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Comment author: David_Althaus 28 September 2017 06:46:13PM *  3 points [-]

As long as people make sensible judgements about the health states that actually occur, it doesn't matter what they say in impossible ones.

Good point. But I wonder whether they reinterpret the meanings of some of the dimensions of the ED-Q5 in order to make sense of some of the health states they are asked to rate.

Unless you know where neutral is you can't specify the minimum point on the scale, because it doesn't make sense.


What would -1 mean here? DALYs and QALYs aren't well-being scales and can't straightforwardly be interpreted as such.

This depends on the study. I'm afraid it will take me a couple of paragraphs to explain the methodology, but I hope you'll bear with me :)

The literature review by Tilling et al. (2010) concluded that only 8% of all TTO studies even allow for subjects to rate health states as worse than death (i.e. as below 0), so for the vast majority of studies, the minimum point on the scale is indeed 0. I think this is problematic since e.g. health states like 33333 (if they are permanent) are probably worse than death for many, maybe even most people.

Of the few TTO studies that allow for negative values, the protocols by Torrence et al. (1982) and Dolan (1997) are used by almost all of them. Below a quote by Tilling et al. (2010), describing these two methods:

The method developed by Torrance et al. (1982) gives respondents a choice between a scenario of living in full health for ti years followed by the state to be valued for tj years (ti + tj= T), followed by death, and an alternative scenario, which is to die immediately. The value T is fixed (e.g., 10 y). The value of ti (and therefore also the value of tj) is varied until a point of indifference is found between the 2 scenarios. The utility value for that health state is then given by – ti/tj. [... Dolan (1997)] used a method similar to this, but the 1st scenario is to live in the health state to be valued for tj years followed by full health for ti years (i.e., the ordering of the 2 states is reversed).”

These two TTO protocols, in theory, would allow for extremely negative (and even infinite) negative values. Tilling et al. (2010) explain:

“[...] negative values can be extremely negative. A participant who would not accept any amount of time, however short, in a poor state of health is implying that such a state is infinitely bad.”

How do researchers respond? Again, I’ll quote Tilling et al. (2010, emphasis mine):

“Given the mathematical intractability of dealing with negative infinity (a single value of negative infinity in a sample of respondents would give a mean value of negative infinity), researchers usually censor such responses. Under such censoring, the lower bound is determined by the (relatively arbitrary) choice of the smallest unit of time the TTO procedure will iterate toward.”

In the two most commonly used TTO protocols, the smallest unit of time the TTO procedure iterates toward for SWD is 1 year. Consequently, the lower bound is -9. (Sometimes, the smallest united of time is 3 months, so the lowest possible value is -39.)

To give a concrete example: The subject is indifferent between A) living for 2 years in full health and for 8 years in health state 33333 and B) dying immediately. Thus, the value for health state 33333, for this subject, is - 8/2 = - 4.

Now almost all researchers then transform these values, such that the lowest possible value is -1. In my view, this is somewhat arbitrary.

Below some quotes by Devlin et al. (2011) on the matter:

“Because the elicitation procedure produces such extreme negative values, researchers have responded by doing ex post transformations to bound negative valuations to - 1 in various ways (Lamers, 2007). Crucially, once transformed, the negative numbers for SWD can no longer be interpreted as ‘utility’ scores, measured on the same scale as those for SBD (Patrick et al., 1994). Yet standard practice in calculating QALYs is to treat all values reported in value sets as commensurable. For example, an improvement from - 0.2 (an SWD) to 0, experienced over one year is interpreted as, producing a gain of 0.2 QALYs, and this is treated [...] as identical to an improvement from 0 to 0.2 experienced for one year, whereas the underlying ‘untransformed value’ for the SWD might suggest these two improvements in health are valued quite differently.”


“A related issue is whether or not values of negative states should be bounded to 1. It is not obvious why there should be no states worse than 1. For example, the phrase ‘it would have been better if he had never been born’ could truly be applied to people who have undergone torture and other types of brief but extreme suffering. There is no theoretical basis for imposing a limit on the level of disutility associated with these extreme sufferings.”

And here another quote by Tilling et al (2010):

“[...] it is not obvious why there should be no states worse than –1. Although it makes data analysis easier to transform values in this fashion, arguably 1 y of extreme pain and discomfort might provide as much disutility as 2 y of full health provides in utility.”

I hope this explains my previous comment.


Devlin, N. J., Tsuchiya, A., Buckingham, K., & Tilling, C. (2011, 02). A uniform time trade off method for states better and worse than dead: Feasibility study of the ‘lead time’ approach. Health Economics, 20(3), 348-361.

Dolan, P. (1997). Modeling Valuations for EuroQol Health States. Medical Care, 35(11), 1095-1108.

Tilling, C., Devlin, N., Tsuchiya, A., & Buckingham, K. (2010, 09). Protocols for Time Tradeoff Valuations of Health States Worse than Dead: A Literature Review. Medical Decision Making, 30(5), 610-619.

Torrance, G. W., Boyle, M. H., & Horwood, S. P. (1982, 12). Application of Multi-Attribute Utility Theory to Measure Social Preferences for Health States. Operations Research, 30(6), 1043-1069.