# Is the value of a QALY constant?

Standard cost-effectiveness analysis assumes that any gain in quality-adjusted life years (QALYs) should be valued equally. This does not sound unreasonable, but is it true in practice?

Consider two potential violations of constant value of QALY gains: scope insensitivity and severity independence. I define each of these below:

• Scope insensitivity. This assumes that individuals value QALY gains linearly. Thus, a QALY gain of 0.4 is valued twice as much as a QALY gain of 0.2 and four times as much as a QALY gain of 0.1
• Severity independence. This assumes that QALY gains of a given size are valued equally regardless of your initial health state. Thus if you have a QALY gain of 0.1, it assumes that gain is valued equally if you are paralyzed in a wheelchair or if you have some minor back pain. Numerically, it means that a QALY gain of 0.1 is the same if you have a baseline quality of life (QoL) of 0.25 as you would with a baseline QoL of 0.75 [where QoL is measured on a scale from 0 to 1].

Do scope insensitivity and severity independence hold in practice? This is an question we can answer empirically. In fact a recent paper by Nielsen et al. 2021 does just that. They use data from Danish respondents to the EQ-5D survey. First the measure individual valuations of health improvements and translate them into QALYs. Next, they estimate the willingness to pay (WTP) for these health gains.

Either they were to imagine that they were in the aforementioned health state and asked to state their WTP for reducing the time spent in the health state, or they were to imagine that they were at risk of falling into the health state and asked to state their WTP for reducing the risk. The magnitude of the time and risk reduction was tailored according to the responses to the previous SG/TTO questions such that all respondents were asked to state their WTP for the same QALY gains. For each respondent, WTP for a gain of both 0.05 and 0.1 was elicited in random order (Q2–Q3 and Q5–Q6). This was done using the random card sorting procedure. The set of payment cards presented to respondents aimed to keep the “range” constant in terms of implied WTP‐Q across the scenarios where 0.05 and 0.1 QALY was on offer.
The design thus constitutes four survey arms with four different combinations of elicitation method (SG‐risk, SG‐time, TTO‐risk, TTO‐time) which each contained two chains.

When applying these methods, they found that both scope insensitivity and severity independence were violated.

The “scope” coefficient was found to be positive (except in Model 2) and significant implying that WTP for a QALY (WTP‐Q) gain of 0.1 was more than twice the WTP for the half‐sized (0.05) QALY gain10. Likewise, the “severity” coefficient was found to be positive and significant implying that for two equally sized health gains, a QALY gain is valued higher in the more inferior health state (22222) than in the less severe health state (21121).

The authors then test to see if applying different inclusion and exclusion criteria change the result. While applying the additional exclusion criteria did reduce sample size and precision, the qualitative findings were similar: both scope insensitivity and severity independence did not hold.

Looks like QALY is not always a QALY, at least in terms of how it is valued.

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