# Bad reasons not to use the EQ-5D-5L

We’ve seen a few editorials and commentaries popping up about the EQ-5D-5L recently, in Health Economics, PharmacoEconomics, and PharmacoEconomics again. All of these articles have – to varying extents – acknowledged the need for NICE to exercise caution in the adoption of the EQ-5D-5L. I don’t get it. I see no good reason not to use the EQ-5D-5L.

If you’re not familiar with the story of the EQ-5D-5L in England, read any of the linked articles, or see an OHE blog post summarising the tale. The important part of the story is that NICE has effectively recommended the use of the EQ-5D-5L descriptive system (the questionnaire), but not the new EQ-5D-5L value set for England. Of the new editorials and commentaries, Devlin et al are vaguely pro-5L, Round is vaguely anti-5L, and Brazier et al are vaguely on the fence. NICE has manoeuvred itself into a situation where it has to make a binary decision. 5L, or no 5L (which means sticking with the old EQ-5D-3L value set). Yet nobody seems keen to lay down their view on what NICE ought to decide. Maybe there’s a fear of being proven wrong.

So, herewith a list of reasons for exercising caution in the adoption of the EQ-5D-5L, which are either explicitly or implicitly cited by recent commentators, and why they shouldn’t determine NICE’s decision. The EQ-5D-5L value set for England should be recommended without hesitation.

We don’t know if the descriptive system is valid

Round argues that while the 3L has been validated in many populations, the 5L has not. Diabetes, dementia, deafness and depression are presented as cases where the 3L has been validated but the 5L has not. But the same goes for the reverse. There are plenty of situations in which the 3L has been shown to be problematic and the 5L has not. It’s simply a matter of time. This argument should only hold sway if we expect there to be more situations in which the 5L lacks validity, or if those violations are in some way more serious. I see no evidence of that. In fact, we see measurement properties improved with the 5L compared with the 3L. Devlin et al put the argument to bed in highlighting the growing body of evidence demonstrating that the 5L descriptive system is better than the 3L descriptive system in a variety of ways, without any real evidence that there are downsides to the descriptive expansion. And this – the comparison of the 3L and the 5L – is the correct comparison to be making, because the use of the 3L represents current practice. More fundamentally, it’s hard to imagine how the 5L descriptive system could be less valid than the 3L descriptive system. That there are only a limited number of validation studies using the 5L is only a problem if we can hypothesise reasons for the 5L to lack validity where the 3L held it. I can’t think of any. And anyway, NICE is apparently satisfied with the descriptive system; it’s the value set they’re worried about.

We don’t know if the preference elicitation methods are valid for states worse than dead

This argument is made by Brazier et al. The value set for England uses lead time TTO, which is a relatively new (and therefore less-tested) method. The problem is that we don’t know if any methods for valuing states worse than dead are valid because valuing states worse than dead makes no real sense. Save for pulling out a Ouija board, or perhaps holding a gun to someone’s head, we can never find out what is the most valid approach to valuing states worse than dead. And anyway, this argument fails on the same basis as the previous one: where is the evidence to suggest that the MVH approach to valuing states worse than dead (for the EQ-5D-3L) holds more validity than lead time TTO?

We don’t know if the EQ-VT was valid

As discussed by Brazier et al, it looks like there may have been some problems in the administration of the EuroQol valuation protocol (the EQ-VT) for the EQ-5D-5L value set. As a result, some of the data look a bit questionable, including large spikes in the distribution of values at 1.0, 0.5, 0.0, and -1.0. Certainly, this justifies further investigation. But it shouldn’t stall adoption of the 5L value set unless this constitutes a greater concern than the distributional characteristics of the 3L, and that’s not an argument I see anybody making. Perhaps there should have been more piloting of the EQ-VT, but that should (in itself) have no bearing on the decision of whether to use the 3L value set or the 5L value set. If the question is whether we expect the EQ-VT protocol to provide a more accurate estimation of health preferences than the MVH protocol – and it should be – then as far as I can tell there is no real basis for preferring the MVH protocol.

We don’t know if the value set (for England) is valid

Devlin et al state that, with respect to whether differences in the value sets represent improvements, “Until the external validation of the England 5L value set concludes, the jury is still out.” I’m not sure that’s true. I don’t know what the external validation is going to involve, but it’s hard to imagine a punctual piece of work that could demonstrate the ‘betterness’ of the 5L value set compared with the 3L value set. Yes, a validation exercise could tell us whether the value set is replicable. But unless validation of the comparator (i.e. the 3L value set) is also attempted and judged on the same basis, it won’t be at all informative to NICE’s decision. Devlin et al state that there is a governmental requirement to validate the 5L value set for England. But beyond checking the researchers’ sums, it’s difficult to understand what that could even mean. Given that nobody seems to have defined ‘validity’ in this context, this is a very dodgy basis for determining adoption or non-adoption of the 5L.

5L-based evaluations will be different to 3L-based evaluations

Well, yes. Otherwise, what would be the point? Brazier et al present this as a justification for a ‘pause’ for an independent review of the 5L value set. The authors present the potential shift in priority from life-improving treatments to life-extending treatments as a key reason for a pause. But this is clearly a circular argument. Pausing to look at the differences will only bring those (and perhaps new) differences into view (though notably at a slower rate than if the 5L was more widely adopted). And then what? We pause for longer? Round also mentions this point as a justification for further research. This highlights a misunderstanding of what it means for NICE to be consistent. NICE has no responsibility to make decisions in 2018 precisely as it would have in 2008. That would be foolish and ignorant of methodological and contextual developments. What NICE needs to provide is consistency in the present – precisely what is precluded by the current semi-adoption of the EQ-5D-5L.

5L data won’t be comparable to 3L data

Round mentions this. But why does it matter? This is nothing compared to the trickery that goes on in economic modelling. The whole point of modelling is to do the best we can with the data we’ve got. If we have to compare an intervention for which outcomes are measured in 3L values with an intervention for which outcomes are measured in 5L values, then so be it. That is not a problem. It is only a problem if manufacturers strategically use 3L or 5L values according to whichever provides the best results. And you know what facilitates that? A pause, where nobody really knows what is going on and NICE has essentially said that the use of both 3L and 5L descriptive systems is acceptable. If you think mapping from 5L to 3L values is preferable to consistently using the 5L values then, well, I can’t reason with you, because mapping is never anything but a fudge (albeit a useful one).

There are problems with the 3L, so we shouldn’t adopt the 5L

There’s little to say on this point beyond asserting that we mustn’t let perfect be the enemy of the good. Show me what else you’ve got that could be more readily and justifiably introduced to replace the 3L. Round suggests that shifting from the 3L to the 5L is no different to shifting from the 3L to an entirely different measure, such as the SF-6D. That’s wrong. There’s a good reason that NICE should consider the 5L as the natural successor to the 3L. And that’s because it is. This is exactly what it was designed to be: a methodological improvement on the same conceptual footing. The key point here is that the 3L and 5L contain the same domains. They’re trying to capture health-related quality of life in a consistent way; they refer to the same evaluative space. Shifting to the SF-6D (for example) would be a conceptual shift, whereas shifting to the 5L from the 3L is nothing but a methodological shift (with the added benefit of more up-to-date preference data).

To sum up

Round suggests that the pause is because of “an unexpected set of results” arising from the valuation exercise. That may be true in part. But I think it’s more likely the fault of dodgy public sector deals with the likes of Richard Branson and a consequently algorithm-fearing government. I totally agree with Round that, if NICE is considering a new outcome measure, they shouldn’t just be considering the 5L. But given that right now they are only considering the 5L, and that the decision is explicitly whether or not to adopt the 5L, there are no reasons not to do so.

The new value set is only a step change because we spent the last 25 years idling. Should we really just wait for NICE to assess the value set, accept it, and then return to our see-no-evil position for the next 25 years? No! The value set should be continually reviewed and redeveloped as methods improve and societal preferences evolve. The best available value set for England (and Wales) should be regularly considered by NICE as part of a review of the reference case. A special ‘pause’ for the new 5L value set will only serve to reinforce the longevity of compromised value sets in the future.

Yes, the EQ-5D-3L and its associated value set for the UK has been brilliantly useful over the years, but it now has a successor that – as far as we can tell – is better in many ways and at least as good in the rest. As a public body, NICE is conservative by nature. But researchers needn’t be.

Credits

# The irrelevance of inference: (almost) 20 years on is it still irrelevant?

The Irrelevance of Inference was a seminal paper published by Karl Claxton in 1999. In it he outlines a stochastic decision making approach to the evaluation of health technologies. A key point that he makes is that we need only to examine the posterior mean incremental net benefit of one technology compared to another to make a decision. Other aspects of the distribution of incremental net benefits are irrelevant – hence the title.

I hated this idea. From a Bayesian perspective estimation and inference is a decision problem. Surely uncertainty matters! But, in the extra-welfarist framework that we generally conduct cost-effectiveness analysis in, it is irrefutable. To see why let’s consider a basic decision making framework.

There are three aspects to a decision problem. Firstly, there is a state of the world, $\theta \in \Theta$ with density $\pi(\theta)$. In this instance it is the net benefits in the population, but could be the state of the economy, or effectiveness of a medical intervention in other contexts, for example. Secondly, there is the possible actions denoted by $a \in \mathcal{A}$. There might be a discrete set of actions or a continuum of possibilities. Finally, there is the loss function $L(a,\theta)$. The loss function describes the losses or costs associated with making decision $a$ given that $\theta$ is the state of nature. The action that should be taken is the one which minimises expected losses $\rho(\theta,a)=E_\theta(L(a,\theta))$. Minimising losses can be seen as analogous to maximising utility. We also observe data $x=[x_1,...,x_N]'$ that provide information on the parameter $\theta$. Our state of knowledge regarding this parameter is then captured by the posterior distribution $\pi(\theta|x)$. Our expected losses should be calculated with respect to this distribution.

Given the data and posterior distribution of incremental net benefits, we need to make a choice about a value (a Bayes estimator), that minimises expected losses. The opportunity loss from making the wrong decision is “the difference in net benefit between the best choice and the choice actually made.” So the decision falls down to deciding whether the incremental net benefits are positive or negative (and hence whether to invest), $\mathcal{A}=[a^+,a^-]$. The losses are linear if we make the wrong decision:

$L(a^+,\theta) = 0$ if $\theta >0$ and $L(a^+,\theta) = \theta$ if $\theta <0$

$L(a^-,\theta) = - \theta$ if $\theta >0$ and $L(a^+,\theta) = 0$ if $\theta <0$

So we should decide that the incremental net benefits are positive if

$E_\theta(L(a^+,\theta)) - E_\theta(L(a^-,\theta)) > 0$

which is equivalent to

$\int_0^\infty \theta dF^{\pi(\theta|x)}(\theta) - \int_{-\infty}^0 -\theta dF^{\pi(\theta|x)}(\theta) = \int_{-\infty}^\infty \theta dF^{\pi(\theta|x)}(\theta) > 0$

which is obviously equivalent to $E(\theta|x)>0$ – the posterior mean!

If our aim is simply the estimation of net benefits (so $\mathcal{A} \subseteq \mathbb{R}$), different loss functions lead to different estimators. If we have a squared loss function $L(a, \theta)=|\theta-a|^2$ then again we should choose the posterior mean. However, other choices of loss function lead to other estimators. The linear loss function, $L(a, \theta)=|\theta-a|$ leads to the posterior median. And a ‘0-1’ loss function: $L(a, \theta)=0$ if $a=\theta$ and $L(a, \theta)=1$ if $a \neq \theta$, gives the posterior mode, which is also the maximum likelihood estimator (MLE) if we have a uniform prior. This latter point does suggest that MLEs will not give the ‘correct’ answer if the net benefit distribution is asymmetric. The loss function is therefore important. But for the purposes of the decision between technologies I see no good reason to reject our initial loss function.

Claxton also noted that equity considerations could be incorporated through ‘adjustments to the measure of outcome’. This could be some kind of weighting scheme. However, this is where I might begin to depart from the claim of the irrelevance of inference. I prefer a social decision maker approach to evaluation in the vein of cost-benefit analysis as discussed by the brilliant Alan Williams. This approach allows for non-market outcomes that extra-welfarism might include but classical welfarism would exclude; their valuations could be arrived at by a political, democratic process or by other means. It also permits inequality aversion and other features that I find are a perhaps more accurate reflection of a political decision making approach. However, one must be aware of all the flaws and failures of this approach, which Williams so neatly describes.

In a social decision maker framework, the decision that should be made is the one that maximises a social welfare function. A utility function expresses social preferences over the distribution of utility in the population, the social welfare function aggregates utility and is usually assumed to be linear (utilitarian). If the utility function is inequality averse then the variance obviously does matter. But, in making this claim I am moving away from the arguments of Claxton’s paper and towards a discussion of the relative merits extra-welfarism and other approaches.

Perhaps the statement that inference was irrelevant was made just to capture our attention. After all the process of updating our knowledge of the net benefits of alternatives from data is inference. But Claxton’s statement refers more to the process of hypothesis testing and p-values (or Bayesian ranges of equivalents), the use of which has no place in decision making. On this point I wholeheartedly agree.

# Data sharing and the cost of error

The world’s highest impact factor medical journal, the New England Journal of Medicine (NEJM), seems to have been doing some soul searching. After publishing an editorial early in 2016 insinuating that researchers requesting data from trials for re-analysis were “research parasites“, they have released a series of articles on the topic of data sharing. Four articles were published in August: two in favour and two less so. This month another three articles are published on the same topic. And, the journal is sponsoring a challenge to re-analyse data from a previous trial. We reported earlier in the year about a series of concerns at the NEJM and these new steps are all welcome to address those challenges. However, while the articles consider questions of fairness about sharing data from large, long, and difficult trials, little has been said about the potential costs to society of un-remedied errors in data analysis. The costs of not sharing data can be large as the long running saga over the controversial PACE trial illustrates.

The PACE trial was a randomised, controlled trial to assess the benefits of a number of treatments for chronic fatigue syndrome including graded exercise therapy and cognitive behavioural therapy. However, after publication of the trial results in 2011, a number of concerns were raised about the conduct of the trial, its analysis, and reporting. This included a change in the definitions of ‘improvement’ and ‘recovery’ mid-way through the trial. Other researchers sought access to the data from the trial for re-analysis, but such requests were rebutted with what a judge later described as ‘wild speculations’. The data were finally released and recently re-analysed. The new analysis revealed what many suspected – that the interventions in the trial had little benefit. Nevertheless, the recommended treatments for chronic fatigue syndrome had changed as a result of the trial. (STAT has the whole story here).

A cost-effectiveness analysis was published alongside the PACE trial. The results showed that chronic behavioural therapy (CBT) was cost-effective compared to standard care, as was graded exercise therapy (GET). Quality of life was measured in the trial using the EQ-5D, and costs were also recorded, making calculation of incremental cost-effectiveness ratios straightforward. Costs were higher for all the intervention groups. The table reporting QALY outcomes is reproduced below:

At face value the analysis seems reasonable. But, in light of the problems with the trial, including that none of the objective measures of patient health, such as walking tests and step tests, nor labour market outcomes, showed much sign of improvement or recovery, these data seem less convincing. In particular, their statistically significant difference in QALYs – “After controlling for baseline utility, the difference between CBT and SMC was 0.05 (95% CI 0.01 to 0.09)” – may well just be a type I error. A re-analysis of these data is warranted (although gaining access may yet still be hard).

If there actually was no real benefit from the new treatments, then benefits have been lost from elsewhere in the healthcare system. If we assume the NHS achieves £20,000/QALY (contentious I know!) then the health service loses 0.05 QALYs for each patient with chronic fatigue syndrome put on the new treatment. The prevalence of chronic fatigue syndrome may be as high as 0.2% among adults in England, which represents approximately 76,000 people. If all of these were switched to new, ineffective treatments, the opportunity cost could potentially be as much as 3,800 QALYs.

The key point is that analytical errors have costs if the analyses go on to lead to changes in recommended treatments. And when averaged over a national health service these costs could become quite substantial. Researchers may worry about publication prestige or fairness in using other people’s hard won data, but the bigger issue is the wider costs of letting an error go unchallenged.

Credits