I hope this question is on-topic here. It is related to a paper published in PharmacoEconomics. It is related to medical sciences, but also to economics and statistics. I did not find an appropriate tag.

This paper describes a protocol for evaluating health states in the EQ-5D-Y-3L instrument. The goal of this process is to assign a numeric value to each of the 243 possible health-states, in order to compute cost-utility trade-offs. An example question in this survey is shown in Figure 2 in that paper:

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The subject is asked which of the two options is better: living 6 months in full health, or living 10 years with a lot of problems in all 5 dimensions of the index.

If the subject answers that the two options are about the same, then we can conclude that, for this subject, 10 years in the "sick" state are equal to 1/2 year in the "healthy" state; so we can say that a year in the "sick" state is worth 1/20 QALY.

But if the subject answers that the two options are not the same? In this case, we only have an inequality: we know that the sick state is worth less or more than 1/20 QALY, but we do not have an exact number.

MY QUESTION: how are such answers, that only yield inequalites, used to generate a numeric QALY value for health states?

1 Answer 1


The paper you've linked is very much "in the weeds" of the details of this type of analysis. It's assumed that people reading it understand how time trade off (TTO) experiments are run.

Here's a good description from Oppe et al 2016 (PMCID 5023738):

The objective of the TTO is to determine the length of life-time the respondent would be willing to forego to live in a better health state (typically ‘full health’) and avoid living in a bad health state. This is achieved by presenting respondents with a series of choice tasks, each involving two alternative hypothetical lives. The two lives are presented such that the respondent is forced to choose between a longer life in the health state of interest and a shorter life in better health. Depending on which life is chosen, the amount of time in better health is altered until a point of preferential indifference is reached. [Emphasis added]

So this user interface changes when you click A or B until you finally agree A & B are about the same.

There is some nuance when the disease state is a fate worse than death. But the Oppe paper nicely goes over that.

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