*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.*

## Principles

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.

## Implementation

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.

## Applications

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.

**Credit **