND

Quality-adjusted life-year (QALY) calculations in economic evaluations are typically based on general public or patient health state valuations elicited with the time tradeoff method (TTO). Such health state valuations elicited among the general public have been shown to be affected by respondents' subjective life expectancy (SLE). This suggests that TTO exercises based on time frames other than SLE may lead to biased estimates. It has not yet been investigated whether SLE also affects patient valuations.

OBJECTIVE

To empirically investigate whether patients' SLE affects TTO valuations of their current health state.

METHODS

Patients with different severities of diabetic retinopathy were asked in a telephone interview to value their own health status using TTO. The TTO time frame (t) presented was based on age- and sex-dependent actuarial life expectancy. Patients were then asked to state their SLE. Simple and multiple regression techniques were used to assess the effect of the patients' SLE on their TTO responses.

RESULTS

In total, 145 patients completed the telephone interview. Patients' TTO values were significantly influenced by their SLE. The TTO value decreased linearly with every additional year of difference between t and the patients' SLE; that is, patients were more willing to give up years the shorter their SLE compared with t.

CONCLUSION

Patients' SLE influenced their TTO valuations, suggesting that respondents' SLE may be the most appropriate time frame to use in TTO exercises in patients. The use of other time periods may bias the TTO valuations, as the respondents may experience the presented time frame as a gain or a loss. The effect seems to be larger in patient valuations than in general public valuations.

A test of independence of discounting from quality of life

The quality-adjusted life-years (QALY) model assumes quality and quantity of life can be multiplied into a single index and requires quality and quantity to be mutually independent, which need not hold empirically. This paper proposes a new test for measuring independence of utility of life duration from quality of life in a riskless setting. We use a large representative sample of Dutch citizens and include two health states generally considered better than dead (BTD) and one health state considered worse than dead (WTD). Independence cannot be rejected when comparing the BTD health states, but is rejected when comparing the BTD states with the WTD state. In particular, utility of life duration becomes more concave for the WTD state. This may suggest that independence holds only for BTD health states. This has implications for the QALY model and would require using sign-dependent utility of life duration functions.

Increasing marginal utility of small increases in life-expectancy? Results from a population survey

The standard practice in cost-effectiveness analyses of health care is to assign a linear value to increasing lifetime gains. The aim of the current study was to examine the possible existence of non-linear utility for short life extensions. A representative sample of the Norwegian population, aged 40-59 years (n=2402), was asked to imagine that they had a limited remaining lifetime (1 year or 10 years) and were offered a treatment that would increase lifetime by a specified amount of time from 1 week to 1 year. In all scenarios, the price per week of life extension was held constant. The proportion of respondents that accepted the treatment increased with increasing extensions, indicating a convex utility function. The result suggests increasing marginal utility for life extensions up to 1 year.

Trying to estimate a monetary value for the QALY

In this paper we study the feasibility of estimating a monetary value for a QALY (MVQ). Using two different surveys of the Spanish population (total n = 892), we consider whether willingness to pay (WTP) is (approximately) proportional to the health gains measured in QALYs. We also explore whether subjects' responses are prone to any significant biases. We find that the estimated MVQ varies inversely with the magnitude of health gain. We also find two other (ir)regularities: the existence of ordering effects; and insensitivity of WTP to the duration of the period of payment. Taken together, these effects result in large variations in estimates of the MVQ. If we are ever to obtain consistent and stable estimates, we should try to understand better the sources of variability found in the course of this study.

The correction of TTO-scores for utility curvature using a risk-free utility elicitation method

This paper describes and employs a new method to correct time tradeoff (TTO)-scores for utility of life duration curvature. In contrast to most previous attempts to do so, it uses a risk-free method that corresponds well to the risk-free properties of the TTO-method. In addition, the method is robust to several biases that occur under methods that incorporate risk. Our results show a significant degree of curvature in utility of life duration and therefore a clear bias in TTO-scores. The risk-free method seems to be useful to correct TTO-scores for this influence and leads to significantly higher quality-adjustment factors.

Explaining the characteristics of the power (CRRA) utility family

The power family, also known as the family of constant relative risk aversion (CRRA), is the most widely used parametric family for fitting utility functions to data. Its characteristics have, however, been little understood, and have led to numerous misunderstandings. This paper explains these characteristics in a manner accessible to a wide audience.