# 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.

# Alastair Canaway’s journal round-up for 20th March 2017

Every Monday our authors provide a round-up of some of the most recently published peer reviewed articles from the field. We don’t cover everything, or even what’s most important – just a few papers that have interested the author. Visit our Resources page for links to more journals or follow the HealthEconBot. If you’d like to write one of our weekly journal round-ups, get in touch.

The use of quality-adjusted life years in cost-effectiveness analyses in palliative care: mapping the debate through an integrative review. Palliative Medicine [PubMed] Published 13th February 2017

February saw a health economics special within the journal Palliative Medicine – the editorials are very much worth a read to get a quick idea of how health economics has (and hasn’t) developed within the end of life care context. One of the most commonly encountered debates when discussing end of life care within health economics circles relates to the use of QALYs, and whether they’re appropriate. This paper aimed to map out the pros and cons of using the QALY framework to inform health economic decisions in the palliative care context. Being a review, there were no ground-breaking findings, more a refresher on what the issues are with the QALY at end of life: i) restrictions in life years gained, ii) conceptualisation of quality of life and its measurement, and iii) valuation and additivity of time. The review acknowledges the criticisms of the QALY but concludes that it is still of use for informing decision making. A key finding, and one which should be common sense, is that the EQ-5D should not be relied on as the sole measure within this context: the dimensions important to those at end of life are not adequately captured by the EQ-5D, and other measures should be considered. A limitation for me was that the review did not include Round’s (2016) book Care at the End of Life: An Economic Perspective (disclaimer: I’m a co-author on a chapter), which has significant overlap and builds on a number of the issues relevant to the paper. That aside, this is a useful paper for those new to the pitfalls of economic evaluation at the end of life and provides an excellent summary of many of the key issues.

The causal effect of retirement on mortality: evidence from targeted incentives to retire early. Health Economics [PubMed] [RePEc] Published 23rd February 2017

It’s been said that those who retire earlier die earlier, and a quick google search suggests there are many statistics supporting this. However, I’m unsure how robust the causality is in such studies. For example, the sick may choose to leave the workforce early. Previous academic literature had been inconclusive regarding the effects, and in which direction they occurred. This paper sought to elucidate this by taking advantage of pension reforms within the Netherlands which meant certain cohorts of Dutch civil servants could qualify for early retirement at a younger age. This change led to a steep increase in retirement and provided an opportunity to examine causal impacts by instrumenting retirement with the early retirement window. Administrative data from the entire population was used to examine the probability of dying resulting from earlier retirement. Contrary to preconceptions, the probability of men dying within five years dropped by 2.6% in those who took early retirement: a large and significant impact. The biggest impact was found within the first year of retirement. An explanation for this is that the reduction of stress and lifestyle change upon retiring may postpone death for the civil servants which were in poor health. The paper is an excellent example of harnessing a natural experiment for research purposes. It provides a valuable contribution to the evidence base whilst also being reassuring for those of us who plan to retire in the next few years (lottery win pending).

Mapping to estimate health-state utility from non–preference-based outcome measures: an ISPOR Good Practices for Outcomes Research Task Force report. Value in Health [PubMed] Published 16th February 2017

Finally, I just wanted to signpost this new good practice guide. If you ever attend HESG, ISPOR, or IHEA, you’ll nearly always encounter a paper on mapping (cross-walking). Given the ethical issues surrounding research waste and the increasing pressure to publish, mapping provides an excellent opportunity to maximise the value of your data. Of course, mapping also serves a purpose for the health economics community: it facilitates the estimation of QALYs in studies where no preference based measure exists. There are many iffy mapping functions out there so it’s good to see ISPOR have taken action by producing a report on best practice for mapping. As with most ISPOR guidelines the paper covers all the main areas you’d expect and guides you through the key considerations to undertaking a mapping exercise, this includes: pre-modelling considerations, data requirements, selection of statistical models, selection of covariates, reporting of results, and validation. Additionally there is also a short section for those who are keen to use a mapping function to generate QALYs but are unsure which to pick. As with any set of guidelines, it’s not exactly a thriller, it is however extremely useful for anyone seeking to conduct mapping.

Credits

# Thesis Thursday: Edward Webb

On the third Thursday of every month, we speak to a recent graduate about their thesis and their studies. This month’s guest is Dr Edward Webb who graduated with a PhD from the University of Copenhagen. If you would like to suggest a candidate for an upcoming Thesis Thursday, get in touch.

Title
Attention and perception in decision-making and interactions
Supervisors
Alexander Sebald, Peter Norman Sørensen
http://www.econ.ku.dk/forskning/Publikationer/ph.d_serie_2007-/Ph.D.181.pdf

Attention and perception aren’t things we often talk about in health economics. Why are they important?

There’s been a lot of work done on attention and perception in economics recently, which I think is a great development. They are really vital topics since unless you know how people perceive the information available to them, and what aspects of their environment are most likely to command their attention, it’s difficult to forecast their behaviour.

I think attention and perception will become more widely talked about in health in future, as there’s many cases in which they have a lot of relevance. For example, you might want to know whether rare symptoms grab doctors’ attention because they’re unusual, or whether they don’t notice them because they’re not expecting them. (There’s a great study by Drew, Vo and Wolfe where radiologists looking at CT scans of the chest failed to notice a picture of a gorilla embedded in them by the experimenters.)

Or if you’re planning some dietary intervention, you might want to take into account how unhealthy food such as pizza and chips attracts people’s attention much more than healthy food, and to look at why this is the case.

What can the new theoretical frameworks described in your thesis tell us about individual behaviour?

Most of the literature in psychology is about how individuals behave. I tried a lot in my thesis to move beyond studying individual decision making to look at how the effects of attention and perception change in different economic environments, as this can often be counter-intuitive.

As an example, in one of the chapters of my thesis I explore the effects of individuals having limited ability to tell the quality of different products apart. It turns out that the effects on a market can be radically different depending on whether there are fixed or marginal costs of quality.

I was also very interested in looking at how individuals with limited or biased attention interact with profit maximising firms. There’s an expectation that companies will rip people off and exploit them, and certainly, that can happen, but I was able to show that it’s not necessarily the case. The case of individuals having limited ability to tell products’ quality apart which I mentioned above is a good example. When firms rely on product differentiation to earn profits, they’re actually harmed by people with this limitation, rather than exploiting them.

Did you find yourself reaching beyond the economics literature for guidance, either in the subject matter or the techniques that you used?

Yes, I read quite a lot outside the standard economics literature during my thesis. Behavioural and experimental economics more or less sits on the boundary between economics and psychology, so it felt very natural to seek guidance from other disciplines. This was especially the case for the eye-tracking experiment that I carried out with the help of my co-authors Andreas Gotfredsen, Carsten S. Nielsen and Alexander Sebald. I needed to learn quite a bit about psychological work on visual attention.

I like that economics is as much a set of analytic tools as a subject area, which gives it the advantage of being able to take on nontraditional topics.

You studied in Denmark, yet your thesis is written in English. Did this raise any additional challenges in completing your PhD?

Danish people speak better English than what I can! Language really wasn’t a problem at all at work, since English is very much the language of academia. Seminars were in English, PhD students and a lot of masters students wrote their theses in English and nearly all postgraduate and some undergraduate teaching was in English. I did feel quite privileged to have the advantage of being a native speaker of the language, and appreciative that most of my colleagues were fine with working in a second language. That’s why I was always very willing to help people out with proofreading English. I only hope I didn’t make too many mistakes!

On the social side, you can get away with living in Denmark without speaking Danish, and many people do. Indeed, I probably wouldn’t have made the effort of becoming a (moderate) Danish speaker if my partner wasn’t Danish.

Copenhagen, and Denmark in general, is a fantastic place to live and work, and I’d urge anyone who is thinking about moving there not to be put off by the language barrier.

How did your experiences during your PhD contribute to your decision to work in the field of health economics?

The question makes it sound like I had a coherent plan! In reality, I’m terrible about thinking about the long term. (I must be a natural Keynesian.) I ended up moving back to the UK after I graduated ironically because of my Danish partner, as she had found a job here. She also works in health, as a medical physicist and cancer researcher at Leeds. I applied for economics jobs in the area and was over the moon to secure a place at the Academic Unit of Health Economics at Leeds.

It’s a little more applied and hands-on than what I was working on before, which is great. I came into economics because I was interested in finding out how people act and interact, and so it’s fantastic to have the opportunity now to work principally with discrete choice experiments, trying to work out patients’ and clinicians’ preferences.

Since I started at Leeds a few months ago I’ve really enjoyed my time. The environment is very stimulating and all my colleagues are extremely friendly and easy going and are always willing to help out or discuss an interesting new idea.