Healthy Year Equivalent

Healthy Year Equivalent and the Valuation of Whole Health Profiles

The healthy year equivalent, or HYE, turns a person's preference for an entire path of health over time into a single count of years lived in full health. Mehrez and Gafni proposed it in 1989 as a rival outcome measure for cost-utility analysis, arguing that the QALY builds the value of a health path from separately weighted states and so reflects individual preferences only in part. The proposal set off a long theoretical debate, which showed how close the HYE is to the time trade-off and why risk attitude matters once outcomes are uncertain. In applied work the QALY prevailed, and the HYE remains useful mainly as a way of seeing which assumptions QALY-based evidence rests on.

Why Mehrez and Gafni wanted a profile-based measure

A QALY gives each health state a weight, multiplies it by the time spent in that state and adds the products. Bleichrodt restates the classic conditions under which this is a correct representation of a person's utility, namely mutual utility independence between life years and health status, a constant proportional trade-off of life years for health status, and risk neutrality with respect to life years. He shows that, under uncertainty, using QALYs imposes three further restrictions that the HYE does not need. These are additive independence of health in different periods, stable intertemporal preferences and equal weights for health improvements in different periods, and empirical evidence suggests they cannot be expected to hold in all applications.

Mehrez and Gafni argued that the QALY, being a health status index, does not stem directly from the individual's utility function and so only partly reflects true preferences, which could lead a decision maker to choose an option the person does not prefer. Dolan later framed the contrast as health states against health profiles and noted that additive separability, under which the value of one period does not depend on the periods around it, appears not to hold in the limited evidence then available.

The defining equivalence between a profile and healthy years

The HYE is defined by an indifference. A person compares a lifetime health profile, which can include changes of state and a date of death, with a life lived wholly in full health, and the HYE is the number of healthy years that gives exactly the same utility as the profile.

$$U(Q) = U(\text{full health for } H^{*} \text{ years})$$

where $Q$ is the lifetime health profile being valued, $U$ is the person's utility function over whole profiles and $H^{*}$ is the healthy year equivalent of $Q$. Wakker gives an example in which ten years, five with a hoarse voice followed by five unable to speak, are worth the same as 9.5 years in full health.

Bleichrodt notes that the definition needs preferences that increase with healthy years, as the QALY also assumes, and that profiles worse than death may give negative HYEs.

The two-stage standard gamble procedure

Mehrez and Gafni set out a measurement algorithm in 1991 built on the standard gamble and consisting of two lottery questions. They gave versions for any lifetime profile and for the simpler chronic case, and reported a satisfactory test of reproducibility. In the first stage the respondent chooses between the profile for certain and a gamble between full health for the maximum duration and immediate death.

$$Q \sim \left[\, \text{full health for } T \text{ years with probability } p^{*} ,\ \text{death with probability } 1 - p^{*} \,\right]$$

where $\sim$ means the respondent is indifferent, $T$ is the maximum duration offered and $p^{*}$ is the probability at which indifference is reached. In the second stage the same gamble, fixed at $p^{*}$, is compared with a varying number of certain healthy years.

$$\left[\, \text{full health for } T \text{ years with probability } p^{*} ,\ \text{death with probability } 1 - p^{*} \,\right] \sim \text{full health for } H^{*} \text{ years}$$

where $H^{*}$ is the number of healthy years at which the respondent is indifferent, and this is the HYE. Because the gamble is identical in both indifferences, expected utility theory implies that the profile and $H^{*}$ healthy years have equal utility. In Wakker's hoarse and mute example, the first stage gives 0.97 with a ten-year maximum and the second gives 9.5 healthy years.

Worked example with two respondents and different risk attitudes

All numbers in this example are illustrative. A profile $P$ consists of 4 years in a moderate state followed by 6 years in a severe state and then death, and the maximum duration offered is 10 years. Two respondents would each accept exactly 6.4 years in full health in place of $P$ if asked directly, and they differ only in their attitude to risk over healthy years.

$$U_A(x) = \frac{x}{10} \qquad U_B(x) = \sqrt{\frac{x}{10}}$$

where $x$ is a number of years in full health, $U_A$ is the utility function of respondent A, who is risk neutral, and $U_B$ is that of respondent B, who is risk averse. Both functions give 0 for no years and 1 for 10 years.

1. First stage. With full health for 10 years scored 1 and death scored 0, the stage-one probability equals the utility of $P$, which is the utility of 6.4 healthy years. Respondent A therefore reports $p^{*}$ = 6.4 / 10 = 0.64, and respondent B reports $p^{*} = \sqrt{0.64} = 0.80$, because a risk-averse person needs better odds before giving up a certain outcome.

2. Second stage. Respondent A needs $H^{*}/10 = 0.64$, so $H^{*}$ = 6.4 years. Respondent B needs $\sqrt{H^{*}/10} = 0.80$, so $H^{*}$ = 10 × 0.64 = 6.4 years.

3. What cancelled. The first-stage answers differ, yet the HYEs are equal, because the second stage converts the gamble back into certain years with the same utility function that produced it. Each HYE equals the direct time trade-off answer.

4. Comparison with a QALY. Suppose chronic-state time trade-off weights of 0.80 for the moderate state and 0.55 for the severe state had been elicited separately. The QALY total for $P$ is 0.80 × 4 + 0.55 × 6 = 6.5, against an HYE of 6.4. The gap of 0.1 years is the part of each respondent's valuation of the whole sequence that a sum of separately elicited chronic-state weights misses, for example because additive separability or constant proportional trade-off fails.

5. A risky choice. Treatment X gives a 50% chance of $P$ and a 50% chance of 10 years in full health, while treatment Y gives 8.15 years in full health for certain. The expected HYE of X is 0.5 × 6.4 + 0.5 × 10 = 8.2 years, which ranks X above Y. For respondent B the expected utility of X is 0.5 × 0.80 + 0.5 × 1 = 0.90, while Y gives $\sqrt{0.815} = 0.903$, so B prefers Y, and the certain equivalent of X for B is only 10 × 0.81 = 8.1 years. For respondent A the expected utility of X is 0.5 × 0.64 + 0.5 × 1 = 0.82 against 0.815 for Y, so A prefers X. The expected HYE matched only the risk-neutral respondent.

What the debate established about risk and the time trade-off

Johannesson, Pliskin and Weinstein concluded that the HYE adds flexibility to the risk-neutral QALY by letting the rate of trade-off between life years and quality depend on life span, at the cost of many more time trade-off assessments. They judged the claim that the HYE incorporates attitudes toward risk incorrect, and held that it assumes risk neutrality with respect to healthy years, which makes it less suitable for decisions under uncertainty than the general risk-averse form of the QALY.

Culyer and Wagstaff argued that HYEs are identical to QALY scores from a time trade-off, so the preference assumptions behind HYEs are as restrictive as those behind time trade-off QALYs. Gafni, Birch and Mehrez replied that the critics failed to distinguish choice under uncertainty from choice under certainty, and Mehrez and Gafni denied that HYEs assume risk neutrality over healthy years.

Wakker answered that expected utility also governs riskless choices, so under that theory the HYE equals the time trade-off answer and carries no information about risk attitude. If risk neutrality over healthy years is assumed, the HYE conflicts with the common empirical finding of risk aversion, and if it is not assumed, the HYE adds nothing to general expected utility theory.

Bias and feasibility in eliciting HYEs

Real respondents depart from expected utility, pushing the two stages apart. Wakker cites evidence that response-mode effects lead to overestimated probabilities in the first stage and overestimated certainty equivalents in the second, and since both raise the result, he predicted HYE values above those from direct time trade-off questions.

Field studies show that the task can be done but is demanding. In a dental caries study with a random adult sample in Hamilton, Ontario, 96% completed the HYE exercise, which added about 17 minutes to the interview, with the extra time rising with age. A study of 194 patients after joint replacement concluded that patients can understand the HYE procedure, but a significant proportion gave invariant answers, assigning full HYEs to their profiles, which could inflate the mean HYE.

Greenberg and Pliskin found that all but one of the cost-utility studies they identified for 1981 to 2000 used QALYs. Hauber later judged that the QALY appears to have won, with difficulty of estimation the main argument against the HYE.

Where the HYE sits in economic evaluation and HTA

The NICE manual (PMG36, sections 4.2.14 and 4.3.1) asks for health effects in QALYs. Section 4.2.15 adds that where QALY assumptions such as constant proportional trade-off and additive independence between health states are inappropriate, evidence of this should be produced, and that analyses using alternative measures may be presented as an additional non-reference-case analysis. An HYE analysis would therefore sit beside a QALY analysis rather than replace it.

Bleichrodt raised a further barrier. The HYE was built as an individual measure, and in its original form it gives no guidance on aggregating individual values for a societal allocation decision, while making it consistent with an aggregation rule imposes a particular form on individual utility functions.

Gold, Stevenson and Fryback describe health-adjusted life years as measures combining morbidity and mortality in a single number, with QALYs and DALYs as types of HALY. The HYE shares that aim but does not need the health state utility values on which a QALY total is built.

Misreadings to avoid

Most errors with HYEs come from overstating what the two-stage procedure measures. Five recur in the literature.

1. Reading the HYE as risk-adjusted. Under expected utility the risk attitude revealed in the first stage cancels in the second, as steps 1 to 3 of the example show.
2. Averaging HYEs over uncertain outcomes. An expected HYE ranks treatments as a risk-neutral person would, which step 5 shows can reverse a risk-averse person's choice.
3. Assuming an HYE always differs from a QALY. Bleichrodt shows the two give identical results when the QALY conditions hold, although the Hamilton dental study found some differences even for chronic constant states.
4. Treating the HYE as a societal measure. Aggregating individual HYEs requires an explicit equity rule.
5. Ignoring the elicitation burden. Each profile needs its own pair of questions, and Bleichrodt notes that approximations proposed to ease this give up the claim that HYEs fully reflect preferences.

Wakker still saw one use for the HYE, which is communication, since a lay person understands 9.5 years in full health in a way a utility of 0.97 does not convey.

Sources

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