Method of the month: Distributional cost effectiveness analysis

Once a month we discuss a particular research method that may be of interest to people working in health economics. We’ll consider widely used key methodologies, as well as more novel approaches. Our reviews are not designed to be comprehensive but provide an introduction to the method, its underlying principles, some applied examples, and where to find out more. If you’d like to write a post for this series, get in touch. This month’s method is distributional cost effectiveness analysis.


Variation in population health outcomes, particularly when socially patterned by characteristics such as income and race, are often of concern to policymakers. For example, the fact that people born in the poorest tenth of neighbourhoods in England can expect to live 19 fewer years of healthy life than those living in the richest tenth of neighbourhoods in the country, or the fact that black Americans born today can expect to die 4 years earlier than white Americans, are often considered to be unfair and in need of policy attention. As policymakers look to implement health programmes to tackle such unfair health disparities, they need the tools to enable them to evaluate the likely impacts of alternative programmes available to them in terms of the programmes’ impact on reducing these undesirable health inequalities, as well as their impact on improving population health.

Traditional tools for prospectively evaluating health programmes – that is to say, estimating the likely impacts of health programmes prior to their implementation – are typically based on cost-effectiveness analysis (CEA). CEA selects those programmes that improve the health of the average recipient of the programme the most, taking into consideration the health opportunity costs involved in implementing the programme. When using CEA to select health programmes there is, therefore, a risk that the programmes selected will not necessarily reduce the health disparities of concern to policymakers as these disparities are not part of the evaluation process used when comparing programmes. Indeed, in some cases, the programmes chosen using CEA may even unintentionally exacerbate these health inequalities.

There has been recent methodological work to build upon the standard CEA methods explicitly incorporating concerns for reducing health disparities into them. This equity augmented form of CEA is called distributional cost effectiveness analysis (DCEA). DCEA estimates the impacts of health interventions on different groups within the population and evaluates the health distributions resulting from these interventions in term of both health inequality and population health. Where necessary, DCEA can then be used to guide the trade-off between these different dimensions to pick the most “socially beneficial” programme to implement.


The six core steps in implementing a DCEA are outlined below – full details of how DCEA is conducted in practice and applied to evaluate alternative options in a real case study (the NHS Bowel Cancer Screening Programme in England) can be found in a published tutorial.

1. Identify policy-relevant subgroups in the population

The first step in the analysis is to decide which characteristics of the population are of policy concern when thinking about health inequalities. For example, in England, there is a lot of concern about the fact that people born in poor neighbourhoods expect to die earlier than those born in rich neighbourhoods but little concern about the fact that men have shorter life expectancies than women.

2. Construct the baseline distribution of health

The next step is to construct a baseline distribution of health for the population. This baseline distribution describes the health of the population, typically measured in quality-adjusted life expectancy at birth, to show the level of health and health inequality prior to implementing the proposed interventions. This distribution can be standardised (using methods of either direct or indirect standardisation) to remove any variation in health that is not associated with the characteristics of interest. For example, in England, we might standardise the health distribution to remove variation associated with gender but retain variation associated with neighbourhood deprivation. This then gives us a description of the population health distribution with a particular focus on the health disparities we are trying to reduce. An example of how to construct such a ‘social distribution of health’ for England is given in another published article.

3. Estimate post-intervention distributions of health

We next estimate the health impacts of the interventions we are comparing. In producing these estimates we need to take into account differences by each of the equity relevant subgroups identified in the:

  • prevalence and incidence of the diseases impacted by the intervention,
  • rates of uptake and adherence to the intervention,
  • efficacy of the intervention,
  • mortality and morbidity, and
  • health opportunity costs.

Standardising these health impacts and combining with the baseline distribution of health derived above gives us estimated post-intervention distributions of health for each intervention.

4. Compare post-intervention distributions using the health equity impact plane

Once post-intervention distributions of health have been estimated for each intervention we can compare them both in terms of their level of average health and in terms of their level of health inequality. Whilst calculating average levels of health in the distributions is straightforward, calculating levels of inequality requires some value judgements to be made. There is a wide range of alternative inequality measures that could be employed each of which captures different aspects of inequality. For example, relative inequality measures would conclude that a health distribution where half the population lives for 40 years and the other half lives for 50 years is just as unequal as a health distribution where half the population lives for 80 years and the other half lives for 100 years. An absolute inequality measure would instead conclude that the equivalence is with a population where half the population lives for 80 years and the other half lives for 90 years.

Two commonly used inequality measures are the Atkinson relative inequality measure and the Kolm absolute inequality measure. These both have the additional feature that they can be calibrated using an inequality aversion parameter to vary the level of priority given to those worst off in the distribution. We will see these inequality aversion parameters in action in the next step of the DCEA process.

Having selected a suitable inequality measure we can plot our post interventions distributions on a health equity impact plane. Let us assume we are comparing two interventions A and B, we can plot intervention A at the origin of the plane and plot intervention B relative to A on the plane.



If intervention B falls in the north-east quadrant of the health equity impact plane we know it both improves health overall and reduces health inequality relative to intervention A and so intervention B should be selected. If, however, intervention B falls in the south-west quadrant of the health equity impact plane we know it both reduces health and increases health inequality relative to intervention A and so intervention A should be selected. If intervention B falls either in the north-west or south-east quadrants of the health equity impact plane there is no obvious answer as to which intervention should be preferred as there is a trade-off to be made between health equity and total health.

5. Evaluate trade-offs between inequality and efficiency using social welfare functions

We use social welfare functions to trade-off between inequality reduction and average health improvement. These social welfare functions are constructed by combining our chosen measure of inequality with the average health in the distribution. This combination of inequality and average health is used to calculate what is known as an equally distributed equivalent (EDE) level of health. The EDE summarises the health distribution being analysed as one number representing the amount of health that each person in a hypothetically perfectly equal health distribution would need to have for us to be indifferent between the actual health distribution analysed and this perfectly equal health distribution. Where our social welfare function is built around an inequality measure with an inequality aversion parameter this EDE level of health will also be a function of the inequality aversion parameter. Where inequality aversion is set to zero there is no concern for inequality and the EDE simply reflects the average health in the distribution replicating results we would see under standard utilitarian CEA. As the inequality aversion level approaches infinity, our focus becomes increasingly on those worse off in the health distribution until at the limit we reflect the Rawlsian idea of focusing entirely on improving the lot of the worst-off in society.


Social welfare functions derived from the Atkinson relative inequality measure and the Kolm absolute inequality measure are given below, with the inequality aversion parameters circled. Research carried out with members of the public in England suggests that suitable values for the Atkinson and Kolm inequality aversion parameters are 10.95 and 0.15 respectively.

Atkinson Relative Social Welfare Function Kolm Absolute Social Welfare Function

When comparing interventions where one intervention does not simply dominate the others on the health equity impact plane we need to use our social welfare functions to calculate EDE levels of health associated with each of the interventions and then select the intervention that produces the highest EDE level of health.

In the example depicted in the figure above we can see that pursuing intervention A results in a health distribution which appears less unequal but has a lower average level of health than the health distribution resulting from intervention B. The choice of intervention, in this case, will be determined by the form of social welfare function selected and the level of inequality this social welfare function is parameterised to embody.

6. Conduct sensitivity analysis on forms of social welfare function and extent of inequality aversion

Given that the conclusions drawn from DCEA may be dependent on the social value judgments made around the inequality measure used and the level of inequality aversion embodied in it, we should present results for a range of alternative social welfare functions parameterised at a range of inequality aversion levels. This will allow decision makers to clearly understand how robust conclusions are to alternative social value judgements.


DCEA is of particular use when evaluating large-scale public health programmes that have an explicit goal of tackling health inequality. It has been applied to the NHS bowel cancer screening programme in England and to the rotavirus vaccination programme in Ethiopia.

Some key limitations of DCEA are that: (1) it currently only analyses programmes in terms of their health impacts whilst large public health programmes often have important impacts across a range of sectors beyond health; and (2) it requires a range of data beyond that required by standard CEA which may not be readily available in all contexts.

For low and middle-income settings an alternative augmented CEA methodology called extended cost effectiveness analysis (ECEA) has been developed to combine estimates of health impacts with estimates of impacts on financial risk protection. More information on ECEA can be found here.

There are ongoing efforts to generalise the DCEA methods to be applied to interventions having impacts across multiple sectors. Follow the latest developments on DCEA at the dedicated website based at the Centre for Health Economics, University of York.


Chris Sampson’s journal round-up for 11th June 2018

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.

End-of-life healthcare expenditure: testing economic explanations using a discrete choice experiment. Journal of Health Economics Published 7th June 2018

People incur a lot of health care costs at the end of life, despite the fact that – by definition – they aren’t going to get much value from it (so long as we’re using QALYs, anyway). In a 2007 paper, Gary Becker and colleagues put forward a theory for the high value of life and high expenditure on health care at the end of life. This article sets out to test a set of hypotheses derived from this theory, namely: i) higher willingness-to-pay (WTP) for health care with proximity to death, ii) higher WTP with greater chance of survival, iii) societal WTP exceeds individual WTP due to altruism, and iv) societal WTP may exceed individual WTP due to an aversion to restricting access to new end-of-life care. A further set of hypotheses relating to the ‘pain of risk-bearing’ is also tested. The authors conducted an online discrete choice experiment (DCE) with 1,529 Swiss residents, which asked respondents to suppose that they had terminal cancer and was designed to elicit WTP for a life-prolonging novel cancer drug. Attributes in the DCE included survival, quality of life, and ‘hope’ (chance of being cured). Individual WTP – using out-of-pocket costs – and societal WTP – based on social health insurance – were both estimated. The overall finding is that the hypotheses are on the whole true, at least in part. But the fact is that different people have different preferences – the authors note that “preferences with regard to end-of-life treatment are very heterogeneous”. The findings provide evidence to explain the prevailing high level of expenditure in end of life (cancer) care. But the questions remain of what we can or should do about it, if anything.

Valuation of preference-based measures: can existing preference data be used to generate better estimates? Health and Quality of Life Outcomes [PubMed] Published 5th June 2018

The EuroQol website lists EQ-5D-3L valuation studies for 27 countries. As the EQ-5D-5L comes into use, we’re going to see a lot of new valuation studies in the pipeline. But what if we could use data from one country’s valuation to inform another’s? The idea is that a valuation study in one country may be able to ‘borrow strength’ from another country’s valuation data. The author of this article has developed a Bayesian non-parametric model to achieve this and has previously applied it to UK and US EQ-5D valuations. But what about situations in which few data are available in the country of interest, and where the country’s cultural characteristics are substantially different. This study reports on an analysis to generate an SF-6D value set for Hong Kong, firstly using the Hong Kong values only, and secondly using the UK value set as a prior. As expected, the model which uses the UK data provided better predictions. And some of the differences in the valuation of health states are quite substantial (i.e. more than 0.1). Clearly, this could be a useful methodology, especially for small countries. But more research is needed into the implications of adopting the approach more widely.

Can a smoking ban save your heart? Health Economics [PubMed] Published 4th June 2018

Here we have another Swiss study, relating to the country’s public-place smoking bans. Exposure to tobacco smoke can have an acute and rapid impact on health to the extent that we would expect an immediate reduction in the risk of acute myocardial infarction (AMI) if a smoking ban reduces the number of people exposed. Studies have already looked at this effect, and found it to be large, but mostly with simple pre-/post- designs that don’t consider important confounding factors or prevailing trends. This study tests the hypothesis in a quasi-experimental setting, taking advantage of the fact that the 26 Swiss cantons implemented smoking bans at different times between 2007 and 2010. The authors analyse individual-level data from Swiss hospitals, estimating the impact of the smoking ban on AMI incidence, with area and time fixed effects, area-specific time trends, and unemployment. The findings show a large and robust effect of the smoking ban(s) for men, with a reduction in AMI incidence of about 11%. For women, the effect is weaker, with an average reduction of around 2%. The evidence also shows that men in low-education regions experienced the greatest benefit. What makes this an especially nice paper is that the authors bring in other data sources to help explain their findings. Panel survey data are used to demonstrate that non-smokers are likely to be the group benefitting most from smoking bans and that people working in public places and people with less education are most exposed to environmental tobacco smoke. These findings might not be generalisable to other settings. Other countries implemented more gradual policy changes and Switzerland had a particularly high baseline smoking rate. But the findings suggest that smoking bans are associated with population health benefits (and the associated cost savings) and could also help tackle health inequalities.


Sam Watson’s journal round-up for 15th January 2018

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.

Cost-effectiveness of publicly funded treatment of opioid use disorder in California. Annals of Internal Medicine [PubMed] Published 2nd January 2018

Deaths from opiate overdose have soared in the United States in recent years. In 2016, 64,000 people died this way, up from 16,000 in 2010 and 4,000 in 1999. The causes of public health crises like this are multifaceted, but we can identify two key issues that have contributed more than any other. Firstly, medical practitioners have been prescribing opiates irresponsibly for years. For the last ten years, well over 200,000,000 opiate prescriptions were issued per year in the US – enough for seven in every ten people. Once prescribed, opiate use is often not well managed. Prescriptions can be stopped abruptly, for example, leaving people with unexpected withdrawal syndromes and rebound pain. It is estimated that 75% of heroin users in the US began by using legal, prescription opiates. Secondly, drug suppliers have started cutting heroin with its far stronger but cheaper cousin, fentanyl. Given fentanyl’s strength, only a tiny amount is required to achieve the same effects as heroin, but the lack of pharmaceutical knowledge and equipment means it is often not measured or mixed appropriately into what is sold as ‘heroin’. There are two clear routes to alleviating the epidemic of opiate overdose: prevention, by ensuring responsible medical use of opiates, and ‘cure’, either by ensuring the quality and strength of heroin, or providing a means to stop opiate use. The former ‘cure’ is politically infeasible so it falls on the latter to help those already habitually using opiates. However, the availability of opiate treatment programs, such as opiate agonist treatment (OAT), is lacklustre in the US. OAT provides non-narcotic opiates, such as methadone or buprenorphine, to prevent withdrawal syndromes in users, from which they can slowly be weaned. This article looks at the cost-effectiveness of providing OAT for all persons seeking treatment for opiate use in California for an unlimited period versus standard care, which only provides OAT to those who have failed supervised withdrawal twice, and only for 21 days. The paper adopts a previously developed semi-Markov cohort model that includes states for treatment, relapse, incarceration, and abstinence. Transition probabilities for the new OAT treatment were determined from treatment data for current OAT patients (as far as I understand it). Although this does raise the question about the generalisability of this population to the whole population of opiate users – given the need to have already been through two supervised withdrawals, this population may have a greater motivation to quit, for example. In any case, the article estimates that the OAT program would be cost-saving, through reductions in crime and incarceration, and improve population health, by reducing the risk of death. Taken at face value these results seem highly plausible. But, as we’ve discussed before, drug policy rarely seems to be evidence-based.

The impact of aid on health outcomes in Uganda. Health Economics [PubMed] Published 22nd December 2017

Examining the response of population health outcomes to changes in health care expenditure has been the subject of a large and growing number of studies. One reason is to estimate a supply-side cost-effectiveness threshold: the health returns the health service achieves in response to budget expansions or contractions. Similarly, we might want to know the returns to particular types of health care expenditure. For example, there remains a debate about the effectiveness of aid spending in low and middle-income country (LMIC) settings. Aid spending may fail to be effective for reasons such as resource leakage, failure to target the right population, poor design and implementation, and crowding out of other public sector investment. Looking at these questions at an aggregate level can be tricky; the link between expenditure or expenditure decisions and health outcomes is long and causality flows in multiple directions. Effects are likely to therefore be small and noisy and require strong theoretical foundations to interpret. This article takes a different, and innovative, approach to looking at this question. In essence, the analysis boils down to a longitudinal comparison of those who live near large, aid funded health projects with those who don’t. The expectation is that the benefit of any aid spending will be felt most acutely by those who live nearest to actual health care facilities that come about as a result of it. Indeed, this is shown by the results – proximity to an aid project reduced disease prevalence and work days lost to ill health with greater effects observed closer to the project. However, one way of considering the ‘usefulness’ of this evidence is how it can be used to improve policymaking. One way is in understanding the returns to investment or over what area these projects have an impact. The latter is covered in the paper to some extent, but the former is hard to infer. A useful next step may be to try to quantify what kind of benefit aid dollars produce and its heterogeneity thereof.

The impact of social expenditure on health inequalities in Europe. Social Science & Medicine Published 11th January 2018

Let us consider for a moment how we might explore empirically whether social expenditure (e.g. unemployment support, child support, housing support, etc) affects health inequalities. First, we establish a measure of health inequality. We need a proxy measure of health – this study uses self-rated health and self-rated difficulty in daily living – and then compare these outcomes along some relevant measure of socioeconomic status (SES) – in this study they use level of education and a compound measure of occupation, income, and education (the ISEI). So far, so good. Data on levels of social expenditure are available in Europe and are used here, but oddly these data are converted to a percentage of GDP. The trouble with doing this is that this variable can change if social expenditure changes or if GDP changes. During the financial crisis, for example, social expenditure shot up as a proportion of GDP, which likely had very different effects on health and inequality than when social expenditure increased as a proportion of GDP due to a policy change under the Labour government. This variable also likely has little relationship to the level of support received per eligible person. Anyway, at the crudest level, we can then consider how the relationship between SES and health is affected by social spending. A more nuanced approach might consider who the recipients of social expenditure are and how they stand on our measure of SES, but I digress. In the article, the baseline category for education is those with only primary education or less, which seems like an odd category to compare to since in Europe I would imagine this is a very small proportion of people given compulsory schooling ages unless, of course, they are children. But including children in the sample would be an odd choice here since they don’t personally receive social assistance and are difficult to compare to adults. However, there are no descriptive statistics in the paper so we don’t know and no comparisons are made between other groups. Indeed, the estimates of the intercepts in the models are very noisy and variable for no obvious reason other than perhaps the reference group is very small. Despite the problems outlined so far though, there is a potentially more serious one. The article uses a logistic regression model, which is perfectly justifiable given the binary or ordinal nature of the outcomes. However, the authors justify the conclusion that “Results show that health inequalities measured by education are lower in countries where social expenditure is higher” by demonstrating that the odds ratio for reporting a poor health outcome in the groups with greater than primary education, compared to primary education or less, is smaller in magnitude when social expenditure as a proportion of GDP is higher. But the conclusion does not follow from the premise. It is entirely possible for these odds ratios to change without any change in the variance of the underlying distribution of health, the relative ordering of people, or the absolute difference in health between categories, simply by shifting the whole distribution up or down. For example, if the proportions of people in two groups reporting a negative outcome are 0.3 and 0.4, which then change to 0.2 and 0.3 respectively, then the odds ratio comparing the two groups changes from 0.64 to 0.58. The difference between them remains 0.1. No calculations are made regarding absolute effects in the paper though. GDP is also shown to have a positive effect on health outcomes. All that might have been shown is that the relative difference in health outcomes between those with primary education or less and others changes as GDP changes because everyone is getting healthier. The question of the article is interesting, it’s a shame about the execution.