Is payment by diagnosis for dementia a good strategy?

There is a considerable furore surrounding the new proposal to pay GPs £55 for each dementia diagnosis. The Patients Association called it “a step too far” that would mean a “bounty on the head” of some patients (link), while the Daily Mail quoted a GP as describing the programme as ‘an intellectual and ethical travesty.’ Vitriol aside, there are clearly some issues with incentivising clinicians on the basis of making diagnoses.

Payment by diagnosis could be compared to other schemes, such as the Pay for Performance (P4P) scheme, which Sutton et al (2012) demonstrated had a mortality reducing effect in hospitals in England. However, P4P created incentives by paying doctors on the basis of specific process variables, such as prescribing aspirin at discharge for patients with acute myocardial infarction. These incentives act by altering the opportunity cost of time. For clinicians qua clinicians they may prioritise their time differently in order to increase their revenue from medical practice so that they are more likely to engage in clinical tasks with higher earnings potential. For clinicians qua individuals they may allocate more time to labour, substituting from leisure or work at home, at the benefit of patients. The P4P interventions operate at a specific part of the healthcare causal chain, at the level of process or specific interventions, which may then generate an increase in detection rates or a reduction in adverse events, all leading to improved patient outcomes. Incentivising physicians by diagnosis, however, operates at a different part of the healthcare process. Certainly, the payment for diagnosis may ensure GPs spend more time diagnosing or working with potential dementia patients, in order to boost dementia detection rates; however, equally, a diagnosis per se does not require much time to make and doctors may be incentivised to make incorrect diagnoses. Furthermore, in distorting the opportunity costs of physician time, GPs will allocate more time to identifying dementia patients at the potential risk of neglecting other patients.

Dementia is a concern for an ageing population. Only around 50% of dementia cases are thought to have been diagnosed. The global burden of dementia and Alzheimer’s disease was estimated to be $422 billion in 2009, of which $124 billion was unpaid care (Wimo et al, 2010). One strategy for reducing the burden of dementia is earlier detection – before the development of frank dementia most patients have a period of cognitive decline and suffer from what is termed mild cognitive impairment (MCI) (Petersen et al, 1999). While the deterioration of cognitive function is inexorable in dementia patients, it may possibly be slowed with appropriate therapy, which would then potentially delay or prevent a patient requiring highly costly care for late stage dementia (Gestios et al, 2010, 2012, Petersen et al, 2005, Teixera et al, 2012). There would also be considerable benefit to people with MCI and their families where the devastating impact of dementia can be reduced. Whether or not an incentive for dementia diagnoses would lead to earlier detection remains to be seen. Nonetheless, it would seem that incentivising testing for MCI in order to improve early detection, would be a more appropriate strategy. Indeed, this is the aim with type 2 diabetes where the potential benefits of a screening programme have been discussed widely (Gillies et al, 2008, Kahn et al, 2010, Schaufler and Wolff, 2010, among many examples). Simply paying doctors every time they diagnose a case of diabetes would, at face value, be less effective, particularly since earlier cases may be harder to detect – the harder to detect cases would require more time on the part of the clinician, the marginal benefit of which may be smaller than the marginal cost to the clinician. Incentivising for conducting tests arguably does not discriminate on the same basis.

While this may be a step in the right direction to improve dementia detection rates, there may have been a more effective method of incentivising GPs than payment by diagnosis.

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Posted by on October 22, 2014 in Supply of Health Services


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Do economists care about patients?

I stand accused. Not of a particularly heinous crime, but of something that has given me pause for thought recently. During a discussion about a piece of work involving patient outcomes, I was accused of ‘thinking like an economist’. Had this come from an economist, it would have been meant in a complementary sense – ‘now you’re thinking like an economist!’ Alas, it was not an economist but a clinician and medical researcher who said it and as such was meant more along the lines of ‘Unfortunately, you’re thinking like an economist’. In particular, the comment was meant to suggest that I was missing the importance of the patient, that I was focussed solely on the numbers, that I knew the price of everything and the value of nothing. Perhaps I am exaggerating the meaning but the sentiment still stands. I felt that this was unfair, both to me in that particular circumstance, but to economists and economics in general. However, I do see why people may come to this understanding of economics; economic discourse to the untrained ear is abstract and separate from the real world, economics is often very mathematical.

Typically, most economic fields do not work as closely alongside natural science as does health economics. Medical sciences and health economics often overlap greatly in their interests; many health economists publish in both medical and economics journals. However, their approach differs somewhat and the difference between them highlights an important difference between the natural and social sciences. Indeed, medical statistics and health econometrics are often considered different subjects, despite the similarities in the tools they use to approach the problems they face. Perhaps, then, it is important to analyse the distinction between the fields to find out the implications of ‘thinking like an economist’.

Economics is a social science. I am not going to provide a treatise on the philosophy of social science but will provide some thoughts on the distinction between the social sciences and the natural sciences. Arguably, the goal of science, social or natural, is to provide and validate statements which are epistemically objective. That is, we may say it produces falsifiable statements and facts. The difference between the natural and social sciences is that the former studies objects which are ontologically objective whereas the latter studies objects that are ontologically subjective. Or, to phrase it in another way, the objects of study of the natural sciences are observer independent and would exist and function whether or not there were humans or science; the social sciences studies observer dependent objects. The economy is a system of social relations in which economists participate and about which economists already have preconceived notions and have already made value judgements.

An education in the natural sciences involves teaching a student to ‘think scientifically’. To formulate and test falsifiable hypotheses about observer independent objects. An education in the social sciences involves teaching a student to re-observe the world in which they live, and to provide them with the tools to simplify it. This way we can think clearly about processes of causality in the social world. In economics, this often involves the use of mathematics and, importantly, a simplified vocabulary. This ‘econspeak’ does not identify new, economic objects – it is not more fundamental or philosophical than everyday language, it serves to simplify the social world. And, since economic words describe a social reality and since the social world is itself entirely linguistic, the meaning of economic words can always be restated in terms of everyday language and have the same meaning. For example, elasticity can be restated as ‘how much one variable changes in response to a change in another variable’, which can then be understood in terms of everyday social life – ‘how many more oranges would I buy if the price of oranges went up by 10p?’ But, in the natural sciences, the subject specific words cannot be restated in everyday language since they are not part of our world. The name of a specific protein cannot be restated in language any more simply, I could describe its function or its structure, but these explanations just skirt around the object, trying to identify it exactly. Our alternative ways of stating elasticity mean exactly the same thing.

Health economics is a social science. Medical science is perhaps more tricky to define. It has elements of both natural and social science since it studies how proteins and cells and ontologically objective objects function but also how behaviour affects health. Medicine is the application of science to improve health and is a social activity. But, many medical scientists come from a natural scientific background rather than a social scientific background. Thus, unless otherwise trained, economic representations of the social world will seem alien and abstract.

I certainly do not deny that economists lack the social interaction with many patients that health service staff have and that this may create a distance between the analyst and the people they study. This may even lead to a lack of understanding on the part of the economist about the nature of things and the state of the world that they examine. I would certainly advocate enhanced dialogue between practitioners of a variety of disciplines – this can only enhance the work being conducted – indeed, this goes both ways. Economists and clinicians alike may better learn about their subject matter. Social science has a lot to contribute to the understanding of medicine and its practice. Greater dialogue may mean greater understanding and fewer accusations such as this.


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Nurses on strike

Monday saw the first strike by health service staff in England and Wales for 32 years. This dispute surrounds the refusal of the government to implement a 1% pay rise recommended by the NHS pay review body. The reason for not awarding the pay increase given by the Secretary of State for Health, Jeremy Hunt, was that it is “unaffordable”.

There are a number of intersecting interests involved in any industrial action such as this where various stakeholders have a number of positions to consider. For example, the Secretary of State for Health must balance his mandate to protect public health with political considerations such as re-election and positioning within his party. The reasons for rejecting the pay increase, however, are typically given an economic flavour; in particular, Jeremy Hunt warned that an increase in pay this year may lead to the laying off of a large number of nurses next year, leading to a reduction in the quality of care. But, an examination of some of the economic issues surrounding the rejection of pay increases in the healthcare sector may suggest that the driving forces are more likely to be of a political nature.

In England and Wales, the wage paid to nurses is regulated by the state, and is homogeneous across all areas regardless of the local wage rate. Propper and van Reenen (2010) showed that in areas where the regulated nursing wage is lower than the ‘outside’ market wage there are reductions in the quality of nursing staff and hence healthcare quality, which they measured using hospital mortality rates for acute myocardial infarction. Moreover, they found that ‘the effect is “convex” in that the negative effect of regulation on hospital quality is much stronger in the high-cost areas (where regulated wages are much lower than the outside wage) than the positive effect in the low-cost areas (where regulated wages are higher than the outside wage).’ While these findings may be used to argue against a nationally regulated pay structure for health service staff, they certainly suggest that suppressing the nursing wage is likely to have deleterious consequences to patient health outcomes.

Much of the reasoning behind reducing pay is to do with constraining expenditure in the healthcare sector which, across most developed countries, is rising as a proportion of GDP. Nonetheless, there are sound arguments as to why we might expect healthcare to take up an increasing proportion of national expenditure, and furthermore, why this is not a worry. In particular, the Cost Disease argument (which has been previous discussed here and here), suggests that healthcare will take up a bigger and bigger proportion of the GDP pie, but that this pie will grow at least as quick. This is, in part, due to the low marginal rate of substitution between capital and labour and less than average rate of productivity growth in the healthcare sector. If these arguments hold, then governments may be unnecessarily reducing real terms health expenditure. Indeed, in many cases the government targets for NHS spending are wholly unrealistic (Appleby, 2012).

There have certainly been changes to the composition of the labour force in the healthcare sector. The density of nurses has declined from 12.21 per 1,000 people in 1997 to 8.93 per 1,000 people in 2013 while the density of physicians has increased from 2.3 to 2.79 per 1,000 over the same period (World Health Organisation – data here). This may perhaps reflect a replacement of some nursing tasks with capital or the evolving nature of medical care. However, in many areas, recommended nurse to patient ratios are not met; for example, in neonatal care, one recent survey of neonatal units found that 54% of observed shifts were understaffed with respect to recommended nurse to patient ratios (Pillay, 2012). However, given the relative lack of evidence on the cost-effectiveness of nurse to patient ratios, it cannot be said that the reduction in total nursing labour is the result of calculated cost-effectiveness decisions.

Taken together, it would seem that suppressing the nursing wage rate, or reducing the number of nurses, would have negative consequences on patient outcomes. There may certainly be an argument that the losses in quality are worth the costs saved, whether you agree with it or not, but no evidence has been presented to support this point. At a macroeconomic level, the austerity plan presented by many Western governments, the UK’s included, is rejected by a large proportion of economists.* As many economists and commentators have suggested the austerity programme is likely to be used to satisfy political ends rather than economic ones.** The reduction (in real terms) of the nursing wage may support political gains at the expense of healthcare quality and worse patient outcomes.

*For a discussion of these issues and numerous links, see the blogs of Paul Krugman, Simon Wren-Lewis, Martin Wolf, Jonathan Portes, and Chris Dillow among many others.

**Again, this wide ranging discussion is captured by many commentators, see, for example, here and here, from the above mentioned blogs, and this article.


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#HEJC for 24/10/2014

The next #HEJC discussion will take place Friday 24th October, at 1pm London time on Twitter. To see what this means for your time zone visit or join the Facebook event. For more information about the Health Economics Journal Club and how to take part, click here.

The paper for discussion is a working paper published by Glasgow Caledonian University’s Yunus Centre. The authors are Neil McHugh and colleagues. The title of the paper is:

Extending life for people with a terminal illness: a moral right or an expensive death? Exploring societal perspectives

Following the meeting, a transcript of the Twitter discussion can be downloaded here.

Links to the article



Summary of the paper

A lot of research effort has been spent on whether health economists’ most ingrained normative assumption should hold; is a QALY of equal value regardless of to whom it accrues. In the UK, the National Institute for Health and Care Excellence has given weighting to ‘special cases'; namely, life-extending drugs for patients near the end of their life (mainly for cancer). However, existing empirical research about whether societal values support such a weighting has given conflicting results.

McHugh et al, in their new working paper, present the first major mixed methods study of societal perspectives for QALY-weighting. The authors use Q methodology – which involves the ranking of opinion statements according to agreement – to elicit societal perspectives on the relative value of life extension for people with terminal illness. Opinion statements were collected from 4 sources:

  • newspaper articles
  • a NICE public consultation
  • 16 interviews with key informants
  • 3 focus groups with the general public

The Q sort was conducted with people from academia, the pharmaceutical industry, charities, patient groups, religious groups, clinicians, people with experience of terminal illness and a sample of the general public. The authors’ final sample included 61 Q sorts and factor analysis identified 3 distinguishable perspectives, which can be summarised as:

  1. A population perspective (value for money, no special cases)
  2. An individual perspective (value of life, not cost)
  3. A mixed perspective

Factor 1 individuals are unlikely to support any QALY-weighting, maintaining a utilitarian-type health-maximising perspective. Factor 2 respondents reject the denial of life extending treatments and assert that patients and their families should decided whether or not they wish to receive the treatment; regardless of cost. This group appear to disagree with cost-effectiveness analysis altogether. Factor 3 represents a more nuanced view, asserting that value is broader than health gain alone. However, factor 3 was associated with a focus on quality of life, and so support for expensive life-extending treatment would depend on this. It is unclear whether QALY-weighting would adequately achieve this.

Discussion points

  • Is the question of QALY-weighting a normative one or a positive one?
  • Are the three factors likely to be robust across ethical dilemmas other than terminal illness?
  • To what extent are the opinions associated with the 3 factors likely to be robust to further deliberation?
  • Are factor 2 respondents simply wrong?
  • Should QALY-weighting be based on democratic processes?
  • Is it of concern that current policy appears to reflect the views of health economists better than other groups?
  • Where do you stand?

Can’t join in with the Twitter discussion? Add your thoughts on the paper in the comments below.

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Posted by on October 15, 2014 in #HEJC, Health and its Value


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Review: Happiness by Design (Paul Dolan)

Happiness by Design: Finding Pleasure and Purpose in Everyday Life

Hardcover, 256 pages, ISBN: 9780241003107, published 28 August 2014

Amazon / Google Books / Allen Lane

Many economists balk at the mention of happiness research. I consider myself a sceptic. But people care about attaining happiness, and governments care about measuring it. And why not? There are behaviours and outcomes that are difficult to explain without its careful consideration. Why might cancer patients report lower levels of life satisfaction when their disease is in remission? Understanding such quirks can help us to improve outcomes for patients and, as Paul Dolan argues in his new book, enhance our own lives on a day-to-day basis.

Paul Dolan’s career – as far as we’re concerned – has come in two waves. Until 2006 he was professor of health economics at the University of Sheffield, where his first wave came to an end. You’d be hard pressed to find a health economist unfamiliar with his work from this period, such as that on the EQ-5D. Since then, Dolan has embarked on a programme of work developing measures of happiness and using experiments to shed light on individual behaviour and ways of influencing it for good. Happiness by Design goes some way to summarise the second wave of Dolan’s career, and shares with the reader the potentially life-enhancing implications of the research.

Be happy

Dolan describes the route to happiness as analogous to a production function. Firstly, there are inputs from various stimuli, such as the TV, this blog post or your back pain. Secondly, the production process corresponds to the allocation of your attention to these stimuli. Finally, the output is your level of happiness. A key message of HbD is this: learn to allocate more attention to positive stimuli – and less to negative stimuli – and you will be happier.

In order to achieve this, Dolan proposes a nudge-like context-focused approach. We should design our surroundings such that our behaviour is automatically guided towards maximising our happiness. Clearly some cognitive effort is required to achieve this, but Dolan’s approach is designed to be minimal. Change your banking password to Sav£M0ney; stop taking your cigarettes to work; or put a recurring event in your calendar to Skype your best friend. All of these could improve your happiness by influencing your behaviour.

The arguments in HbD are compelling. Almost every claim is backed-up by research, with 30 pages of references for you to trawl through should you fancy it. At times this results in the book reading a little like a review of Dolan’s work to date, which might be alienating for lay readers but comfortably familiar for academics (or nerds more generally). I only have a rudimentary understanding of behavioural science, but I suspect I may have struggled with some concepts and terminology without it. Nevertheless, the book remains engaging throughout. We’re given examples from the author’s own life, where he or the people around him have (or haven’t) dealt with the challenges to happiness, making the ideas easier to grasp and the concepts more relatable.

When it comes to policy prescriptions, Dolan argues that we shouldn’t care so much about ratings of life satisfaction. These are too subject to biases, such as the current weather. Rather, we should estimate levels of happiness over time. Such data could be obtained using the day reconstruction method (DRM). Dolan hints at a QALY-esque, area-under-the-curve type quantification of happiness over time, without fully proposing such a thing. HbD also gives a very useful whistlestop tour of the cognitive biases that influence our behaviour and determine our happiness. As a health economist, with limited exposure to behavioural science, HbD gets you thinking about the implications of these for health.

I have never read a self-help book, but it seems to me that HbD serves well as one. Throughout, the book encourages interaction. There are thought experiments in which the reader can participate, and doing so will enhance the experience. As a consistently happy person, with a relatively sunny disposition, I found myself identifying with many of the traits that Dolan encourages us to adopt in the name of happiness. I listen to a lot of music, my phone does not receive Facebook notifications, and I prefer to spend money on experiences rather than products. But am I happy because I adopt these behaviours, or do I adopt these behaviours because I am happy? Unfortunately, HbD will do little to dispel your concerns about causality. Though the book is evidence-based throughout, few of the references convincingly demonstrate causal relationships between behaviour and happiness.

Like John Stuart Mill before him, Dolan advances a unidimensional approach. Happiness is all that matters. We may think that we wish to experience sentiments of achievement or authenticity, for example, but these are ‘mistaken desires’. However, unlike Mill, Dolan appears to allow one concession: purpose. On this, I am less convinced.


Dolan proposes that individuals choose to behave in particular ways not only because of the pleasure associated with the choice, but also because of sentiments of ‘purpose’. The pleasure-purpose principle (PPP) states that people’s happiness is determined by sentiments of pleasure and purpose. If we only consider pleasure then we are missing something; though people may experience less pleasure at work, this may be counterbalanced by feelings of purpose.

Pleasure and purpose are subject to diminishing marginal returns and, so Dolan argues, many people would benefit from achieving a more balanced ratio. There is no evidence to support this, but it is nevertheless a compelling argument. We can all imagine behaving in ways that are pleasurable and ways that feel purposeful, and that there is often a trade-off between these. However, on closer inspection, I feel the PPP is of limited use. Take my writing of this review. I would probably consider this to be a purposeful activity. I am presently experiencing at best a modicum of pleasure; the opportunity cost being the pleasure I’d get from sitting and reading or listening to music. It feels somewhat purposeful, though, and that’s why I’m doing it. But it appears to me that we can dissect this sentiment of purpose and rationalise it to feelings of pleasure. For example:

  • I gained pleasure from reading the book; a condition of which was me writing this review
  • I expect to gain pleasure in the near future as I see this page receive hits and my ego is massaged
  • I expect to gain pleasure in the more distant future as my better understanding of this book, and my exposure as a writer, improves my employability and the quality of my future writing.

Each of these sources of pleasure lends to increases in my happiness. So the question is, what is left for purpose? Purposeful health behaviours, such as going for a run, share similar implications for pleasure. It seems clear to me that sentiments of purpose are at least partly explained by anticipation of future pleasure, making the two ‘P’s difficult to separate. Even if sentiments of purpose are distinguishable from sentiments of pleasure, I do not see how we could avoid double-counting in policy or evaluative applications. I remain open to being convinced by the PPP, but unfortunately HbD falls short in this regard. A real proof-of-principle would lie in a behaviour which provides some sentiment of purpose but absolutely no pleasure. I cannot imagine such an activity existing, let alone anybody choosing to do it. Of course, there are situations where people may choose to behave in purposeful ways that ultimately do not provide pleasure, but this is surely more likely due to biases in people’s expectations. Another explanation could lie in the concern for equity and for the well-being of others which, as Dolan points out in HbD, affects our own happiness. Part of the reason I experience purposefulness in my work in health economics is that I expect it to be of some (small) benefit to others at some point in the future, and this thought gives me pleasure when I complete a piece of work. Dolan provides a table that ranks various professions by the percentage of people agreeing that they are happy. Interestingly, the jobs that one might consider most ‘purposeful’ in this respect – e.g. nurses and teachers – occupy the middle ground.

It seems more likely to me that the PPP may actually be a reflection of our desire to smooth the pleasure we experience over time. Behaviours that maximise our pleasure in the present – skiving off work to watch TV and eat doughnuts, say – may have negative implications for future pleasure. As such, we invest some of our time in activities with the purpose of increasing future pleasure.

Last word

HbD provides many useful tools for improving your happiness; even for someone already satisfied with their life. I intend to use some in my day-to-day life. I believe this to have been Dolan’s primary purpose in writing the book, in which case – as far as this reader is concerned – HbD is a great success.

doi: 10.6084/m9.figshare.1152711

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Posted by on August 28, 2014 in Health and its Value, Reviews


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Bean counting and the NHS

I was recently questioned about the future of the NHS, during a live debate on the BBC Radio 4 programme Moral Maze, on 9 July 2014. One of the panelists took me to task for being a “bean counter”. I got side-tracked by this somewhat less-than-flattering characterisation of my professional role as a health economist, and so only managed to get across three of the six points I had planned to make. For what they are worth, this blog sets out all six points. And, as an added bonus, it then concludes by explaining why I am proud to be a ‘bean counter’.

This blog sets out personal ethical views on a number of controversial matters of social value judgement. That is what the BBC programme makers asked me to do, and I hope my professional colleagues will not ‘tut tut’ too loudly when they see me doing it. Professional economists are supposed to help decision makers and stakeholders think through the implications of a range of alternative value judgements, rather than to impose their own particular personal or professional value judgements. However, this blog post merely voices my own value judgements – it does not impose them on anyone.

Point number one is that the NHS performs rather well compared with other health systems across the world. It is relatively cheap, relatively good, and very fair. The UK currently spends about 9% of national income on health care, just under the OECD average, compared with 18% in the US. People in the UK are on average healthier than those in the US – even rich people with access to the best available health care in the US. And the UK regularly comes top of Commonwealth Fund surveys of fairness in high income health systems. The UK NHS is widely regarded as the fairest health system in the world, with the possible exception of Cuba.

Point number two is that financial strain on the NHS will get worse in decades to come – potentially much worse. This is due to a fundamental clash between health economics and tax politics. The tax politics is obvious. Voters do not like high taxes, so there is a limit to how far taxes can be raised, even to pay for something as popular as health care. The health economics is less obvious, but surprisingly simple when you think about it. As countries get richer, they spend a higher percentage of national income on health care. There is a simple reason for this. As we get richer, which is more valuable – a third car, yet more electronic gadgets, or an extra year of life? (I am here paraphrasing Hall and Jones, who predicted that health spending in the US will rise to 30% of national income by 2050). In the technical economic jargon, health care is a ‘superior’ or ‘luxury’ good. Do not be misled by this jargon – it does not mean that health care is an unimportant frippery. Quite the opposite. Effective health care that extends life and improves quality of life is much more important than fripperies. That is why rich people want to spend such a large share of their incomes on it.

Point three is that my own preferred solution to this problem – and here you will notice that personal ethical opinions are coming thick and fast – is gradually to ration NHS care more explicitly and extensively, within whatever budget the electorate are willing to vote for. That would enable the preservation of a tax-funded national health service that continues to provide a fairly comprehensive package of cost-effective health services to all citizens, that is nearly free at the point of delivery. (The NHS has never been 100% comprehensive or 100% free at the point of delivery). The rationing should be done through a transparent deliberative process, and based on a range of ethical principles, including cost-effectiveness, need, and compassion. Chief among these principles, however, should be cost-effectiveness – the principle that scarce NHS resources should be used to do as much good as possible in terms of extending people’s lives and improving their quality of life.

Point four is that more extensive rationing is a better and fairer solution to the problem of preserving the NHS than more extensive user charges. User charges should not be imposed on cost-effective forms of health care, such as GP visits. Charges for GP visits deter people – especially poorer people – from seeking preventive and diagnostic care. Without effective prevention and diagnosis, health problems progress to become more harmful to the patient and more costly to the NHS. If health care is cost-effective it should be provided free on the NHS; and otherwise not. People can then pay for non-cost-effective care themselves, either out of pocket or via ‘top up’ private health insurance. The slogan “all necessary care should be free” should be re-interpreted as the slogan “all cost-effective care should be free”.

Point five is that fervent ideological debates about ‘competition’ and ‘choice’ and ‘markets’ and ‘privatisation’ are largely red herrings. What matters is that the NHS provides a fairly comprehensive range of cost-effective care to all citizens, so that everyone receives the care they need at a cost they can afford. Who owns or manages health care provider organisations does not matter directly in and of itself. Ownership and management may matter indirectly, of course – but only insofar as they impact upon the cost, quality and social distribution of health care. The direction and size of such impacts in different contexts is a factual matter, to be settled in the court of evidence and experience, rather than a matter for fervent ideological debate.

Point six is that a more extensively rationed NHS can still preserve the founding principles of the NHS. On the delivery side, it can preserve the principle of ‘equality of access’ to all necessary health care – where ‘necessary’ means ‘cost-effective’. And on the financing side, continued tax funding continues to preserves the principle of ‘solidarity’, that the strong should help the weak – the rich should help the poor, the young should help the old, and the healthy should help the sick. Finally, the NHS also preserves the benefit of financial risk protection. As was stated in the public information leaflet sent to all UK citizens at the founding of the NHS in 1948, one of the main benefits of the NHS is that “it will spare your family from money worries in time of ill health”.

In conclusion, the best way to preserve the NHS is to engage in more explicit and extensive rationing. This in turn will require more of what my Moral Maze inquisitor called “bean counting”. More evidence will be needed to inform a suitably transparent and deliberative rationing process. In particular, more evidence will be needed about the impacts of different NHS services on cost, length and quality of life, patient experience, need, compassion and dignity, and other ethically important outcomes and processes. This form of ‘bean counting’ is not an ignoble exercise. The ‘beans’ in question here are people’s lives. People’s lives matter, and if seeking to improve the length and quality of people’s lives makes me a “bean counter” then I am proud to be one.


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Bayesian evidence synthesis and bootstrapping for trial-based economic evaluations: comfortable bed fellows?

By Mohsen Sadatsafavi and Stirling Bryan

In economic evaluation of health technologies, evidence synthesis is typically about quantification of the evidence in terms of parameters. Bootstrapping is a non-parametric inferential method in trial-based economic evaluations. On the surface the two paradigms seem incompatible. In a recent paper, we show that a simple and intuitive modification of the bootstrap can indeed accommodate parametric evidence synthesis.

When the recruitment phase of a pragmatic randomized controlled trial (RCT) is over, two groups of investigators will become busy. The clinical evaluation team is interested in inference about the population value of the primary outcome, typically a measure of relative effect (e.g. relative risk [RR] of the clinical outcome of interest) between the treatment groups. The economic evaluation team is in charge of inference chiefly on the population value of the incremental cost effectiveness ratio (ICER).

A widely used method of characterizing uncertainty around the ICER in RCT-based cost-effectiveness analyses is the bootstrap. For a typical two-arm RCT, the investigator obtains a bootstrap sample of the data to calculate the difference in costs and difference in effectiveness between the two treatments. Repeating this step many times provides a sample from the joint distribution of the difference in costs and effectiveness that can be used to calculate the ICER and to represent uncertainty around its value (such as to calculate credible intervals, to draw the cost-effectiveness plane and acceptability curve). As an example, the table below gives results from repeated bootstrap samples of a hypothetical two-arm RCT:

Bootstrap # Difference in costs ($) Difference in effectiveness (QALYs)
1  $1,670.1  0.0130
2  $1592.9  0.0143
10,000  $1,091.0  0.0133
Average $1,450.2 0.0151
ICER 1,450.2/0.0151=96,039.7

In deriving the costs and effectiveness values within each bootstrap loop, many steps might be involved, such as imputation of missing values and adjusting for covariates. This is what makes the bootstrap method so powerful, as all such steps are enveloped within the bootstrap, allowing for the uncertainty in all inferential steps to be accounted for.

The dilemma of external evidence

Imagine at the time of such analyses, another ‘external’ trial is published which reports results for the same interventions and treatment protocol, in the same population, with the same clinical outcome measure. Also imagine the external RCT reports the maximum-likelihood and 95% confidence interval of the RR of treatment, which we find to be more favorable for the new treatment versus the standard treatment than the RR in the current RCT. Of course, this carries some information about the effect of the treatment at the population level. But how can this be incorporated in the inference?

The task in front of the clinical evaluation team is rather straightforward: the RR from the two RCTs can be combined using meta-analytic techniques to provide an estimate for the population RR. But what about the economic evaluation team? We can speculate that, given the observed treatment effect in the external RCT, the population value of the ICER could be more favorable for the new treatment than what the current RCT suggests.

But is there any way to make the above-mentioned subjective line of reasoning into a formal and objective form of inference? This is what we have addressed in our recent paper. Before we explain our solution, we note that there are already at least two ways of performing this task: (a) to desist statistical inference and use decision-analytic modeling (which can use the pooled RR as an input parameter), and (b) to resort to parametric Bayesian inference. The former is not really a solution as long as the desire for statistical inference for cost-effectiveness is concerned, and the latter is a complete paradigm shift which also imposes a myriad of parametric assumptions (think of the regression equations, error terms, and link functions required to connect cost and effectiveness outcomes to the clinical variable, and the clinical variable to external evidence).

Can evidence synthesis be carried out using the bootstrap?

Yes! And our proposed solution is rather intuitive: the investigator first parameterises the external evidence using appropriate probability distributions (e.g. a log-normal distribution for RR constructed from the reported point estimate and interval bounds). For each bootstrap sample, the investigator calculates, in addition to cost and effectiveness outcomes, the parameters for which external evidence is available, and uses the constructed probability distribution to weight the bootstrap sample according to its degree of plausibility against external evidence. The ICER is the weighted-average of difference in costs over the weighted-average of difference in effectiveness:

Bootstrap # Difference in costs ($) Difference in effectiveness (QALYs) Treatment effect (RR) Weight according to  external evidence
1 $1,670.1   0.0130  0.521  0.058
2 $1592.9   0.0143  0.650  0.068
10,000 $1,091.0  0.0151  0.452  0.025
Weighted Average $1,034.2 0.0161
ICER  1,034.2/0.0161=64,236.0

A more practical method of assigning weights to bootstraps, instead of using the weights directly, is to ‘accept’ each bootstrap with a probability that is proportional to its weight. Rejected bootstraps are removed from the analysis. This gives the investigator an idea about the ‘effective’ number of bootstraps, and makes the subsequent calculations independent of the weights.

Why does it work?

The theory is provided in the paper, but in a nutshell, a Bayesian interpretation of the bootstrap allows one to see the bootstrap estimate of the difference in costs and difference in effectiveness as their posterior distribution conditional on the current RCT. It can be shown that the weights transform this to the posterior distribution conditional on the current AND external RCT.

An appealing feature of the method is the minimal parametric assumptions. Unlike the parametric Bayesian methods, the investigator need not make any assumption on the distribution of costs and effectiveness outcomes and how the clinical outcome affects the cost and effectiveness values. The effect is channeled directly through the experience of patients in the course of the trial, represented through the correlation structure between clinical outcomes, costs, and effectiveness variables at the individual level.

Further developments

There are indeed many gaps to be filled. The method only focuses on parallel-arm RCTs and leaves the problem open for other designs. In addition, rejection sampling can be wasteful, and if there are several parameters, then the method becomes quite unwieldy. An interesting potential solution is to create auto-correlated Markov Chain bootstraps that tend to concentrate on the high probability areas of the posterior distribution. In general, this sampling paradigm is quite flexible and can be used to incorporate external evidence in other contexts such as model-based evaluations or evaluations based on observational data.


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