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

Tuskegee and the health of black men. The Quarterly Journal of Economics [RePEc] Published February 2018

In 1932, a study often considered the most infamous and potentially most unethical in U.S. medical history began. Researchers in Alabama enrolled impoverished black men in a research program designed to examine the effects of syphilis under the guise of receiving government-funded health care. The study was known as the Tuskegee syphilis experiment. For 40 years the research subjects were not informed they had syphilis nor were they treated, even after penicillin was shown to be effective. The study was terminated in 1972 after its details were leaked to the press; numerous men died, 40 wives contracted syphilis, and a number of children were born with congenital syphilis. It is no surprise then that there is distrust among African Americans in the medical system. The aim of this article is to examine whether the distrust engendered by the Tuskegee study could have contributed to the significant differences in health outcomes between black males and other groups. To derive a causal estimate the study makes use of a number of differences: black vs non-black, for obvious reasons; male vs female, since the study targeted males, and also since women were more likely to have had contact with and hence higher trust in the medical system; before vs after; and geographic differences, since proximity to the location of the study may be informative about trust in the local health care facilities. A wide variety of further checks reinforce the conclusions that the study led to a reduction in health care utilisation among black men of around 20%. The effect is particularly pronounced in those with low education and income. Beyond elucidating the indirect harms caused by this most heinous of studies, it illustrates the importance of trust in mediating the effectiveness of public institutions. Poor reputations caused by negligence and malpractice can spread far and wide – the mid-Staffordshire hospital scandal may be just such an example.

The economic consequences of hospital admissions. American Economic Review [RePEcPublished February 2018

Is health care infected by Baumol’s cost disease? Test of a new model. Health Economics [PubMed] [RePEcPublished 9th February 2018

A few years ago we discussed Baumol’s theory of the ‘cost disease’ and an empirical study trying to identify it. In brief, the theory supposes that spending on health care (and other labour-intensive or creative industries) as a proportion of GDP increases, at least in part, because these sectors experience the least productivity growth. Productivity increases the fastest in sectors like manufacturing and remuneration increases as a result. However, this would lead to wages in the most productive sectors outstripping those in the ‘stagnant’ sectors. For example, salaries for doctors would end up being less than those for low-skilled factory work. Wages, therefore, increase in the stagnant sectors despite a lack of productivity growth. The consequence of all this is that as GDP grows, the proportion spent on stagnant sectors increases, but importantly the absolute amount spent on the productive sectors does not decrease. The share of the pie gets bigger but the pie is growing at least as fast, as it were. To test this, this article starts with a theoretic two-sector model to develop some testable predictions. In particular, the authors posit that the cost disease implies: (i) productivity is related to the share of labour in the health sector, and (ii) productivity is related to the ratio of prices in the health and non-health sectors. Using data from 28 OECD countries between 1995 and 2016 as well as further data on US industry group, they find no evidence to support these predictions, nor others generated by their model. One reason for this could be that wages in the last ten years or more have not risen in line with productivity in manufacturing or other ‘productive’ sectors, or that productivity has indeed increased as fast as the rest of the economy in the health care sector. Indeed, we have discussed productivity growth in the health sector in England and Wales previously. The cost disease may well then not be a cause of rising health care costs – nevertheless, health care need is rising and we should still expect costs to rise concordantly.

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# Hawking is right, Jeremy Hunt does egregiously cherry pick the evidence

I’m beginning to think Jeremy Hunt doesn’t actually care what the evidence says on the weekend effect. Last week, renowned physicist Stephen Hawking criticized Hunt for ‘cherry picking’ evidence with regard to the ‘weekend effect’: that patients admitted at the weekend are observed to be more likely than their counterparts admitted on a weekday to die. Hunt responded by doubling down on his claims:

Some people have questioned Hawking’s credentials to speak on the topic beyond being a user of the NHS. But it has taken a respected public figure to speak out to elicit a response from the Secretary of State for Health, and that should be welcomed. It remains the case though that a multitude of experts do continue to be ignored. Even the oft-quoted Freemantle paper is partially ignored where it notes of the ‘excess’ weekend deaths, “to assume that [these deaths] are avoidable would be rash and misleading.”

We produced a simple tool to demonstrate how weekend effect studies might estimate an increased risk of mortality associated with weekend admissions even in the case of no difference in care quality. However, the causal model underlying these arguments is not always obvious. So here it is:

A simple model of the effect of the weekend on patient health outcomes. The dashed line represents unobserved effects

So what do we know about the weekend effect?

1. The weekend effect exists. A multitude of studies have observed that patients admitted at the weekend are more likely to die than those admitted on a weekday. This amounts to having shown that $E(Y|W,S) \neq E(Y|W',S)$. As our causal model demonstrates, being admitted is correlated with health and, importantly, the day of the week. So, this is not the same as saying that risk of adverse clinical outcomes differs by day of the week if you take into account propensity for admission, we can’t say $E(Y|W) \neq E(Y|W')$. Nor does this evidence imply care quality differs at the weekend, $E(Q|W) \neq E(Q|W')$. In fact, the evidence only implies differences in care quality if the propensity to be admitted is independent of (unobserved) health status, i.e. $Pr(S|U,X) = Pr(S|X)$ (or if health outcomes are uncorrelated with health status, which is definitely not the case!).
2. Admissions are different at the weekend. Fewer patients are admitted at the weekend and those that are admitted are on average more severely unwell. Evidence suggests that the better patient severity is controlled for, the smaller the estimated weekend effect. Weekend effect estimates also diminish in models that account for the selection mechanism.
3. There is some evidence that care quality may be worse at the weekend (at least in the United States). So $E(Q|W) \neq E(Q|W')$. Although this has not been established in the UK (we’re currently investigating it!)
4. Staffing levels, particularly specialist to patient ratios, are different at the weekend, $E(X|W) \neq E(X|W')$.
5. There is little evidence to suggest how staffing levels and care quality are related. While the relationship seems evident prima facie, its extent is not well understood, for example, we might expect a diminishing return to increased staffing levels.
6. There is a reasonable amount of evidence on the impact of care quality (preventable errors and adverse events) on patient health outcomes.

But what are we actually interested in from a policy perspective? Do we actually care that it is the weekend per se? I would say no, we care that there is potentially a lapse in care quality. So, it’s a two part question: (i) how does care quality (and hence avoidable patient harm) differ at the weekend $E(Q|W) - E(Q|W') = ?$; and (ii) what effect does this have on patient outcomes $E(Y|Q)=?$. The first question answers to what extent policy may affect change and the second gives us a way of valuing that change and yet the vast majority of studies in the area address neither. Despite there being a number of publicly funded research projects looking at these questions right now, it’s the studies that are not useful for policy that keep being quoted by those with the power to make change.

Hawking is right, Jeremy Hunt has egregiously cherry picked and misrepresented the evidence, as has been pointed out again and again and again and again and … One begins to wonder if there isn’t some motive other than ensuring long run efficiency and equity in the health service.

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# Variations in NHS admissions at a glance

Variations in admissions to NHS hospitals are the source of a great deal of consternation. Over the long-run, admissions and the volume of activity required of the NHS have increased, without equivalent increases in funding or productivity. Over the course of the year, there are repeated claims of crises as hospitals are ill-equipped for the increase in demand in the winter. While different patterns of admissions at weekends relative to weekdays may be the foundation of the ‘weekend effect’ as we recently demonstrated. And yet all these different sources of variation produce a singular time series of numbers of daily admissions. But, each of the different sources of variation are important for different planning and research aims. So let’s decompose the daily number of admissions into its various components.

## Data

Daily number of emergency admissions to NHS hospitals between April 2007 and March 2015 from Hospital Episode Statistics.

## Methods

A similar analysis was first conducted on variations in the number of births by day of the year. A full description of the model can be found in Chapter 21 of the textbook Bayesian Data Analysis (indeed the model is shown on the front cover!). The model is a sum of Gaussian processes, each one modelling a different aspect of the data, such as the long-run trend or weekly periodic variation. We have previously used Gaussian processes in a geostatistical model on this blog. Gaussian processes are a flexible class of models for which any finite dimensional marginal distribution is Gaussian. Different covariance functions can be specified for different models, such as the aforementioned periodic or long-run trends. The model was run using the software GPstuff in Octave (basically an open-source version of Matlab) and we have modified code from the GPstuff website.

## Results

The four panels of the figure reveal to us things we may claim to already know. Emergency admissions have been increasing over time and were about 15% higher in 2015 than in 2007 (top panel). The second panel shows us the day of the week effects: there are about 20% fewer admissions on a Saturday or Sunday than on a weekday. The third panel shows a decrease in summer and increase in winter as we often see reported, although perhaps not quite as large as we might have expected. And finally the bottom panel shows the effects of different days of the year. We should note that the large dip at the end of March/beginning of April is an artifact of coding at the end of the financial year in HES and not an actual drop in admissions. But, we do see expected drops for public holidays such as Christmas and the August bank holiday.

While none of this is unexpected it does show that there’s a lot going on underneath the aggregate data. Perhaps the most alarming aspect of the data is the long run increase in emergency admissions when we compare it to the (lack of) change in funding or productivity. It suggests that hospitals will often be running at capacity so other variation, such as over winter, may lead to an excess capacity problem. We might also speculate on other possible ‘weekend effects’, such as admission on a bank holiday.

As a final thought, the method used to model the data is an excellent way of modelling data with an unknown structure without posing assumptions such as linearity that might be too strong. Hence their use in geostatistics. They are widely used in machine learning and artificial intelligence as well. We often encounter data with unknown and potentially complicated structures in health care and public health research so hopefully this will serve as a good advert for some new methods. See this book, or the one referenced in the methods section, for an in depth look.

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