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.


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

The question ‘what is a QALY worth’ could invoke any number of reactions in a health economist, from chin scratching to eye rolling. The perspective that we’re probably most familiar with in the UK is that the value of a QALY is the value of health foregone in order to achieve it (i.e. opportunity cost within the health care perspective). An alternative perspective is that the value of a QALY is the consumption value of health; how much consumption would individuals be willing to give up in order to obtain an additional QALY? This second perspective facilitates a broader societal perspective. It can tell us whether or not the budget is set at an appropriate level, while the health care perspective can only take the budget as given. This study relates mainly to decisions made with the ‘consumption value’ perspective. One approach that has been proposed is to assess willingness to pay for a QALY using a time trade-off exercise that incorporates trade-offs between length and quality of life and income. This study builds on the original work by using a multiplicative utility function to estimate willingness to pay and also bringing in prospect theory to allow for reference dependence and loss aversion. 550 participants were asked to choose between living 10 years in their current health state with their current salary or to live a reduced number of years in their current health state with a luxury income (pre-specified by the participant). Respondents were also asked to make a similar choice, but framed as a loss of income, between living 10 years at a subsistence income or fewer years with their current income. A quality of life trade-off exercise was also conducted, in which people traded reduced health and a lower income. The findings support the predictions of prospect theory. Loss aversion is found to be stronger for duration than for quality of life. Individuals were more willing to sacrifice life years to move from subsistence income to current income than to move from current income to luxury income. The results imply that quality of life and income are closer substitutes than longevity and income. That makes sense, given the all-or-nothing nature of being alive. Crucially, the findings highlight the need to better understand the shape of the underlying lifetime utility function. In all tasks, more than half of respondents were either non-traders or over-traded, indicating a negative willingness to pay. That should give pause for thought when it comes to any aggregation of the results. Willingness to pay studies often throw up more questions than answers. This one does so more than most, particularly about sources of bias in people’s responses. The authors identify plenty of opportunities for future research.

Beyond QALYs: multi-criteria based estimation of maximum willingness to pay for health technologies. The European Journal of Health Economics [PubMed] Published 3rd March 2017

Life is messy. Evaluating things in terms of a single outcome, whether that be QALYs, £££s or whatever, is necessarily simplifying and restrictive. That’s not necessarily a bad thing, but we’d do well to bear it in mind. In this paper, Erik Nord sets out a kind of cost value analysis that does away with QALYs (gasp!). The author starts by outlining some familiar criticisms of the QALY approach, such as its failure to consider the inherent value of life and people’s differing reference points. Generally, I see these as features rather than bugs, and it isn’t QALYs themselves in the crosshairs here so much as cost-per-QALY analysis. The proposed method flips current practice by putting societal preferences about fair and efficient resource allocation before attaching values to the outcomes. As such, it acknowledges the fact that society’s preferences for gains in quality of life differ from those for gains in length of life. For example, society may prefer treating the more severely ill (independent of age) but also exhibit a ‘fair innings’ preference that is related to age. Thus, quality and quantity of life are disaggregated and the QALY is no more. A set of tables is presented that can be read to assess ‘value’ in alternative scenarios, given the assumptions set out in the paper. There is merit in the approach and a lot that I like about the possibilities of its use. But for me, the whole thing was made less attractive by the way it is presented in the paper. The author touts willingness to pay – for quality of life gains and for longevity gains – as the basis for value. Anything that makes resource allocation more dependent on willingness to pay values for things without a price (health, life) is a big no-no for me. But the method doesn’t depend on that. Furthermore, as is so often the case, most of the criticisms within relate to ways of using QALYs, rather than the fundamental basis for their estimation. This only weakens the argument for an alternative. But I can think of plenty of problems with QALYs, some of which might be addressed by this alternative approach. It’s unfortunate that the paper doesn’t outline how these more fundamental problems might be addressed. There may come a day when we do away with QALYs, and we may end up doing something similar to what’s outlined here, but we need to think harder about how this alternative is really better.