Monday, 30 April 2012

Mayor of London

With just 3 days to the election, former Labour Party and GMB union man Dan Hodges becomes the latest Labour Party supporter to come out against Ken Livingstone, in fact he is urging Labour supporters to vote for Boris:

"That’s why on Thursday I’ll be casting my vote for Boris Johnson. I’ll be supporting my local Labour GLA candidate Len Duvall, and voting Labour in the top-up. But I’ll also be voting against Labour’s mayoral candidate, and I hope he loses."

 And here's why: 

"Forget the number of cycle lanes or who attends how many meetings of the Mayor’s office on crime. The number one responsibility of the Mayor is to unify our capital, and give a voice to all of its citizens. And there is a single, absolute, uncontestable truth known to anyone who has worked with Ken Livingstone, written about Ken Livingstone, observed Ken Livingstone or spent more than five minutes in a room with Ken Livingstone. Ken Livingstone is one of the most crudely divisive figures in British politics.

And there is another truth that has emerged over this campaign, one which Labour activists cannot stomach, but which needs to be faced all the same. The candidate who has come closest, at a time of renewed political polarization, to being a unifying figure is Boris Johnson. As Labour’s own campaign coordinator Tom Watson admitted last week, “there are a number of people who tell us on the doorstep that they would vote Labour if there was a general election tomorrow but are currently considering voting Conservative because they either a) like Boris Johnson or b) don’t like Ken”.
Unpalatable though it may be, it’s the Blue rosette-wearing, Bullingdon-baiting posh boy who is reaching out across party lines. It is Boris Johnson who is defying the laws of political gravity, and is now favourite – thanks to the support of hundreds of thousands of Labour voters – to prevail on Thursday. And it’s Ken Livingstone, self-styled man of the people, who has become so unpopular with those supporters that he has had to remove his name and photo from his own campaign leaflets.
No more excuses, and turning of blind eyes, and resigned shrugs about “Ken just being Ken”. London needs someone who can speak for all of London, not just the balkanized segments whose votes he craves. If that guy happens to be a Tory, or a Martian, it doesn’t bother me. I’m obviously not quite as tribal as I thought I was.
We’ve held our noses and voted for Ken again and again and again. Not this time. On Thursday hold your nose, and vote for Boris Johnson."

Meanwhile, despite promising a month ago to clean up his act and campaign "on the issues that matter to Londoners", this morning Ken's campaign is putting out a photoshopped image of Boris, Cameron and Osborne looking like blue space slugs. That is actually Ken's campaign message in the final week: "Vote for the red newt not the blue slug!". And this man would be Mayor of London?

Vote Boris on Thursday.

Friday, 27 April 2012

Europe's Embarrassing Problem

No, not the Euro, the other one - measles.

"While every country in the Americas, including its poorest, wiped measles off the map in 2002, Europe has been unable to do so. Cases have quadrupled since 2009, and the reemergence has become a threat to other countries. In 2011, the United States had 222 cases, the highest number since 1996, and most importations come from Europe."

So says Kai Kupferschmidt in the latest Science magazine.

Notice that the USA is concerned about a rise in cases to 222 in 2011, whereas Europe had 26,074 cases just from January to October 2011. Even worse, Kai points out that:

"Measles' stubborn persistence in Europe would also be a stumbling block in any plan to eradicate the disease globally."


Here in the UK we were well on our way to eradicating measles thanks to the MMR vaccine introduced in 1988 and the MR catch-up campaign in 1994, as this graph from the Department of Health shows:

"MR campaign" was the measles and rubella catch-up vaccination campaign run in 1994 to vaccinate 5-16 year olds who missed the MMR vaccine which didn't exist when they were babies. The yellow line (using the scale on the right) shows the percentage of population vaccinated against measles.

Three things jump out from this graph.

  1. MMR vaccine is amazing, it came close to stamping out measles in this country.
  2. MMR is better than single measles vaccine. There's no conspiracy theory here.
  3. Andrew Wakefield published his discredited lies about MMR and autism in 1998, watch the yellow line nosedive. Way to go Dr Andrew *slow hand clap*
You hear a lot of rose-tinted claptrap from adults about childhood diseases, "measles didn't do us any harm when we were kids", but the people who say that are the ones who didn't die from it. Survivor bias. 

In 1988, the year that MMR was introduced in the UK, 16 people died of measles. Between the start of the measles vaccination in the late 1960s and the MMR vaccine arriving in 1988 the UK typically saw between 10 and 20 measles deaths every year. If you're one of my old school friends born in 1977 or 1978, those years saw 23 and 20 measles deaths respectively. That was everyday life before MMR.

Before the single measles vaccine it was even worse: seeing 50-100 measles deaths in one year was quite normal, and a bad year such as 1961, 1963 or 1965 over 100 were killed by measles. Back in the 1950s it was worse still: the year my dad was born, 1950, there were 221 measles deaths followed by another 317 in 1951. The majority of all these measles deaths were children, of course.

It's little surprise that people hailed the measles vaccine in the 1960s and then the MMR vaccine in the 1980s as a wonder, and why there was a big push to get older children caught up with the MMR vaccine once people had seen just how effective it was. In the UK alone, thousands of deaths and millions of cases of measles have been avoided thanks to measles and MMR vaccination programmes.

More recently, there's been a huge worldwide effort to cut measles deaths through vaccination. Around half a million people died from measles in 2000, but ten years of effort to vaccinate brought that down to 140,000 in 2010. Most of these remaining deaths are in India and parts of Africa where vaccination levels remain low. It's hard to think of any health programme that's saved more lives and avoided more suffering than vaccination, apart from water sanitation.

Meanwhile, measles outbreaks continue to rage across Europe thanks to European parents who do not vaccinate their children, in contrast to the Americas where concerted vaccination effort has almost eliminated the disease even in poor nations. As the rest of the world strives to eradicate measles, Europe remains a major source of infection not because of poverty or lack of vaccine availability but through choice.

* Measles data from the UK's Health Protection Agency:

Sunday, 15 April 2012

The eurozone recession strategy

Nouriel Roubini has written an excellent article summing up the basic problem in the EU: a big push to solve the problem of too much government debt by cutting government spending without any apparent thought to boosting economic growth. This is a self-defeating recipe for, at best, anaemic growth and, at worst, continuous recession. Unfortunately, the UK government seems to be pursuing a depressingly similar plan. 

Roubini captures the problem neatly:

"The trouble is that the eurozone has an austerity strategy but no growth strategy. And, without that, all it has is a recession strategy that makes austerity and reform self-defeating, because, if output continues to contract, deficit and debt ratios will continue to rise to unsustainable levels. Moreover, the social and political backlash eventually will become overwhelming."

Regarding the social backlash, it amazes me that the Greeks have remained so stoic considering the demands being made of them. If the economy does not start to grow this year, people may reach the conclusion that all this was for nought at which point all bets are off. Unsurprisingly, opinion polls in Greece show strong and rising support for political parties which advocate a "default and exit" approach and if the current plan continues to yield nothing but hardship people will naturally start to wonder whether the alternative could be much worse.

Thursday, 12 April 2012

Statistical joke

"This chart indicates the probability that I am
bleeding heavily from my index finger."

A trio of statisticians was on a train going to a conference, sitting alongside them was a trio of economists. As they chatted about this and that, the economists learnt that the statisticians only had one train ticket between the three of them.
"How do you expect to get away with that?" Asked one economist.
"No problem, we have a technique for that," came the reply.

When the conductor came along checking tickets the three statisticians all hid in a toilet. The conductor knocked on the toilet door, their one ticket was slipped underneath, punched and handed back.

"That is an impressively cunning plan!" observed the senior economist after the statisticians had returned to their seats, "I wish we'd thought of that."

Seeing the opportunity to reduce costs, for the return journey the economists bought just one ticket between them and boarded the train. Shortly afterwards, the statisticians boarded and sat next to them. They exchanged pleasantries whereupon the economists excitedly revealed that they had adopted the statisticians' technique and planned to travel using just one ticket between three.

"Jolly good," nodded the senior statistician, "though in fact we have no ticket at all this time."
"What? How can you get away with that?" gasped the economist,
"Don't worry, we have an advanced technique for that,".

Just then the conductor was sighted so the economists disappeared to the toilet with their ticket and their plan. Meanwhile, two of the statisticians went to the adjacent toilet while the third paused a moment then walked over to the economists' toilet and knocked firmly, "Tickets, please!". The ticket was slipped underneath and the third statistician joined his colleagues.

A few moments later the conductor knocked on the toilet door: the overture to a long, heated and rather embarrassing scene involving one angry conductor, three red-faced economists caught together in flagrante in a train toilet and much amusement for the rest of the train.

The lesson: make sure you understand the principles behind a statistical technique before trying to apply it.

Monday, 9 April 2012

Simpson's Paradox

Simpson's Paradox is one of those subtly baffling situations in which statistics leads you along a perfectly logical path, where everything is simple and obvious, until suddenly you're left with your head spinning in confusion. It illustrates how the ideas of "on average" and "overall" can be surprisingly misleading, so beware of taking them at face value.

Edward Simpson, a WWII codebreaker in Bletchley Park, described the effect named after him back in 1941.

To see how it works let's look at a 1986 study* into different methods for treating kidney stones: keyhole surgery versus open surgery. All the figures below are taken from this study, they are real results from actual patients.

Treatment of kidney stones using keyhole and open surgery

Treatment         Success  Failure  Total  Success%
Keyhole Surgery       289       61    350       83%
Open Surgery          273       77    350       78%

The table shows the result of 700 patients, 350 receiving each treatment, how many were successful and unsuccessful under each treatment, and finally the percentage success rate per treatment

So based on 350 patients undergoing each treatment, this paper found that the overall chance of a successful operation was 83% with keyhole surgery versus 78% using open surgery. So keyhole surgery was, on average, more successful than open surgery. That's simple enough. But not all kidney stones are the same, so let's pull out just the results for large stones, defined in the paper as 2cm or more in diameter:

Treatment of large kidney stones

Treatment         Success  Failure  Total  Success%
Keyhole Surgery        55       25     80       69%
Open Surgery          192       71    263       73%

Ahh, interesting: this shows a higher success rate for open surgery. So in this study it seems that despite keyhole surgery being more successful overall, when dealing with large kidney stones open surgery is better: it succeeded 73% of the time, compared with 69% for keyhole surgery. This must mean that for small stones keyhole surgery is far has to be, otherwise how could it come out ahead of open surgery on average? Let's check:

Treatment of small kidney stones

Treatment         Success  Failure  Total  Success%
Keyhole Surgery       234       36    270       87%
Open Surgery           81        6     87       93%

So open surgery has a higher chance of success, by 93% to 87%. Er, what? How can open surgery be more effective at treating small stones as well? One treatment is better in all situations, but worse overall?

What's going on?

So the study found that open surgery is better than keyhole surgery for large stones and it's also better for small stones, but overall it's worse! How can that be? You may be thinking that I've omitted to mention a "medium" category, but there isn't one. You can check the tables to confirm that the total number of patients (700) is equal to all the small cases (357) plus all the large cases (343): nothing is missing. 

So what's going on? How can open surgery be better for both large and small stones, but come off worse overall? Simpson's Paradox! But is it just a statistical trick or is there something real going on? Remember we're dealing with real research into real patients with real (and probably very painful) kidney stones. The point of the research is to find out which treatment gives patients get the best chance of success, so what is a doctor supposed to recommend based on this? A coin flip?

The answer becomes clear if we look closer at the two tables breaking down small and large cases. Here they are again.

Treatment of large kidney stones

Treatment         Success  Failure  Total  Success%
Keyhole Surgery        55       25     80       69%
Open Surgery          192       71    263       73%

Treatment of small kidney stones

Treatment         Success  Failure  Total  Success%
Keyhole Surgery       234       36    270       87%
Open Surgery           81        6     87       93%

First, notice that regardless of which treatment is used, the chance of success when treating a small stone (87% or 93%) is always much higher than the chance of success when treating a large stone (69% or 73%). Small stones seem to be inherently easier to treat.

Second, notice that keyhole surgery was mostly used to treat small stones whereas open surgery was mostly used to treat large stones. The overall table shows 350 treatments using keyhole surgery, but more than 3/4 of them were treating the inherently less risky small stones. In contrast, 3/4 of the open surgery treatments were on patients with a large kidney stone. 

So in this study, keyhole surgery was mainly used to treat the lower risk cases, while open surgery was mainly used in the higher risk cases. This flatters the performance of keyhole surgery when you put all the results together because you're not comparing like with like. The true picture emerges when you separate (or stratify) the easier and harder cases. The stratified results produce a fairer, like-for-like comparison, revealing that in this study open surgery outperformed keyhole surgery for both large and small stones.

Mr Brilliant and Mr Average

Here's another way to picture it. Imagine a hospital with two surgeons, Mr Brilliant and Mr Average. To give patients the best chance of success you would aim to give all the difficult cases to Mr Brilliant since he has the best chance of pulling off a successful treatment. Mr Average can then concentrate on simple, run-of-the-mill cases where the chance of success is always quite high. In that situation, it's quite possible that Mr Brilliant could have a lower overall success rate than Mr Average, despite being the better surgeon. Such a crude comparison flatters Mr Average because Mr Brilliant is taking all the difficult cases. To make the comparison fair you need to compare the surgeons' performance on similar cases.

In an ideal world, statistically speaking, you would allocate patients between the two surgeons at random so they'd both tackle the same mix of easy and difficult cases. That would make it very easy to see who's best, but it doesn't generally happen this way in real life because hospitals tends to prioritise the successful outcome for the patient over the easy life for the statistician. Hey-ho.

Final Thought

I've focussed on one study into treating for kidney stones dating back to 1986. In practice this one study is rather old and its findings outdated. My aim here was to look at the interesting statistical features of its findings rather than to recommend to you a particular treatment for kidney stones - I'm not a doctor. My guess is that treatments and patient outcomes have moved on a lot in the last 30 years.

* Charig, R., Webb, D.R., Payne, S.R and Wickham, J.E.A. (1986) Comparison of treatment of renal culculi by open surgery, percutaneous nephrolithotomy, and extracorporeal shockwave lithotripsy. British Medical Journal, 292, 879-882.

Success was defined as the stones being eliminated or reduced to <2mm. Success % rounded to 2 significant figures. The paper also looked at a 3rd treatment: using sound waves to break up kidney stones.