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.


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


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.



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.



Weekend effect explainer: why we are not the ‘climate change deniers of healthcare’

The statistics underlying the arguments around the weekend effect are complicated. Despite over a hundred empirical studies on the topic, and an observed increase in the risk of mortality for weekend admissions in multiple countries, there is still no real consensus on what is going on. We have previously covered the arguments on this blog and suggested that the best explanation for the weekend effect is that healthier patients are less likely to be admitted to hospital at the weekend. Nevertheless, a little knowledge can be a dangerous thing (the motto of the Dunning-Kruger effect), and some people can be very confident about the interpretation of the statistics despite their complicated nature. For example, one consultant nephrologist wrote in a comment on a recent article that those who attribute the weekend effect to differences in admission are becoming ‘the climate change deniers of healthcare’ as they are not taking into account all the risk-adjusted analyses!

It may certainly be the case that there is a reduction in healthcare quality at the weekend. But it is also important for policy makers to understand that it is still possible to observe a weekend effect even with quite comprehensive mortality risk adjustment. The image below links to an app that simulates multiple weekend effect studies from a model where there is no weekend effect but potentially different chances of admission at the weekend and on weekdays. We are assuming that those who turn up to A&E but are not admitted and sent home are the healthiest patients. In the app, you can change the parameters: the proportion of attendances that are admitted on weekends and weekdays, the mortality rate among patients who are admitted, and, crucially, the amount of variation in patient mortality explained (a sort of “R-squared”) by our risk adjustment. It will display crude and adjusted odds ratios as well as a distribution of possible results from similar studies. (Be patient though, simulating lots of large studies seems to take a while on the server!).


As is evident, even with a very high proportion of variance explained, we can still get an odds ratio not equal to one and an observed weekend effect if the proportion of attendances who are admitted differs between weekend and weekday. And, with the very large sample sizes often used for these studies, these will likely appear “statistically significant“. Recent evidence from the UK has suggested that 27% of A&E attendances are admitted at the weekend compared to 30% on a weekday. Even when we can explain 90% of the variation in mortality, we can still get a ‘weekend effect’ with these small differences in propensity for admission. And, if there is any element of publication bias, or the ‘garden of forking paths’ [PDF] we will see lots of statistically significant weekend effect studies published.

When there is a misunderstanding about statistics, one often blames the audience for not understanding, but it is often the case that an idea has just not been explained well enough. I can’t judge whether little web apps will actually help explain concepts like this, but hopefully it’s a step in the right direction.


Sam Watson’s journal round-up for 7th November 2016

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 view from above: applications of satellite data in economics. Journal of Economic Perspectives [RePEc] Published October 2016

Images of the earth from above have been used for economic analysis for the better part of a century. Photographs taken from aeroplanes were used to map agricultural land use in the US in the 1930s and 1940s, for example. Since that time the remotely sensed data available to economists have grown exponentially as modern satellites provide very high resolution imagery across a wide range of spectral bands. This discussion article summarises the methods and use of these new data, which have already shown to be useful for those working in health. We recently discussed the issue of measuring neighbourhood effects in slums, one recent paper used satellite imagery of Kibera, Nairobi to identify dwellings that had replaced their roofs. Such information could be linked to other data sources such as the Demographic and Health Surveys, as another recent paper has done. Another health-related example provided in this article is a paper that used satellite data to map air pollution from forest fires, which are then used to estimate excess infant deaths in Indonesia. Satellite data can provide an important source of information for areas where few other data are available, they have high spatial resolution, and have a wide geographic coverage, making them a potential boon for health research. Nevertheless, the use of these data is still in its early days, and the best statistical methods, particularly for causal inference, are still to be settled upon.

Arrival by ambulance explains variation in mortality by time of admission: retrospective study of admissions to hospital following emergency department attendance in England. BMJ Quality and Safety [PubMedPublished October 2016

The UK government’s plans to increase provision of health care services at the weekend – the seven day NHS policy – has generated large controversies. The policy has been justified on the basis of the so-called ‘weekend effect’, that patients who are admitted to hospital at the weekend are more likely to die than their counterparts admitted on a weekday. This evidence has been widely questioned, as we have discussed here, here, and here. Part of the problem is that patients who are admitted at the weekend differ from those admitted on a weekday in that they are more likely to be in worse health. So far, there has been little success in the development of adequate and convincing risk adjustment schemes using routine data. This article attempts to address this issue by using mode of arrival at the accident and emergency department to control for severity of illness. The authors report that under a standard risk adjustment model, there appears to be some evidence of an increased risk of mortality among weekend and weeknight admissions relative to Wednesday daytime admissions (odds ratio approximately 1.07), which is slightly lower than the risks reported elsewhere. However, after adjusting for mode of arrival, nights no longer appear worse, and only Sunday daytime admissions show evidence of an increased risk of mortality relative to Wednesday daytime admissions. Mode of arrival is a relatively blunt measure of severity of illness as you either do not arrive by ambulance or you do. But, an important tenet of any statistical analysis is to examine the robustness of the results to changes in model specification, and this article demonstrates that controlling for mode of arrival affects the results and hence conclusions that can be made from this study. This article adds to the growing evidence base that the evidence surrounding the ‘weekend effect’ is not as clear-cut as some would have you believe.

Worms at work: long-run impacts of a child health investment. The Quarterly Journal of Economics [RePEcPublished October 2016

The treatment of worms (helminths) is cheap, but diagnosis is expensive, so periodic mass de-worming programmes have been recommended by the World Health Organization in high-risk areas. However, a recent Cochrane review concluded that there was strong evidence that such programmes do not improve nutrition, health, or schooling outcomes. But, as this paper notes, the Cochrane review excluded a number of rigorous non-individual randomised studies, such as the analysis of a school based trial in Kenya, which showed large increases in school participation. This article presents a ten year follow up of this Kenyan trial. The authors report that they find increases in the proportion of people reporting their health as ‘very good’ and an increase in the number of hours in the labour market provided by males. But, the effects are small. Nevertheless, the potential government revenues from the increased labour market activity are potentially greater than the direct subsidy cost of the deworming programme, suggesting that it is potentially Pareto improving. Taken in light of the evidence in the Cochrane review, though, I do not remain fully convinced of the benefits of the deworming programme.