# Are we estimating the effects of health care expenditure correctly?

It is a contentious issue in philosophy whether an omission can be the cause of an event. At the very least it seems we should consider causation by omission differently from ‘ordinary’ causation. Consider Sarah McGrath’s example. Billy promised Alice to water the plant while she was away, but he did not water it. Billy not watering the plant caused its death. But there are good reasons to suppose that Billy did not cause its death. If Billy’s lack of watering caused the death of the plant, it may well be reasonable to assume that Vladimir Putin and indeed anyone else who did not water the plant were also a cause. McGrath argues that there is a normative consideration here: Billy ought to have watered the plant and that’s why we judge his omission as a cause and not anyone else’s. Similarly, the example from L.A. Paul and Ned Hall’s excellent book Causation: A User’s GuideBilly and Suzy are playing soccer on rival teams. One of Suzy’s teammates scores a goal. Both Billy and Suzy were nearby and could have easily prevented the goal. But our judgement is that the goal should only be credited to Billy’s failure to block the goal as Suzy had no responsibility to.

These arguments may appear far removed from the world of health economics. But, they have practical implications. Consider the estimation of the effect that increasing health care expenditure has on public health outcomes. The government, or relevant health authority, makes a decision about how the budget is allocated. It is often the case that there are allocative inefficiencies: greater gains could be had by reallocating the budget to more effective programs of care. In this case there would seem to be a relevant omission; the budget has not been spent where it could have provided benefits. These omissions are often seen as causes of a loss of health. Karl Claxton wrote of the Cancer Drugs Fund, a pool of money diverted from the National Health Service to provide cancer drugs otherwise considered cost-ineffective, that it was associated with

a net loss of at least 14,400 quality adjusted life years in 2013/14.

Similarly, an analysis of the lack of spending on effective HIV treatment and prevention by the Mbeki administration in South Africa wrote that

More than 330,000 lives or approximately 2.2 million person-years were lost because a feasible and timely ARV treatment program was not implemented in South Africa.

But our analyses of the effects of health care expenditure typically do not take these omissions into account.

Causal inference methods are founded on a counterfactual theory of causation. The aim of a causal inference method is to estimate the potential outcomes that would have been observed under different treatment regimes. In our case this would be what would have happened under different levels of expenditure. This is typically estimated by examining the relationship between population health and levels of expenditure, perhaps using some exogenous determinant of expenditure to identify the causal effects of interest. But this only identifies those changes caused by expenditure and not those changes caused by not spending.

Consider the following toy example. There are two causes of death in the population $a$ and $b$ with associated programs of care and prevention $A$ and $B$. The total health care expenditure is $x$ of which a proportion $p: p\in P \subseteq [0,1]$ is spent on $A$ and $1-p$ on $B$. The deaths due to each cause are $y_a$ and $y_b$ and so the total deaths are $y = y_a + y_b$. Finally, the effect of a unit increase in expenditure in each program are $\beta_a$ and $\beta_b$. The question is to determine what the causal effect of expenditure is. If $Y_x$ is the potential outcome for level of expenditure $x$ then the average treatment effect is given by $E(\frac{\partial Y_x}{\partial x})$.

The country has chosen an allocation between the programmes of care of $p_0$. If causation by omission is not a concern then, given linear, additive models (and that all the model assumptions are met), $y_a = \alpha_a + \beta_a p x + f_a(t) + u_a$ and $y_b = \alpha_b + \beta_b (1-p) x + f_b(t) + u_b$, the causal effect is $E(\frac{\partial Y_x}{\partial x}) = \beta = \beta_a p_0 + \beta_b (1-p_0)$. But if causation by omission is relevant, then the net effect of expenditure is the lives gained $\beta_a p_0 + \beta_b (1-p_0)$ less the lives lost. The lives lost are those under all possible things we did not do, so the estimator of the causal effect is $\beta' = \beta_a p_0 + \beta_b (1-p_0) - \int_{P/p_0} [ \beta_ap + \beta_b(1-p) ] dG(p)$. Now, clearly $\beta \neq \beta'$ unless $P/p_0$ is the empty set, i.e. there was no other option. Indeed, the choice of possible alternatives involves a normative judgement as we’ve suggested. For an omission to count as a cause, there needs to be a judgement about what ought to have been done. For health care expenditure this may mean that the only viable alternative is the allocatively efficient distribution, in which case all allocations will result in a net loss of life unless they are allocatively efficient, which some may argue is reasonable. An alternative view is simply that the government simply has to not do worse than in the past and perhaps it is also reasonable for the government not to make significant changes to the allocation, for whatever reason. In that case we might say that $P \in [p_0,1]$ and $g(p)$ might be a distribution truncated below $p_0$ with most mass around $p_0$ and small variance.

The problem is that we generally do not observe the effect of expenditure in each program of care nor do we know the distribution of possible budget allocations. The normative judgements are also a contentious issue. Claxton clearly believes the government ought not to have initiated the Cancer Drugs Fund, but he does not go so far as to say any allocative inefficiency results in a net loss of life. Some working out of the underlying normative principles is warranted. But if it’s not possible to estimate these net causal effects, why discuss it? Perhaps it’s due to the lack of consistency. We estimate the ‘ordinary’ causal effect in our empirical work, but we often discuss opportunity costs and losses due to inefficiencies as being due to or caused by the spending decisions that are made. As the examples at the beginning illustrate, the normative question of responsibility seeps into our judgments about whether an omission is the cause of an outcome. For health care expenditure the government or other health care body does have a relevant responsibility. I would argue then that causation by omission is important and perhaps we need to reconsider the inferences that we make.

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# 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

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.

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# How to cite The Academic Health Economists’ Blog

Occasionally we get emails from people who would like to cite our blog posts. Usually, these requests are framed as ‘is this going to be published in a journal?’. It’s no surprise that people are more comfortable citing the traditional academic literature. But researchers are increasingly citing blog posts. Indeed, some of our blog posts have been cited in published academic literature.

There are plenty of guides out there for citing blog posts. You may like to refer to them for specific formatting styles. Cite This For Me is a useful tool for generating references in a variety of styles. Here I’d like to provide a few specific recommendations for citing posts from this blog.

## 1. Cite the author

Our blog posts are written by lots of different authors, not by ‘the blog’. The author’s name – assuming they have not claimed anonymity – will appear at the top of the blog post. Let’s take a recent example. To start with, your citation should look something like:

Watson, S. (2017). Variations in NHS admissions at a glance. The Academic Health Economists’ Blog. Available at: https://aheblog.com/2017/01/25/variations-in-nhs-admissions-at-a-glance/ [Accessed 8 Mar. 2017].

## 2. Use our ISSN

As of this week, the blog now has its own International Standard Serial Number (ISSN). This number uniquely identifies and distinguishes the blog. Our ISSN is 2514-3441. You can find it at the bottom of the sidebar and on our About page. So your citation could become:

Watson, S. (2017). Variations in NHS admissions at a glance. The Academic Health Economists’ Blog (ISSN 2514-3441). Available at: https://aheblog.com/2017/01/25/variations-in-nhs-admissions-at-a-glance/ [Accessed 8 Mar. 2017].

## 3. Use WebCite

Unlike journal articles, websites can change. One of our authors could (in principle) completely change the content of their blog post after publishing it. More importantly, it is possible that our URLs may change in the future. If this were to happen, the link in the reference above would become redundant and the citation would not be useful to readers. What needs to be cited, therefore, is the blog post at the time at which you accessed it. Enter WebCite. WebCite is a service that archives a webpage and provides a permanent link for citation. This can be achieved by completing an archiving form. Our citation becomes:

Watson, S. (2017). Variations in NHS admissions at a glance. The Academic Health Economists’ Blog (ISSN 2514-3441). Available at: https://aheblog.com/2017/01/25/variations-in-nhs-admissions-at-a-glance/ [Accessed 8 Mar. 2017]. (Archived by WebCite® at http://www.webcitation.org/6ooALaGyF)

## 4. Check the comments

Finally, authors may choose to subsequently publish their blog post elsewhere in another format or to upload it to a service such as figshare in order to obtain a DOI. Check the comments below a blog post to see if this is the case as there may be an alternative source that you might prefer to cite.

But as ever, if you’re struggling, get in touch.

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