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NICE and value based pricing: what do we know?

BMJ 2010; 341 doi: https://doi.org/10.1136/bmj.c6390 (Published 10 November 2010) Cite this as: BMJ 2010;341:c6390

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Re:Re:Re:Quality Adjusted Life Years (QALYs) are not suitable for comparative cost-effectiveness research

Dear Dr Prieto

You have offered a method which you call the "Complex Number" method
and claim that it is superior to the standard way of calculating QALYs as
utility multiplied by time. As your paper (1) makes clear, all that is
really involved in your method is a non-linear transformation of the
utility scale before multiplying by time.

It needs to be remembered that utilities are not intrinsic properties
of health states, but are obtained from a valuation exercise in which some
compromise is made between the required properties of the resulting
values. Methods of eliciting utilities attempt to ensure, for example,
that the difference between utilities of 0.1 and 0.3 is the same as the
difference between utilities of 0.6 and 0.8, and would give a 0.2 QALY
gain for a year in the better state in each case.

Applying your non-linear transformation would give a QALY gain of
0.0276 for a year's improvement from a utility of 0.1 to 0.3, but a QALY
gain of 0.0809 for a year's improvement from 0.6 to 0.8. This is a serious
distortion of the elicitation process. Your transformation also gives a
maximum gain of less than 0.3 QALY for a year's improvement between any
two states better than dead. As you state explicitly in your paper, your
method gives a minimum gain of over 0.7 QALY for a year's extended life in
any health state better than dead, however poor the state: I do not see
this as a desirable property of a method.

You claim without any supporting evidence that the zero on the
utility scale is arbitrary and that this is not debatable. In my previous
response, I gave a reason in favour of the view that the zero is entirely
natural. Indeed, it seems to me that the alternative contention that the
zero point is arbitrary is untenable. In my previous response, I leant
over backwards to try to show that this did not matter. Strictly, my
argument only applies if there is no mortality difference between the two
options being compared, and I now acknowledge that limitation.

You have raised the issue of states worse than death. There is
certainly no perfect method of handling those. From my point of view, if
some of the people surveyed rate a state as better than death and others
rate it as worse than death then the only question to ask is how to
average their views.

Your paper (1) does not make clear how you would calculate QALYs from
negative utilities. Your formula would give the same results for a utility
of minus 0.1 as for a utility of plus 0.1 and more QALYs for a year at a
utility of minus 0.2 than for a utility of minus 0.1. I am sure this
cannot be your true intention.

1. Prieto L, Sacristan JA. Problems and solutions in calculating
quality-adjusted life years (QALYs). Health Qual Life Outcomes 2003;1:80.

Competing interests: No competing interests

26 November 2010
Pelham M Barton
Senior Lecturer in Mathematical Modelling
Health Economics Unit, University of Birmingham