Quality-adjusted Life-year Model Research Articles

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.

Cost-effectiveness analysis of statins in primary care: results from the Arteris cohort study

The Swiss Federal Office of Public Health performed a health technology assessment regarding statins in primary care. The chosen models may lead to a situation where a clinically indicated statin therapy is estimated not to be cost effective. We performed a cohort study regarding cardiovascular events, comparing SCORE and AGLA risk categories with tertiles of carotid plaque burden and used two models for cost-effectiveness analysis of high-potency statins. Subjects (n = 2842) were followed up for 5.9 ± 2.9 years with the occurrence of 154 cardiovascular events (extrapolated 10-year risk was 9.2%). Carotid plaque imaging (total plaque area, TPA) significantly improved cardiovascular risk prediction compared with AGLA and SCORE for event-free survival prediction, test accuracy (discrimination) and calibration. Discrimination was significantly improved by about 4% with the inclusion of TPA. Cost-effectiveness analysis using quality-adjusted life years (QALYs) and sensitivity analyses (based on 16 models) ranged between CHF 144,496 and −128,328 per QALY. Cost-effectiveness analysis using direct and indirect costs showed that a treat-them-all strategy in the Swiss population would be cost effective with a return-on-investment per patient in 10 years of between CHF 4442 and 19,059, and the use of carotid imaging was also cost effective (incremental cost-efficiency ratio −2.97 to −7.86). Carotid ultrasound significantly improved cardiovascular risk stratification and is cost effective. The Swiss Medical Board QALY model presents several drawbacks, which are shown in our sensitivity analysis, where results vary considerably and are not useful for clinical decision making. A “treat them all” strategy with statins in the Swiss population aged 30–65 years may be cost effective, when indirect costs of avoidable cardiovascular events are included, even at an unacceptably low value of a statistical life year.

Pediatric Vaccines and Cost-Effectiveness Thresholds: How Much is Too Much to Pay for Prevention?

Cost-effectiveness evaluations play an important role in recommendations for use of pediatric vaccines that are set forth by the US Advisory Committee on Immunization Practices (ACIP). The fact that these evaluations are undertaken and accorded weight suggests that a critical value for designating pediatric vaccines as cost-effective (or not) must exist. For recommended pediatric vaccines, however, reported incremental cost-effectiveness ratios (ICERs) have varied greatly, and there does not appear to be an explicit threshold used by the ACIP to define how much is too much to pay for the prevention of communicable diseases in children. Further complicating this issue is the fact that conventional ICER thresholds—expressed in terms of cost per quality-adjusted life-year (QALY) gained—accord value only to length and quality of life and may not reflect our preferences as individuals or a society. For example, risk, an important attribute of many healthcare decisions, is ignored by the QALY model, as is the distribution of health benefits across different members of society. Are we indeed indifferent about risk and do we really believe that the value of disease prevention in children should be measured by the same “yardstick” as that for older adults? Accordingly, do we really believe that “a QALY is a QALY”? These issues, which are reviewed and discussed in this article, are more than just of theoretical interest; the answers impact how public health policy is determined, which impacts the lives and well-being of entire populations as well as the budgets of payers.

Theoretical bounds on the value of improved health

Policies that improve health and longevity are often valued by combining expected gains in quality-adjusted life years (QALYs) with a constant willingness-to-pay (WTP) per QALY. This constant is derived by dividing value per statistical life (VSL) estimates by expected future QALYs. We explore the theoretical validity of this practice by studying the properties of WTP for improved health and longevity in a framework that makes minimal assumptions about the shape of an agent's utility function. We find that dividing VSL by expected QALYs results in an upper bound on the WTP for a marginal improvement in the quality of life, as measured by gains in health status or longevity. Calibration results suggest that analysts using this approach to monetize health benefits overestimate the value of a program or policy by a factor of two on average. We also derive a lower bound on the WTP for improved health and longevity that permits a novel empirical test for the descriptive validity of the QALY model. Our calibrations suggest that this lower bound is on average 20% smaller than the actual WTP.

Multivariate risk preferences in the QALY model

In recent years the interest in multivariate and higher-order risk preferences has increased noticeably. A growing body of literature has demonstrated both the relevance and the impact of these preferences in several domains, although for health the empirical evidence is lacking. In this study we empirically measure multivariate and higher-order risk preferences for quality of life and longevity, the two elements of the Quality-Adjusted Life Year (QALY) model. We observe overwhelming support for correlation seeking between these two attributes as well as significant evidence of cross-imprudence and cross-intemperance. These findings indicate that higher-order risk preferences appear to deviate more from neutrality for health than for money. Furthermore, we test if preferences for a risky treatment for a disease affecting only quality of life, depend on life expectancy. Our results show no systematic evidence of such a relation, although there is a marginally significant positive relation between riskiness of the comorbidity affecting life expectancy and risk aversion for a treatment affecting quality of life. We therefore observe no definitive deviation from the QALY model, although the model appears to be more robust when expected longevity is high.

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.

Setting Dead at Zero: Applying Scale Properties to the QALY Model.

Introduction. Scaling severe states can be a difficult task. First, the method of measurement affects whether a health state is considered better or worse than dead. Second, in discrete choice experiments, different models to anchor health states on 0 (dead) and 1 (perfect health) produce varying amounts of health states worse than dead. Research Question. Within the context of the quality-adjusted life year (QALY) model, this article provides insight into the value assigned to dead and its consequences for decision making. Our research questions are 1) what are the arguments set forth to assign dead the number 0 on the health–utility scale? And 2) what are the effects of the position of dead on the health–utility scale on decision making? Methods. A literature review was conducted to explore the arguments set forth to assign dead a value of 0 in the QALY model. In addition, scale properties and transformations were considered. Results. The review uncovered several practical and theoretical considerations for setting dead at 0. In the QALY model, indifference between 2 health episodes is not preserved under changes of the origin of the duration scale. Ratio scale properties are needed for the duration scale to preserve indifferences. In combination with preferences and zero conditions for duration and health, it follows that dead should have a value of 0. Conclusions. The health–utility and duration scales have ratio scale properties, and dead should be assigned the number 0. Furthermore, the position of dead should be carefully established, because it determines how life-saving and life-improving values are weighed in cost–utility analysis.

Quality-of-Life–Adjusted Hazard of Death: A Formulation of the Quality-Adjusted Life-Years Model of Use in Benefit-Risk Assessment

BackgroundAlthough the quality-adjusted life-years (QALY) model is standard in health technology assessment, quantitative methods are less frequent but increasingly used for benefit-risk assessment (BRA) at earlier stages of drug development. A frequent challenge when implementing metrics for BRA is to weigh the importance of effects on a chronic condition against the risk of severe events during the trial. The lifetime component of the QALY model has a counterpart in the BRA context, namely, the risk of dying during the study. MethodsA new concept is presented, the hazard of death function that a subject is willing to accept instead of the baseline hazard to improve his or her chronic health status, which we have called the quality-of-life–adjusted hazard of death. ResultsIt has been proven that if assumptions of the linear QALY model hold, the excess mortality rate tolerated by a subject for a chronic health improvement is inversely proportional to the mean residual life. ConclusionsThis result leads to a new representation of the linear QALY model in terms of hazard rate functions and allows utilities obtained by using standard methods involving trade-offs of life duration to be translated into thresholds of tolerated mortality risk during a short period of time, thereby avoiding direct trade-offs using small probabilities of events during the study, which is known to lead to bias and variability.

DO WE HAVE THE CORRECT HEALTH ECONOMICS METHODS TO EVALUATE END OF LIFE CARE? AN ANALYSIS OF STAKEHOLDER PERSPECTIVES

BackgroundThe most common approach to health economic evaluation is based on the principle of maximising total health, with outcomes of value being gains in health and length of life, the...

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.

Incorporating Extrinsic Goals Into Decision and Cost-Effectiveness Analyses

It has not been widely recognized that medical patients as individuals may have goals that are not easily expressed in terms of quality-adjusted life years (QALYs). The QALY model deals with ongoing goals such as reducing pain or maintaining mobility, but goals such as completing an important project or seeing a child graduate from college occur at unique points in time and do not lend themselves to easy expression in terms of QALYs. Such extrinsic goals have been posited as explanations for preferences inconsistent with the QALY model, such as unwillingness to trade away time or accept gambles. In this article, the authors examine methods for including extrinsic goals in medical decision and cost-effectiveness analyses. As illustrations, they revisit 2 previously published analyses, the management of unruptured intracranial arteriovenous malformations (AVMs) and the evaluation of preventive strategies for BRCA + women.

Adding Extrinsic Goals to the Quality-Adjusted Life Year Model

Methods for evaluating health quality are central to medical decision analyses. The most important such method is the quality-adjusted life year (QALY), in which a patient’s length of life is given weight proportional to his/her quality of health. QALYs have become ubiquitous in medical cost-effectiveness as a measure of preference for health outcomes. However, numerous studies have demonstrated that the correlation between measured QALYs and a patient’s current health is at best modest. Moreover, it is known that individuals may trade lifetime for improved health quality when remaining lifetime is long, but not when it is short; and those with poor health quality may prefer to survive only until important life milestones and no longer. These behaviors are inconsistent with the QALY model. To address these concerns, we examine methods for including life goals in health preference models. The QALY model already captures ongoing goals such as minimizing chronic pain or maintaining physical mobility, goals whose achievement has impact proportional to length of life. However, other goals, termed extrinsic goals, such as completing an important project or seeing a child graduate from college, are qualitatively different—their achievement has impact that is independent of length of life, and therefore cannot be captured using QALYs. In this paper, we present a generalization of the QALY model that incorporates both ongoing goals and extrinsic goals. The new model allows the plausible behaviors mentioned above but forbidden by the QALY model.

The QALY Model and Individual Preferences for Health States and Health Profiles over Time: A Systematic Review of the Literature

The numbers of quality-adjusted life years (QALYs) gained are increasingly being used to represent the gains in individual utility from treatment. This requires that the value of a health improvement to an individual is a simple product of gains in quality of life and length of life. The article reports on a systematic review of the literature on 2 issues: whether the value of a state is affected by how long the state lasts, and by states that come before or after it. It was found that individual preferences over health are influenced by the duration of health states and their sequence. However, although there is much variation across individual respondents, the assumptions tend to hold much better when valuations are aggregated across respondents, which is encouraging for economic evaluations that rely on using average (mean or median) values.

The Validity of QALYs under Non‐Expected Utility

This paper examines applications of non-expected utility in the health domain. The most widely used utility model in health economics, the time-linear QALY model, assumes (i) separability of quality of life and life duration, and (ii) linearity of the utility for life duration. We perform new tests, which are robust to violations of expected utility, of these two assumptions. The data support separability, but show that the utility for life duration is concave rather than linear. The finding of concave utility may not be surprising in itself. The contribution of this paper is to demonstrate this empirically without being invalidated by violations of expected utility. It has by now been widely recognised that expected utility is not valid as a descriptive theory of decision under uncertainty. The descriptive violations of expected utility have led to the emergence of several non-expected utility theories. The increasing importance of non-expected utility makes it necessary to reassess applications that were previously based on expected utility. Examples of such reassessments include Karni and Safra (1989), Crawford (1990) and Dekel et al. (1991) for game theory, Machina (1995) and Wakker et al. (1997) for insurance theory and Cubitt and Sugden (1998) for the evolution of preferences. See Starmer (2000) for a review. The present paper examines applications of non-expected utility in the health domain. We focus on the main utility model in health economics, the quality-adjusted life-years (QALY) model, and present new theoretical foundations for, and empirical tests of this model under non-expected utility. QALYs provide a simple way to combine the two dimensions of health, life duration and health status, into a single utility index. They are intuitively appealing, which facilitates communication to policy makers, and analytically tractable, which explains their widespread use in practical studies. A disadvantage of QALYs is that they only represent individual preferences over health under strong assumptions. If these assumptions do not hold, then the use of QALYs may lead to incorrect policy recommendations. To gain insight into the validity of QALYs, it is necessary to assess the restrictiveness of the assumptions that the QALY model imposes. In the most common version of the QALY model, the time-linear QALY model, the utility of the health outcome of spending t years in health state q is equal to tV(g), where V is a utility function over health states. That is, in the time-linear QALY model the utility for duration is linear. It is well known that under expected utility, linearity of utility implies risk neutrality. As it turns out, risk neutrality with

Multiattribute Structure for QALYs

Health status is inherently a multiattribute construct. We examine multiattribute utility decompositions for the quality-adjusted life year (QALY) utility model commonly employed in medical decision and cost-effectiveness analyses. We consider several independence conditions on preference, including the classical notions of preferential independence and utility independence, as well as new related notions of standard-gamble independence and time-tradeoff independence. The latter conditions are helpful in simplifying standard-gamble utility assessment procedures and time-tradeoff assessment procedures in the presence of multiple health attributes. Under the QALY model, all these conditions are equivalent and result in a purely multiplicative decomposition of utility over health states.

A new and more robust test of QALYs

Previous empirical tests of quality-adjusted life-years (QALYs), the most widely used outcome measure in economic evaluations of health care, generally yielded negative results. These tests were, however, for the most part based on expected utility, which is now widely acknowledged to be descriptively inaccurate. The observed violations might, therefore, have been caused by violations of expected utility. We performed a new test of QALYs, which is valid under expected utility and under the two most influential non-expected utility theories, rank-dependent utility and prospect theory, and found considerable support for the QALY model. Our findings suggest that QALYs may be valid if nonexpected utility formulas are used to compute health state utilities.

Equity weights in the allocation of health care: the rank-dependent QALY model

This paper introduces the rank-dependent quality-adjusted life-years (QALY) model, a new method to aggregate QALYs in economic evaluations of health care. The rank-dependent QALY model permits the formalization of influential concepts of equity in the allocation of health care, such as the fair innings approach, and it includes as special cases many of the social welfare functions that have been proposed in the literature. An important advantage of the rank-dependent QALY model is that it offers a straightforward procedure to estimate equity weights for QALYs. We characterize the rank-dependent QALY model and argue that its central condition has normative appeal.

A test of the QALY model when health varies over time

Quality-adjusted life years (QALYs) estimate the utility derived from health profiles by taking account of life expectancy and quality of life. In applying QALYs to situations where health varies over time, it is usual to assume that we can add the utilities from constituent health states. This paper investigates the QALY approach to combining health states over time using two tests. The first test rejects additive independence, the central assumption of the QALY model, for individual respondents. The second test is equivocal. The tests are, therefore, unable to conclusively reject the QALY approach to combining health states over time.

Double discounting of QALYs.

Quality-adjusted life-years (QALYs) calculated from time tradeoff (TTO) based preferences have a time preference component. To impose a conventional discount rate on these implicitly discounted QALYs introduces some degree of double discounting. The purpose of this study was to determine the magnitude of the double discounting effect and the effectiveness of a suggested method for avoiding double discounting in a TTO-based QALY model. Our analysis used holistic and composite preference scores obtained with the TTO technique in a prior study of four hypothetical treatment paths in type 2 diabetes. Discounted composite preference scores were significantly discrepant from holistic preference scores. Adjusting TTO-based quality weights prior to external discounting reduced the discrepancy only slightly. Since time preference effects may vary with health state context, the double discounting effect needs further investigation.