# Sam Watson’s journal round-up for 12th June 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.

Machine learning: an applied econometric approach. Journal of Economic Perspectives [RePEcPublished Spring 2017

Machine learning tools have become ubiquitous in the software we use on a day to day basis. Facebook can identify faces in photos; Google can tell you the traffic for your journey; Netflix can recommend you movies based on what you’ve watched before. Machine learning algorithms provide a way to estimate an unknown function $f$ that predicts an outcome $Y$ given some data $x$: $Y = f(x) + \epsilon$. The potential application of these algorithms to many econometric problems is clear. This article outlines the principles of machine learning methods. It divides econometric problems into prediction, $\hat{y}$, and parameter estimation, $\hat{\beta}$ and suggests machine learning is a useful tool for the former. However, this distinction is a false one, I believe. Parameters are typically estimated because they represent an average treatment effect, say $E(y|x=1) - E(y|x=0)$. But, we can estimate these quantities in ‘$\hat{y}$ problems’ since $f(x) = E(y|x)$. Machine learning algorithms, therefore, represent a non-parametric (or very highly parametric) approach to the estimation of treatment effects. In cases where functional form is unknown, where there may be nonlinearities in the response function, and interactions between variables, this approach can be very useful. They do not represent a panacea to estimation problems of course, since interpretation rests on the assumptions. For example, as Jennifer Hill discusses, additive regression tree methods can be used to estimate conditional average treatment effects if we can assume the treatment is ignorable conditional on the covariates. This article, while providing a good summary of methods, doesn’t quite identify the right niche where these approaches might be useful in econometrics.

Incorporating equity in economic evaluations: a multi-attribute equity state approach. European Journal of Health Economics [PubMedPublished 1st June 2017

Efficiency is a key goal for the health service. Economic evaluation provides evidence to support investment decisions, whether displacing resources from one technology to another can produce greater health benefits. Equity is generally not formally considered except through the final investment decision-making process, which may lead to different decisions by different commissioning groups. One approach to incorporating equity considerations into economic evaluation is the weighting of benefits, such as QALYs, by group. For example, a number of studies have estimated that benefits of end-of-life treatments have a greater social valuation than other treatments. One way of incorporating this into economic evaluation is to raise the cost-effectiveness threshold by an appropriate amount for end-of-life treatments. However, multiple attributes may be relevant for equity considerations, negating a simplistic approach like this. This paper proposed a multi-attribute equity state approach to incorporating equity concerns formally in economic evaluation. The basic premise of this approach is to firstly define a set of morally relevant attributes, to secondly derive a weighting scheme for each set of characteristics (similarly to how QALY weights are derived from the EQ-5D questionnaire), and thirdly to apply these weights to economic evaluation. A key aspect of the last step is to weight both the QALYs gained by a population from a new technology and those displaced from another. Indeed, identifying where resources are displaced from is perhaps the biggest limitation to this approach. This displacement problem has also come up in other discussions revolving around the estimation of the cost-effectiveness threshold. This seems to be an important area for future research.

Financial incentives, hospital care, and health outcomes: evidence from fair pricing laws. American Economic Journal: Economic Policy [RePEcPublished May 2017

There is a not-insubstantial literature on the response of health care providers to financial incentives. Generally, providers behave as expected, which can often lead to adverse outcomes, such as overtreatment in cases where there is potential for revenue to be made. But empirical studies of this behaviour often rely upon the comparison of conditions with different incentive schedules; rarely is there the opportunity to study the effects of relative shifts in incentive within the same condition. This paper studies the effects of fair pricing laws in the US, which limited the amount uninsured patients would have to pay hospitals, thus providing the opportunity to study patients with the same conditions but who represent different levels of revenue for the hospital. The introduction of fair pricing laws was associated with a reduction in total billing costs and length of stay for uninsured patients but little association was seen with changes in quality. A similar effect was not seen in the insured suggesting the price ceiling introduced by the fair pricing laws led to an increase in efficiency.

Credits

# Meeting round-up: 18th European Health Economics Workshop (EHEW)

I attended the European Health Economics Workshop (EHEW) in Oslo. The workshop has been running for almost 20 years and it shows. Most participants have attended many editions of EHEW, which has and continues to shape the field of health economics theory. This is “the theory workshop”. The atmosphere is one of great friendship and constructive feedback, based on long-term collaborations that set the tone of the workshop. I am definitely not a theorist but found a very welcoming group of people, interested in fostering collaboration between theory, experiments, and empirical work.

EHEW is also a perfect example of the law of small numbers. The smaller the workshop, the more useful the feedback. The smaller the workshop, the larger the potential for fruitful research co-authorship.

Over two days, we went through 15 papers, building up to a total of not more than 30 participants, all of whom had an active role. The author presents in 25 minutes, followed by 10 minutes from the discussant and floor debate, a format that has become the golden rule.

We started off the proper way, with a wine reception at our headquarters hotel in downtown Oslo. I have to say, the organizers – Tor Iversen, Oddvar Kaarboe and Jan Erik Askildsen – did a terrific job. We all know what people remember from a workshop or conference: food and venue. It will be hard to beat EHEW Oslo (although we are possibly headed to Paris next year). We spent Friday and Saturday in an old stable, transformed into a delightful meeting room (see below). The catering was also on point, but what really stood out were the dinners. I think we can all agree that the dinner on Friday night was the best conference meal of all time; a 4-course dinner with paired wine at Restaurant Eik (I leave this here in case you ever go to Oslo – trust me, you want to go there.)

What about scientific content, you might ask? Jonathan Kolstad set the tone with an opening keynote lecture on the role of IT in physician response to pay for performance. The lecture combined theory with empirics, and I was rapidly drawn into a data-envy generating process. Tremendous physician and patient level data from the largest provider in Hawaii. Can you imagine the hardships of field work?

As for the presentations, we covered a broad range of topics. Luigi Siciliani, Helmuth Cremer and Francesca Barigozzi teamed up for a session on long-term care. Their theoretical approaches ranged from a standard IO two-sided market approach to strategic bequests and informal caregiving within the family. We had sessions on the regulation of drugs and unhealthy food, hospital, pharmaceutical and insurance markets, and on GP and health behavior. The paper by Marcos Vera-Hernandez (Identifying complementarities across tasks using two-part contracts. An application to family doctors) was a fantastic example of how to combine theory and empirical analysis. Johannes Schunemann gave a thought-provoking talk on The marriage gap: optimal aging and death in partnerships. I don’t quite agree with the assumptions and conclusions of the study, but then again I think that’s why I’m not a theorist… The main problem, in this case, is that there is nothing about the model that is specific to the variables being studied. We also covered the hot topic of antibiotic prescribing, with a model for prescription under uncertainty about resistance that got us all guesstimating our risk aversion.

The discussions within the workshop highlighted the potential benefits from having cross-field feedback. Empirically-minded researchers provided very useful feedback for theory articles, and vice-versa (for the few exceptions to the theory rule). In retrospect, I am convinced this arises from getting less caught up in technicalities of the theoretical model or the econometric specification, and placing a stronger emphasis on the basic assumptions of the models and the corresponding story.

All in all, we had a terrific time in Oslo. I was impressed by the level of collegiality amongst long-term participants, as well as their welcoming attitude towards newbies like myself. We worked hard and partied hard – even brought back dancing to EHEW – and I look forward to meeting up with the theorists in the near future. Lise, it’s on you!

# 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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