# 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

# Chris Sampson’s journal round-up for 13th 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 effects of exercise and relaxation on health and wellbeing. Health Economics [PubMedPublished 9th Month 2017

Encouraging self-management of health sounds like a good idea, but the evidence is pretty weak. As economists, we know that something must be displaced in order to do it. This study considers the opportunity cost of time and how it might affect self-management activity and any associated benefits. Employment and education are likely to increase income and thus facilitate more expenditure on exercise. But the time cost of exercise is also likely to increase, meaning that the impact on demand is ambiguous. The study uses data from a trial of self-management support that included people with diabetes, COPD or IBS. EQ-5D, self-assessed health and the amount of time spent ‘being happy’ were all collected. Information was available for 12 different self-management activities, including ‘do exercises’ and ‘rest and relax’, and the extent to which individuals did these. Outcomes for 3,472 people at 12-month follow-up are estimated, controlling for outcomes at baseline and 6 months. The study assumes that employment and education affect health via their influence on exercise and relaxation. That seems a bit questionable and the other 10 self-management indicators could have been looked at to test this. People in full-time employment were 11 percentage points less likely to use relaxation to manage their condition, suggesting that the substitution effect on time dominates as the opportunity cost of self-management increases. Having a degree or professional qualification increased the probability of using exercise by 5 percentage points, suggesting that the income effect dominates. Those who are more likely to use either exercise or relaxation are also more likely to do the other. An interesting suggestion is that time preference might explain things here. Those with more education may prefer to exercise (as an investment) than to get the instant gratification of rest and relaxation. It’s important that policy recommendations take into consideration the fact that different groups will respond differently to incentives for self-management, at least partly due to their differing time constraints. The thing I find most interesting is the analysis of the different outcomes (something I’ve worked on). Exercise is found to improve self-assessed health, while relaxation increases happiness. Neither exercise or relaxation had a (statistically significant) effect on EQ-5D. Depending on your perspective, this either suggests that the EQ-5D is failing to identify important changes in broad health-related domains or it means that self-management does not achieve the goals (QALYs to the max) of the health service.

New findings from the time trade-off for income approach to elicit willingness to pay for a quality adjusted life year. The European Journal of Health Economics [PubMedPublished 8th March 2017