The problem with Average Length of Stay

Back in the 1970s, before patient based data sets were available electronically,  a limited range of aggregate data was collated from paper forms collected by hospitals. There were were no separate provider organisations in those days. Hospitals were organised into 'Units' within District Health Authorities. Data was collected and analysed within Districts as well as submitted nationally to the NHS through a series of 'central returns'. Some detailed analysis was possible through the collection of samples, but the burden of producing this was quite onerous.

With ingenuity, some performance indicators were devised from the routine aggregate data. These included  'turnover interval' and  'average length of stay'. Both could be calculated from the routine aggregate data, such as occupied beds days, available bed days and number of discharges. They allowed comparison to be made between different hospitals, or changes in one hospital to be followed over time.

These measures were typically used at the level of  a whole hospital over a whole year. They worked reasonably well at this macro level. They also worked reasonably well for the typical pattern of healthcare delivery in the 1970s and 1980s

The pattern of hospital stays has changed a lot in the meantime. The number of beds has more than halved. And the number of admissions has risen. There is extensive use of day case admissions, particularly for surgery. The number of unplanned  admissions has risen, particularly for older people. In the past a period of convalescence after illness or surgery was seen as a good thing. These days stays in hospital are kept to a minimum both for health reasons -  and to free up precious beds.

Turnover interval is rarely talked about today. In contrast, average length of stay occurs extensively in both performance monitoring and planning. It seems to be an instantly attractive concept which is often misunderstood and misused.

The article highlights some important features that you need to understand if you are going to use average length of stay data.



Point 1: Spell Length of Stay is an Integer

Average length of stay is usually presented to at least one decimal place, often more e.g. 4.6 days, 4.63 days. This looks very precise. It hides the fact that, contrary to what some people conclude when they see it,  this is an average calculated entirely from integers. It is not the average of the actual lengths of stay. Every spell length is rounded up or down to a whole number of days. The average is then taken of these modified figures.

The reasons for this are historical. When it was first calculated, average length of stay was

          Total occupied bed days  

           divided by  

          Total deaths and discharges

This continued into the first electronic patient based data (Hospital Episodes Statistics - HES data) in which dates were collected but times were not. So the calculation of discharge date minus admission date also resulted in spell lengths that were integers

It would be possible nowadays to calculate spell lengths in hours, or even minutes. But the method has not been adjusted. So even though spell lengths now are predominantly short, we are continuing to work with a measure which has an inbuilt loss of precision, particularly for short spells.


Point 2: Midnights

It should be clear from the section above, that spell length basically means 'how many midnights was the patient in hospital for'. This can result in some serious distortion.

Imagine two hospital stays.

Stay One: the patient is admitted at 11:55 pm and is discharged ten minutes later at 00:05 am. In this case the spell length would be calculated as 1 day

Stay Two: the patient is admitted at 00:05 am and is discharged at 11:55 pm the same day. The hospital stay is ten minutes short of 24 hours. In this case the spell length would be calculated as 0 days

If we were to calculate spell length in minutes we would end up with
Stay One: 10 minutes
Stay Two: 1430 minutes

Stay Two is 143 times longer than Stay One, but the 'official' Spell Length of Stay comes out back to front with Stay One as one day and Stay Two as zero days.

The illustration above was obviously taken to the extremes to make the point. But this distortion is significant.

Point 3: Skew

When dealing with an even distribution pattern (the so-called 'normal' distribution) the average (arithmetic mean) works well in providing the 'typical' value. When dealing with a significantly skewed distribution, the mean is no use. Generally the median is better for skewed distributions. Even this becomes increasingly  limited if the amount of skew increases.

.

Excel provides a SKEW() function to allow an easy calculation of the extent of skew.

The rule of thumb used by statisticians is is where skewness is outside the range 1 to -1 then it is significantly skewed. So do not use the mean

The distribution pattern for LOS is heavily skewed. The following illustration uses some real LOS data for Emergency Admissions. The Skew is 5.3. The average of this data is shown by the red line:

Who in their right mind would think that the average,   as shown above,  is a meaningful or stable way to represent this heavily skewed distribution?

Average Length of Stay continues to be used widely in the NHS;  median rarely



Point 4: Bi-modal and Poly-modal distributions

If a service contains two or more distinct patient groups or treatment regimes which require  different times in hospital then it is quite likely that the frequency distribution will have more than one mode (or 'peak')

For these kinds of distribution, average is especially unsuitable.

The published information on PbR trim points (see below) shows that there are many different expected stay lengths within non-elective admissions.

A Google or journal search will find plenty of examples of  bimodal length of stay distributions

e.g. Baker et al (1996) Degree of burn, location of burn and length of hospital stay as predictors of psychosocial status and physical  functioning. J. Burn Care Rehabil 1996 Jul-Aug: 17(4): 327-33

e.g. https://www.nature.com/articles/pr1985688 which includes the quote:

 'When the distribution of length of stay is bimodal, as it is for the highest risk and smallest infants, then the geometric mean is a poor measure of central tendency.' 

Point 5: Average Length of Stay only looks at finished spells

We need a spell to end before we can count the spell length of stay. Average length of stay for any time period only includes spells which finish within that time period. The bed use in unfinished spells is not reflected in the calculation.


Point 6:  Average Length of Stay measures activity which is outside the period in question

It is probable that some spells ending in the period in question will have started before the period. The shorter the period being measured, the more likely this is. The shorter the period in question, the further away from it the start dates of some spells are likely to be i.e. the more the activity relates to a period other than that being reported in

Point 7:  Average Length of Stay becomes increasingly volatile as span is reduced

 Average length of stay may be a satisfactory measure for a whole hospital over a whole year. It works less well over smaller spans. The more the level of either service scope  or time span is reduced, the less effective the measure becomes.

Breaking down the view from whole hospitals down to to individual wards, or individual doctors, or breaking down the view by time (from years down to individual months or weeks) and so on makes the calculated values increasingly volatile. i.e. they jump wildly about or have periods of no data

Point 8: Stay Length depends on Day of Week


The number of days that a patient stays in hospital is affected by the day of the week they were admitted on.

Point 9: Length of Stay is treated differently in PbR

Payment by Results (PbR) is the NHS national payments framework established in 2006 and modified most years since.  PbR uses an 'adjusted' Length of Stay for Acute inpatient spells. In essence the adjustment removes critical care days from the overall length of the spell

Point 10: PbR Trim points

Trim points are the cut-off number of days stay for specific HRGs (Healthcare Resource Groups) above which additional money can be claimed. The trim point is calculated as

the upper quartile length of stay for that HRG
plus 1.5 times the inter-quartile range of length of stay

This slightly strange looking calculation is actually quite conventional, being the upper limit of a Tukey boxplot i.e. defining anything greater as outliers.

Two things to note are: 

(a) that this NHS standard calculation does not use average lengths of stay. When it comes to something as important as money, average length of stay is not regarded as a reliable measure

(b) that in the annually published PbR lists, the number of days set as 'trim point' varies widely between different non-elective HRGs. In the 2017-18 lists, the longest trim point is 399 days (for AA61B) and the shortest is 5 days (shared by large number of HRGs) ; the median is 17 days and the average (for what it is worth) is 27 days. 

Point 11: Average LOS includes deaths

Finished spells includes cases where the patient dies in hospital as well as cases where the patient is discharged. In other words it averages out over both ameliorating and deteriorating patient pathways

Point 12: DTOC

Stay lengths will be inflated by the extent of Delayed Transfer of Care (DTOC). This includes where the delays are not officially reportable. 

Point 13: Data Quality

Time recording may not be reliable. Sometime this will be blatantly obvious, such as when discharges of Endoscopy Day Cases are recorded at 2:30 am. Often it will not be immediately obvious from the data alone. The effect of data quality errors will tend to be to extend the apparent length of stays

Point 14: Planning using averages can be very dangerous




















Point 15: Beware of summary statistics in general

Anscombe's Quartet provides a vivid example of how identical summary statistics can be created from widely different patterns of data. Relying on the summary statistics could easily lead to misleading conclusions

Point 16: Spell length of stay depends on provider organisational structure

Imagine a patient pathway in which a person spends 10 days in an Acute Hospital and then moves on to a Community Hospital for a further 10 days before going home.

If these are two separate Trusts then there are two spells each with length two days

If they are part of the same trust then there is one spell with length twenty days

Imagine further than after 3 days in the acute Hospital spell the patient had to be transferred to a regional specialist hospital returning after 4 days. Assuming the Regional Hospital is run by a different Trust then we have two Acute Spells of three days. So potentially the patient with higher acuity will appear to be presented by average LOS of 3 days while the lower acuity patient might be seen as  being reflected by an average LOS of 10 days

Reports: management speak

The colloquial term ‘management speak’ refers to particular types of workplace language used to make things sound better than they really are. 

Often this involves a preference for long words, and for elongated expressions, which are intended to impress. This includes the insertion of unnecessary adjectives and the use of nouns as verbs. There is a preponderance of metaphors, many based on sport or travel. 

Another facet is using phrases which really say the opposite of what they first appear to (such as “with the greatest respect” or “I am absolutely clear… “ or  “we’re going to have to let you go”). Fashions can be recognised, with new phrases sometimes gaining circulation quickly.

Designating something as ‘management speak’ is usually derogatory. In the same way that ‘tourists’ are all the other people visiting a place, it is probably something that we more readily recognise in others than we do in ourselves.

The following list is a collection of phrases that often appear in  21^st century management speak. Amongst these are some ‘buzzwords’ (in italics) dating back to at least the 1990s [see note 1] , many still in active use:

Accountable – acid test - action that – added value – ad hoc report - admin footprint – agenda - agile – align - analysis paralysis – analytics – arena - armchair economics – asset-stripping – attrition – on the back foot - back-office function – back to basics – balanced scorecard – ballpark - get the ball rolling – have enough bandwidth – bean counter – bed in – get into bed with  -  bells and whistles – belly-up - benchmarking – benefits realisation - best fit - best of breed - big bang – big data - big guns - bite the bullet – black box – blip – bloodletting - blue sky planning – body count – body language – bolt hole – under the bonnet - outside the box - bottleneck – bottom feeder – bottom line – bottom out – bottom up - brainstorming  – broad brush - bug – burn out – business-as-usual - business intelligence – business planning - executive buy-in – buy into -  can-do attitude – capacity - capture - career-limiting – cascaded - cash cow – centralise – introduce some challenge - product champion – change agent – change management - change resistance – charisma – cherry pick - chemistry – clock watching - clone – close of play - cold call – comfort zone -  commencement - committed - comms - communication skills – competencies - comprises of - connect with - conventional wisdom – cooking on gas - core business – cost envelope - cost improvement - crisis management - critical mass – culture change - curved ball - customer-focus -  cutting edge – dead in the water - de-centralise – deep dive - deep pockets – deliver  - deliverables – diarise - done deal – dovetail - download – downsize – downstream – downtime – drill-down - drip-feeding  - driver - drop the ball - early adopters - ecosystem - embedded – empower  - engineer - enterprise level – pushing the envelope - excellence – exception reporting - executive buy-in - executive information system - exit interview - facilitate – factor in -fast track – feedback loop - finger on the pulse – fire wall – first cut - fit for purpose – flag up - flat structure – flavour of the month - floor-walker -  focus group - food chain – footfall – frame - front-of-house – future-proofing – game-plan - gap analysis - gardening leave – gatekeeper - generic solution – the get go – glass ceiling – glitch – go with the flow - going forward – golden bullet – golden handshake – governance - granularity – gravitas -  have a handle on - hands-on – hardball – hatchet-man – head up – heads up - headcount - headhunted - headroom -  health economy - heavy hitter - helicopter vision -  hidden agenda – high flyer – hit the ground running - hook - holistic – horizon scanning - hot desk - human resources - first hundred days - idiot proof -  incentivise – implement – indicators - infographic - input – intellectual property – the journey - when he says jump you ask how high  – jumpstart – key player – kick into the long grass -  kick into touch -  kick-start – knowledge engineering – knowledge management – KPI -  leadership - learning curve – learning organisation - left brain – left field -  got legs – legwork – let go -  level playing field – leverage – litmus test - local difficulties - logistics  – in the loop – out of the loop - loss leader - low hanging fruit – mail shot – management by exception – management by wandering about – management-free zone - management material – map out - market testing – massaging the figures – matrix management - mentoring – off message – on  message – methodologies - metrics - mind-set  - mission critical – mission statement – modus operandi - motivational - movers and shakers -  multi-tasking - mushroom management – mystery shopper -  narrative - gone native - natural wastage - nerd – networking – niche – no-brainer – non-starter – number-crunching – talk offline – on board - ongoing - onion skin - open door – opportunity - outsourcing - parachute in -  paperless - paper-light – paradigm – park an issue – partners - passenger – passionate – performance culture – planning blight - keep all the plates spinning – play back - player – poaching – poison chalice – the pond - positive spin – be in possession of -  prioritise – privatise – pump-priming - quality circles – quantum - quick and dirty - quick fix – on my radar – under the radar – raft - RAG rating - ratchet – read my lips – real world – reality check – reconfiguration -  rehearse - re-inventing the wheel – restructuring - results -driven – revenue neutral  - reverse engineering  - right brain – risk averse – roadmap - on a roll -  rollout – run an idea by – run with - scapegoating – scatter gun approach - scenario – not particularly scientific - to scope -  scope creep – screaming for it - self-starter – sex up – shared vision - short-termism – show-stopper – sideways pass – signed up to - singing from the same hymn sheet - smart card – SMART objectives - smell the coffee - soft option – I want solutions not problems - sound bite - Spanish working practices – up to speed - spider organisation -  square one – square pegs in round holes - square the circle -   stakeholder - stalking horse – standalone – standard operating procedure (SOP) - give (or take) a steer – stitch up - strategic level – success regime -  succession planning - the suits  -  sweat an asset – SWOT analysis  - synergy – system-wide – to task – task-and-finish group- team player – tease out - techie - teething problems – telephone numbers – third sector - top-down – touch base - track record – traffic lights - trajectory – transformational - transparency - throwing money at – unpack - up and running – upstairs - upstream – value added - plain vanilla – vapourware – vertical structure –vis-a-vis -  our vision - walk the job – wannabe – war chest – weasel words -what-if scenario -  whistle-blower – whole system - wiggle room – find a window  - window of opportunity - win-win - workaholic – workaround - work-life balance  - world class - WYSIWYG

The Plain English Campaign once noted that 

“Management-speak and goobledegook are still rife in NHS documents. Poor communications still baffle patients and waste huge amounts of taxpayers’ money”  [see note 2]

Conscious or not, management speak is a step away from plain English. Some guidance on plain English is presented in a separate article (see link). Using the vocabulary of management speak is not always wrong. Some phrases and metaphors can be very effective, if used sparingly.

But overuse of ‘management speak’ is a warning sign. It may signify a person for whom the desire to impress has overtaken the desire to communicate [see note 3]. 

Worse, it may signify either a desire to hide the real meaning in a bed of platitudes and waffle, or even  “… a mixture of vagueness and sheer incompetence” [see note 4]

A manager, being asked about the progress of a piece of work he has not started yet, could respond in two contrasting ways:

Direct response:		‘Management speak’ response:
“I have not started it yet.  I intend to complete it within the next two weeks”		“As of now I am concluding the option-appraisal stage and steps to commence transition to the implementation phase are in hand. I am strongly committed to the success of this objective and am optimistic that imminently I will be in a position to report significant progress”

Which would you prefer to hear?

Note 1

Michael Johnson. Business Buzzwords: The Tough New Jargon of Modern Business. Basil Blackwell. 1990

Note 2

Chrissie Maher. Plain English Campaign Cited by B.Friend (1998) Calling a bed a bed HSJ 108 (5594);31-3 in turn cited by S .Carr. Tackling NHS Jargon. Getting the message across. Radcliffe Medical Press.2002

Note 3

http://www.healthpolicyinsight.com/?q=node/1528

Note 4

George Orwell. Politics and the English Language (1946) 

He went on "…prose consists less and less of words chosen for the sake of their meaning, and more of phrases tacked together like the sections of a prefabricated hen-house."

http://www.orwell.ru/library/essays/politics/english/e_polit/

Reports: plain English

Since 1979, the Plain English Campaign [see note 1] has been

“… campaigning against gobbledygook, jargon and misleading public information”

This is not new. In 1906, H.W. and F.G. Fowler [see note 2] suggested that

"Anyone who wishes to become a good writer should endeavour, before he allows himself to be tempted by the more showy qualities, to be direct, simple, brief, vigorous and lucid."

Their recommendations for writing (in what would later be called 'plain English') were: 

Prefer the familiar word to the far fetched. Prefer the concrete word to the abstract. Prefer the single word to the circumlocution. Prefer the short word to the long. Prefer the Saxon word to the Romance.

In 1946, George Orwell [see note 3] produced the following advice:

i.	Never use a metaphor, simile or other figure of speech which you are used to seeing in print.
ii.	Never use a long word where a short one will do.
iii.	If it possible to cut a word out, always cut it out.
iv.	Never use the passive where you can use the active.
v.	Never use a foreign phrase, a scientific word or a jargon word if you can think of an everyday English equivalent.
vi.	Break any of these rules sooner than say anything outright barbarous

A civil servant, Sir Ernest Gowers, was invited to produce a guide for improving ‘official’ English. An immediate success, it was published in 1948 as ‘Plain Words: A Guide to the Use of English‘. Extended and revised, this has been in print ever since [see note 4]. Gowers’s advice, similar to Orwell’s, was:

Use no more words than are necessary to express your meaning, for if you use more you are likely to obscure it and tire your reader. Use familiar words rather than the far fetched, if they express your meaning equally well; for the familiar are more likely to be readily understood. Use words with a precise meaning, rather than those that are vague, for the precise will obviously serve better to make your meaning clear.

Some people think that ‘plain English’ stunts creativity and produces sterile results. This is not automatically so.  But there is a risk that over-simplification can lose meaning just as easily as over-complication can hide it.  

When writing a report, the analyst needs to strike a balance. A report needs to communicate effectively. It does not need to compete with the great works of poetry or literature.

Note 1

http://www.plainenglish.co.uk/about-us.html

Note 2

The King's English (1906), https://archive.org/details/kingsenglish00fowlrich

Note 3

George Orwell. Politics and the English Language.1946.

http://www.orwell.ru/library/essays/politics/english/e_polit/

Note 4

Gowers, Ernest (1948). Plain Words: A Guide to the Use of English. HMSO

Gowers, Ernest (1951). ABC of Plain Words. HMSO

Gowers, Ernest (1954). The Complete Plain Words. HMSO

Gowers, Ernest, Rebecca Gowers (2014). Plain Words.  Particular,  (Penguin). ISBN 0141975539.

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Healthcare Analysis: what is it?

The role of analyst can be set out in contrasting ways. The word ‘Analyst’ now occurs in many different job titles. Arguably, it has become over-used and is starting to lose its meaning [see note 1]. Many other jobs also involve analysis, without having the word ‘Analyst’ made explicit.

There are fashions in job titles. Organisations are influenced by the choices of their peers. Job titles appear, become ubiquitous, are gradually eclipsed by newer styles, and eventually die out.  The activities carried out seem to be more persistent than the titles under which they are performed.

The table below is a snapshot showing the numbers of jobs being advertised simultaneously on the NHS jobs website [see note 2].

Job title type	Band 3	Band 4	Band 5	Band 6	Band 7	Total
Information Analyst	1		9	15	3	28
Data Analyst			2	4	1	7
Performance Analyst		2		1	1	4
Business Analyst				1	3	4
Business Intelligence Analyst			3	4	1	8
Systems Analyst					2	2
Finance Analyst				2	1	3
Application Support Analyst			2	2		4
IT Service Desk Analyst	1	4	4			9
Technical Analyst			1	2	4	7
Business Change Analyst			2			2
Miscellaneous others			4	8	4	16
Total	2	6	27	39	20	94

Clearly, at present, there are a lot of ‘Analyst’ jobs on offer. The levels of seniority vary.

How clearly differentiated are these differently styled roles? The main focus of each is suggested by the job title, but there are areas of overlap.

One way to look at this is to visualise work activities as relating to one or more of the following ‘layers’:

Layer	Involves
Communication	Deciding how things will be portrayed; creating and issuing publicity material
Decision	Senior managers deciding what to do
Planning	Trying to predict the future and determining what will be needed
Monitoring	Looking at how well the organisation is performing against any targets and standards; looking at peer organisations
Measuring	Measuring volumes of activity; trying to understand why things are changing; responding to queries; using reporting tools
Process	Understanding what the organisation does; doing it; documenting and training; devising contingency plans; changing ways of working
Data	Collecting and recording data; data quality and data standards; record keeping
Specialist applications	Determining requirements; assessing products; working with system suppliers; creating applications; implementing and maintaining new systems; training; resolving issues
General IT infrastructure	Configuring and maintaining hardware (servers, routers, network cabling, desktop PCs, printers etc) and software (email, office software, intranets etc); managing user accounts, licensing, upgrades; training and support
Supplies	Managing flows of routine and ad hoc purchases; logistics and storage, stock control; value for money
Buildings	Maintaining the condition of buildings; signposting; car parking; new buildings; site security

The following diagram illustrates the main areas of focus for various stylings of ‘Analyst’ in terms of the ‘layer’ model above:

A ‘Healthcare Analyst’ could be more-or-less any of these, excepting perhaps the more general IT roles. An understanding of the techniques used across all these roles helps select the right approach, or indeed the right person, to tackle any new problem.

It may intuitively feel that ‘Healthcare Analysis’ is rooted in numbers and graphs. This will certainly be a major focus for many, probably the majority of, analysts. But at its simplest, 'Heathcare Analysis' can be defined as the detailed study of selected aspects of healthcare.  ‘Healthcare Research’ could be similarly defined. Indeed, there are many common elements. The essential difference is that ‘Analyst’ roles are mainly intended to support management decisions while ‘Research’ is intended discover new things.

Through an analyst’s eye, healthcare appears a highly complex system of interactions between people with health issues and people offering health solutions.

People with health issues will generally be interacting as individuals. People providing healthcare will generally be acting as part of an organisation. There are exceptions to these generalisations, such as sole practitioners or family therapy. 

Some health issues persist for years. People with multiple health issues may be interacting with multiple health organisations simultaneously.

There are many mechanisms for providing and funding healthcare. Four different national models are shown in the following table [see note 3]:

Model	How it works	Example
The Beverage Model	Single payer national health service	UK
The Bismark Model	Social insurance or not-for-profit sickness funds	Germany
The National Health Insurance Model	Single payer national health insurance	Canada, Taiwan
The Out-of-Pocket Model	Market-driven	Third World

Even within a single country, things can change regularly.  Funding mechanisms impact significantly on the way healthcare is planned, commissioned, delivered and measured. This in turn shapes the focus for analysis and the nature and quality of the information available to support it.

Healthcare managers face a bewildering variety of issues on a daily basis. Much energy is spent trying to balance imbalances of capacity and demand. Much time too is spent wrestling with targets which have generally been set by people from outside their organisations.

Healthcare analysts face a bewildering variety of issues too. Much energy is spent trying to provide healthcare managers with clear explanations of why, or even whether, particular patient flows are speeding up or slowing down.

Although the nature of health problems and healthcare solutions varies enormously, the range of conceptual models and approaches is a lot more compact. Ideas drawn from one area can very often be applied to many other situations. 

Indeed, it is the ability to detect and properly understand patterns which defines a good analyst.

Note 1

Its general meaning can be quite wide ranging “someone whose job is to  study or examine something in detail" . Cambridge Dictionary (see link)

Note 2
Data from the NHS Jobs website (see link) sampled on 22/01/2016. Words denoting hierarchical rank, such as ‘Assistant’, ‘Senior, ‘Principal’ etc. have been removed; so have pointers to more specific subject areas. Bandings are from the NHS Agenda for Change system. Several jobs relating to Public Health information were omitted as they were aligned to a different pay structure

Note 3
This simplified model is used widely
http://www.pnhp.org/single_payer_resources/health_care_systems_four_basic_models.php
http://www.annfammed.org/content/11/1/84.1.full
http://www.pbs.org/wgbh/pages/frontline/sickaroundtheworld/countries/models.html

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