This is it – a leap from the descriptive to the inferential. We are leaving the comfort of the sample we have collected data on and we’re about to make a statement that relates to the world beyond: we are inferring stuff.

Annoyingly, this first step is a phrase disturbingly close to another. The ‘standard error of the mean’ (aka ‘standard error’) is an number we can use to estimate how the mean of our sample relates to the mean of the population at large. In order to keep it clearly different in my mind than ‘standard deviation‘ I tend to think of it as ’standard error of the mean’ and not  just ‘standard error’.

If we measure the height of all 25 children in Year 1 at one Yorkshire primary school, we’ll have an average height and we’ll have the spread of this data:

mean (x) = 103cm

standard deviation (σ) = 4cm

We can use this data to infer that the average height of all Year 1 kids in Yorkshire by calculating the standard error

standard error of the mean = standard deviation / square-root number of items (people) = σ / √n

standard error of the mean = 4 / √(25)

standard error of the mean = 4/5 = 0.8cm

… and estimating the 95% confidence interval using

limits = mean +/- 2*standard error of the mean

So the mean height in Yorkshire Year 1 primary children is 95% likely to be between 101.4cm and 104.6cm.

Using this approach will allow us to start making judgements about how the data we have may compare to other things, and if those comparisons are likely to be due to chance … in the next set of blogs.

In undertaking this estimate, we’re assuming that the primary school picked is representative of the population at large, that the measurements were accurate and that there was no systematic bias, for example either locking the smallest children in cupboards or making tall ones go into Year 2 classes. If any of these heinous offences have been committed then, quite apart from the investigations by police/GMC/Ofsted etc, we won’t be able to reaonsbly make inferences from the data. This is the same for real data too – which is why is is SO IMPORTANT to critically appraise the methods of the study for bias before tacking the ‘hard stuff’ in the numbers: as many folk have said, “you can’t polish a poo”.

- Archi

This month saw the start of #ADC_JC – the Archives of Disease in Childhood twitter journal club.  The aim was to engage paediatric health professionals in social media and discuss a journal paper on twitter in real time.

And it was a success.

We discussed Gill et al’s paper about increasing paediatric admission via Emergency Departments.  Around 40 people contributed to the discussion, which took place over an hour – these were not confined to Brits, but even included some Aussies who were enthused enough to get up at 5am.  And one of the authors of the paper was involved in the discussion too.

The twitter chat was dynamic and exciting.  As well as critical appraisal of the actual paper, we went on to look at ways of improving our practice by dealing with the rise in paediatric emergency admissions.

We are aiming to run the #ADC_JC once a month (follow @ADC_JC for updates) and hope to engage some of the ‘lurkers’ next time too.

The storify summary of #ADC_JC can be found here.

We have – in this microseries of miniblogs – looked at data distributions and describing what we’ve got. We’re ready for the big leap now; from description into inference. What can we say about how our data relate to the world at large? And the first thing to do is to clarify a deeply unhelpful term.

Parametric.

It just means statistical tests  because “my data is Normal“. (And if you’ve done a transformation  to make it Normal, you can use these transformed data with parametric stats.)

Now, can you guess what non-parametric means?

Hurray! It means statistical tests for when ”my data is non-Normal”. That might be skewed continuous stuff, or categorical data like dead/alive counts.

Glad we’ve cleared that up. We’ll be onto bootstrapped estimates of regression covariates before you can slip a 24G in a neonate …

- Archi

Exclusive breastfeeding is regarded by WHO and by most, if not all, paediatric academies, as the ideal for newborns and infants up to 6 months old. It is also recommended that breastfeeding begins as soon as possible after birth. That is why the small pilot study by Flaherman et al is both interesting and controversial.

Researchers randomised exclusively breastfed term newborns that had had 5%-10% weight loss before 36 hours, and were 24-48 hours old at time of recruitment, into two groups: The intervention group was syringe fed 10 ml of an extensively hydrolysed formula after each breastfeeding until mature milk production began; the control group was exclusively breastfed. Both groups were similar. Allocation was concealed. Blinding of parents and researchers was not possible, but the person who assessed outcomes was not aware of the assigned intervention.

The findings are interesting. It seems that infants in the early limited formula group had better outcomes. At 1 week, 2 of 20 infants in the intervention group had received formula in the preceding 24 hours, compared with 9 of 19 in the exclusive breastfeeding control group (risk difference 37%, 95%CI 3.4% to 71.0%). Also, infants in the control group received more formula than the intervention group during that first week. At 3 months, 15 of 19 infants in the intervention group were exclusively breastfed compared to 8 of 19 infants in the control group (risk difference -36.8%, 95%CI -65.6% to -8,1%, calculated from data in the article).

There are a few caveats, though. First, why use an extensively hydrolysed formula in the intervention group? Is it because the authors and/or the patients feel it is ‘less allergenic’ so it would be less likely to harm? Also, one of the authors has been employed by formula companies before. Should we be suspicious? Second, it is surprising that less infants from the control group, who began as exclusively breastfed, were exclusively breastfed at 3 months. Why? Maybe mums who feel they have failed their babies give up more. Researchers and trainers could not be blinded, so maybe there was a difference in how they treated or motivated each group. Lastly, the results, while statistically significant, are imprecise. Confidence intervals are very wide.

So, should be change practice and encourage mothers to give a little bit of formula while mature milk is produced? No. Maybe it won’t hurt, but this paper certainly doesn’t show that it helps. The findings of this study need to be replicated in a larger trial, preferably with independent funding and no conflicts of interest.

The 12^th June 2013 8-9pm (UK time) will be Archives of  Disease in Childhood’s first twitter journal club.  We will be discussing the following paper by Gill et al, which can be accessed online. @ADC_JC #ADC_JC

The twitter journal club will be facilitated by Tessa Davis, who is a paediatric registrar currently on Out-Of-Programme Time in Sydney Children’s Hospital.  (Follow her on twitter @tessardavis as well!)

Erm, I don’t know how to use twitter….?

Don’t worry, it’s pretty straightforward to get started.  I’ve put together three short screencasts about how to get set up – the first Twitter Basics tutorial is here: http://lifeinthefastlane.com/2013/03/techtutes-tuesday-001/

What is a twitter journal club?

In many ways, it’s just like a regular journal club – people get together and discuss a journal articles critically appraise it; and look at the conclusions and lessons we can learn.  The difference is that this will be done on twitter, so it doesn’t matter where in the world you are, you can join in.

How does it work?

The chat will be from 8-9pm (UK time).  During this time, any twitter journal club posts should include the hashtag #ADC_JC (i.e. write that hashtag in your post).

Follow the hashtag #ADC_JC and you can keep track of all the posts and the discussion points as they happen.  A simple way of doing this is using tweetchat.com (an easy-to-use website where you type in your hashtag #ADC_JC and it will show you the feed of posts).  Any post you write in tweetchat automatically includes that hashtag.

Follow the twitter account @ADC_JC.  I will be moderating from this account and also it will be used to let you know about the discussion summary and the next journal club time.

What does the moderator do?

I will be keeping the conversation going and making sure we stay on track.  There will be a few discussion points to focus the chat during the hour.

What happens afterwards?

We will collate all the comments and post them so others can read them afterwards.

Who can join in?

Anyone can join in – that’s the beauty of twitter!

Will it work?

We hope so!  It’s the first paediatric twitter journal club (that we’re aware of) so will be exciting to get it off the ground.  Join in the discussion!

- Tessa Davis

In the next of our guest blog posts, paediatric mental health expert @MaxDavie has leapt into a discussion of one of the Archive’s recent editors choice articles, “Depression in paediatric chronic fatigue syndrome“.

While I don’t have a huge feel for the CFS/ME market, being largely responsible for anthracyline induced cardiotoxicity and ifosphamide tubulopathies, I do have a range of patients with co-existent “physical” and “mental” disorders, and it’s certainly worth a read. Feel free to add your comments below or argue away on Twitter.

Max also blogs here, so pop and visit too.

This useful cross-sectional study tells us that there is a significant increase in rates depression in CFS, compared to the general population, to 29%. The magnitude of this increase is stated by the authors as ten-fold, but for several reasons it is hard to be precise about this:

Firstly, they did not have a control population assessed in the same way as their CFS population, and so comparison is made with other study results.

Secondly, their population was assessed for depression by questionnaire, rather than clinical assessments, and this may have had the effect of exaggerating the disparity when compared to other studies, as there is obvious symptom overlap between CFS and depression.

Finally, this study was done on a population attending a specialist centre, who would tend to be at the more severe end of the CFS spectrum, and so perhaps more likely to be depressed.

All of these factors may lead to an exaggerated increase in prevalence. Nonetheless, there is clearly a very large amount of depression in the CFS population, and this is not in itself a great surprise. However, this study does offer tantalising clues to the following interesting question of causation:

Is the depression as a result of the CFS, is the CFS as a result of premorbid depression, or are both due to a common neurocognitive vulnerability? There will obviously be a bit of all three, but…

• Depression was associated with severity but not length of disease, which suggests the depression is not solely caused by the chronically wearing experience of CFS.

• Notwithstanding the above, the degree of increase in depression is greater than studies examining pre-morbid mental health problems in CFS have found (e.g. Rangel at al 2003), so pre-morbid depression is unlikely to explain all of this increase.

• The finding of correlation with severity but not duration of CFS is consistent with the idea of a neurocognitive vulnerability underpinning the severity of both depression and CFS. This is an idea with interesting research implications, and is another blow against the unhelpful mind/body dichotomy that often rears its head around CFS.

So, what are the implications for the DGH paediatrician struggling with a CFS caseload?:

1. Do not embark on treating CFS without decent support from mental health services

2. Screen for depression when making an assessment for CFS

3. Treat the young person as a whole, not as physically and, separately, mentally unwell.

There are a host of things in the world that undergo transformations. These are often physical, emotional, psychological and spiritual. But numbers need love too, and we are getting to know that deep, deep down, we all love Normality.

The two curves below are clearly not Normal. They are heavily skewed, looking not like bells but battered teardrops or the smeary blobby bits on a marrow slide that haematologists claim to be able to diagnose leukaemia with.

Transformation – doing a simple mathematical alteration of the numbers – can take these and make them beautiful.

The first takes the natural logarithm of the number, to come up with the bell shape. This is known as a ‘log transformation’ and the (original) data are said to have a log-Normal distribution.

The second takes the reciprocal of the number, again to rectify the ugly shape. This too is a ‘transformation’

There are a few very simple transformations that could be examined to see if they make data Normal, and if so, you can use this more powerfully than nonNormal data in doing stats tests. So when you get nonNormal data, try these transformations and see if they make your numbers more lovable:

1/number-squared

1/number

1/square-root

log

square-root

square

You may well then feel transformed.

- Archi

 Can you spot anything wrong with this graph?

It’s from a paper in a major paediatric journal.  I’ve removed it from context, because for me it was a helpful lesson in spotting something important.  I’ve removed the labelling from the X axis, because I’m going to be a bit unkind about the paper, but in short it compares three different risk behaviours – the hatched box is the main behaviour (for example, cycling), and then the clear and black white boxes represent mutually exclusive subsets of that behaviour (for example, wearing lycra and not wearing lycra).  Then the three different clusters represent three possible outcomes, so the first group might be being struck by a car, the second might be caffeine consumption, and so on.)

What happened was this.  The person who was supposed to be teaching us didn’t turn up, and so I led a short “hot journal club” session instead.  I recalled an interesting paper that I’d read, printed out a couple of copies, pulled up on the projector one of a series of templates I’ve got from the JAMA series of old on how to read a paper, and we began to discuss the paper.

The graph above came under scrutiny after we’d got quite a way along; we were trying to answer the question:  ”What measures of occurrence were reported”.

The more we looked at this graph, the more we could understand what it was that the authors wanted us to see, but the less we could understand why it was that it had been allowed.

Traditionally we’re used to seeing odds ratios presented on the X axis of a graph, as in a classic forest plot.  (If you want to know a bit more about relative vs absolute measures, have a look at a previous post.) The ratio is presented as a dot, and then the confidence interval is presented as whiskers.  An example of this would be here:

Obviously this compares different trials, as part of a meta-analysis.  But what the authors are doing in our original paper is comparing different outcomes for three different risk factors, so it’s not an unfair wish to have things presented similarly, is it?

But is this mere pedantry – am I annoyed about the axes being flipped?  Only insofar as it takes a minute or two to spot what else they’ve done.  They’ve presented this so that it looks like a simple, old fashioned histogram.  Visually, the reader finds him or herself scanning for the least amount of black and inferring that the less black there is, the “better” the test.  But simple consideration of what the shaded areas mean reveals that this is highly arbitrary shading.  The histogram seems to be rooted at zero.  What does this mean?  It means absolutely no risk.  Is this implied at all in the data?  No it isn’t.  Put this another way; it would be equally arbitrary - or equally valid – to invert the risk – have it as a relative protection rather than relative risk.  If this were so, we’d see these columns going upwards to infinity; you get perfect protection from the intervention.

I can’t understand why they’ve presented this day like this, and why the editorial and peer review process has allowed it.  I can only come up with two possible explanations.   The first is that they didn’t understand the stats and were excited by a nice graph which showed the data in a positive light.  The second is that they were intentionally spinning their presentation of their data to persuade people that it was more positive than it actually is.  Either way, it’s pretty disappointing for a paper which provoked enough interest to get mentioned on a number of feed services.  

Now you now know you continuous data can be Normal or not Normal (but we might be able to tweak that … see the next post) and we’d like to be able to describe it clearly and accurately.

We could just reproduce every bit, but we really want to compress it to get the meat & meaning across.

For Normal data we need just two values; where the centre of the curve is and how flattened out the bell is. These values are the mean (arithmetic average; greek mu: μ) and the standard deviation (the spread; greek sigma: σ).

Note well – this is standard DEVIATION not standard ERROR – we’ll get there another time.

EDIT: As pointed out by @DamianRoland, this might be a bit cryptic at first read. So here below is an interactive version of how  mean and standard deviation affects the curve shape: The Normal Distribution from the Wolfram Demonstrations Project by Gary H. McClelland

For non-Normal data, we’re a bit more stuck. We still want to say the same stuff, but recognising that the mean & SD don’t cut the mustard. For these data, we still want to know where the centre is, so we tend to use the point where, if all lined up in size order, the middle value would fall. This is the median.

We also want to know it’s spread. So we may use the range: give the minimum and maximum. Or the interquartile range: the values in the size-order line where one quarter of the items (25%ile) , and three-quarters of them (75%ile) lie. Or as in the picture below, the 1st-9th decile spread.

In these simple ways we can give ‘a measure of central tendency’ (mean or median) and ‘an estimate of variability’ (SD or range-based figure) and let folk know what the data look like.

- Archi

I’ve written previously about how doctors should refer to each other, and also about how patients and their families might refer to doctors.  It reminded me that there are ways that people need doctors to be – to behave, dress, talk – in order to get the best out of a professional relationship.

In the UK, the GMC are very clear about this – that the way that we behave as members of a profession contribute to the way that the whole of the profession is perceived.  There has been some grumbling about the application of this to social media.  To be fair to both sides, the advice does look a little heavy handed, although the GMC has been quick to point out that the advice uses the word “should” which is different from when it says “must”, and is only expecting doctors who identify as doctors to behave as doctors…

But back to an earlier point.  If I’m sitting here in shirt sleeves rolled up, and with no tie on, and not even calling myself doctor then how do I develop a therapeutic relationship where patients and their families get something out of the fact that I am actually a doctor?

Terry Pratchett has had a long career of smuggling important concepts into young – and not so young – minds by means of sharp humour and, well, stories involving witches and wizards.  There’s a scene – and I apologise if I’m miss-remembering it – I’m sure a fellow geek will correct me – where a wizard is asked why he wears a hat with the letter W on it.  The reason is, because he is a wizard.  That sounds a bit trite, but it’s a helpful thought.  He’s saying:  The things that I do make me what I am able to do.  So, what things to I do?  Medical students, friends and colleagues might be able to come up with a few more, but off the top of my head I have the following things that make me a doctor in the doctor patient relationship.

1. I’m clean and well presented.  Well, sort of. 
2. I have a stethoscope around my neck.  If I were being unkind, I’d see this as the equivalent of wearing my shirt open with a medallion on display.
3. I’m polite and attentive
4. I write with a fountain pen.
5. I use slightly archaic language.  So, I will say “Ghastly” – and might be one of the last people to use this word – to give the impression that I’m slightly other-worldly.
6. I’m daft with children when it makes sense to be, but only in a way in which they will know that I’m playing.
7. I ritually wash my hands.
8. I perform an examination.  I use the word perform here for a very particular reason.
9. I sit in a hospital, and behind a brand, which means something to those who access it.  There is more than a little bit of the pilgrimage in a visit to the hospital.

There are probably 101 others, but those are all I can think of for the moment.

Do you have things you do which make people understand, and gain from, the fact that you’re the doctor?