I have started a book by Sharon Bertsch McGrayne entitled The theory that would not die. It is about Bayesian statistics, about which I know next to nothing, but which I am told were important to crack the Enigma code during the second world war, hunted down Russian submarines and have recently become respectable following two centuries of controversy.
My son works in central London close to the Dissenters Cemetery where the Rev Thomas Beyes, Fellow of the Royal Society and amateur mathematician, is buried. He also lives in Tunbridge Wells where Bayes was a Presbyterian minister, so my interest is raised. Since my son's job is to do with statistics I am ensnared.
As far as I can tell Bayesian statistics might be a short cut for those statistical imponderables endemic in very large clinical trials; they allow you to change your assumptions as you accumulate data. The purists insist that you don't look at your data until you cross a pre-determined threshold and I remember orthodox statisticians dismissing Bayes with contempt. So I will be interested to read the book. I am only on page 21 and already Bayes has been replaced as the hero by Frenchman Pierre Simon Laplace.
Showing posts with label statistics. Show all posts
Showing posts with label statistics. Show all posts
Tuesday, July 26, 2011
Tuesday, August 10, 2010
Health and fitness.
I had a bad day last Tuesday, spending most of the time asleep on the couch and hardly eating, but since then each day has been an improvement on the one before; so much so that I was able to join my wife on a trip to the supermarket and to go to church of Sunday for the first time in two months. We have been able to watch the service on the Internet, but it isn't quite the same as actually being there.
I'm getting closer to my fighting weight. I tipped the scales this morning at 180 pounds. Before I got ill this time I was 200 pounds and when I left hospital I was 177. However, when I compare my thigh muscles with those of my elder son who recently cycled from Brighton to London for charity, I can see where the weight has gone from.
All my children are to some extent athletic. My older daughter was Dorset Champion for gymnastics floor exercises, and my younger daughter Bournemouth champion at long jump. My older son was Dorset triple jump champion and Bournemouth 100 metres champion. His record for the triple jump stood for 17 years before it was beaten. My younger son was Bournemouth 200 metres champion and represented Dorset at both cricket and Rugby. He still plays cricket and soccer to a good standard, is top of the works leader board at golf, and enjoys surfing, snowboarding and cycling as hobbies.
You might say that we are a sporty family. Where does it come from? My father played cricket at county second XI level and my father-in-law boxed a bit. My own sporting prowess was curtailed by a late puberty. At 15 I was the second smallest boy of my year at school. Although, I had been quite a fast runner at 10 and 11, by the time I thought to enter school sports I got my timing wrong. There were always boys who were faster than I was in the sprints, but when a boy who was definitely much slower than I won the under-14s hurdles, I thought I had found my event. The problem that I had not realised was that he was three weeks younger than I. In those days the cut off for athletic events was March 31st, so by being born on March 12th I was one of the oldest in my year, while he, being born on April 7th, was one of the youngest in his.
The following year I entered the hurdles myself. I still had not had my growth spurt. The height of the hurdles astonished me. They were about a foot higher than when he had won. Of course, I fell at the first and suffered the ignominy of the headmaster rushing over and disentangling me from the broken hurdle (they were constructed by the woodworking class and looked like proper sheep hurdles rather than the ones you see nowadays in Track and Field. Thus ended my athletic career.
After puberty I did feature in the school first XI for both cricket and football, but aged 17 I snapped my anterior cruciate and had to give up all thoughts of a career in professional sport!
I have been reading a book called Outliers by Malcolm Gladwell. He makes a similar point about the month you are born in affecting sporting success. A survey of Canadian Ice Hockey players shows that the most successful players are born in the winter months: January, February and March. The simple explanation for this is that the cut-off date for age-class hockey is January 1st. so that those who are older in their year at the age of 10, say, have an enormous physical advantage over those born in December. At this age boys get selected for representative teams and thus benefit from the extra coaching and practice that they receive, so that the age bias becomes set in stone.
This same effect is seen in soccer in the UK, where it is always the bigger boys that get selected for representative teams. I remember a couple of lads in my class who were selected for the English under-15 squad. they were large boys who had an early puberty and could kick a football a long way (these were the days of heavy leather boots and heavy leather balls that got water-sodden when it rained).
Although this was a grammar school with high academic achievement, neither lad was a star in the classroom. Neither progressed in professional sport and one became a hod-carrier and the other left school after becoming a father at the age of 16.
The book is a fascinating read and I may quote from it again. After last week finding that statistics perform better than experts, you won't be surprised to find that succes is related less to ability than to happenstance.
I'm getting closer to my fighting weight. I tipped the scales this morning at 180 pounds. Before I got ill this time I was 200 pounds and when I left hospital I was 177. However, when I compare my thigh muscles with those of my elder son who recently cycled from Brighton to London for charity, I can see where the weight has gone from.
All my children are to some extent athletic. My older daughter was Dorset Champion for gymnastics floor exercises, and my younger daughter Bournemouth champion at long jump. My older son was Dorset triple jump champion and Bournemouth 100 metres champion. His record for the triple jump stood for 17 years before it was beaten. My younger son was Bournemouth 200 metres champion and represented Dorset at both cricket and Rugby. He still plays cricket and soccer to a good standard, is top of the works leader board at golf, and enjoys surfing, snowboarding and cycling as hobbies.
You might say that we are a sporty family. Where does it come from? My father played cricket at county second XI level and my father-in-law boxed a bit. My own sporting prowess was curtailed by a late puberty. At 15 I was the second smallest boy of my year at school. Although, I had been quite a fast runner at 10 and 11, by the time I thought to enter school sports I got my timing wrong. There were always boys who were faster than I was in the sprints, but when a boy who was definitely much slower than I won the under-14s hurdles, I thought I had found my event. The problem that I had not realised was that he was three weeks younger than I. In those days the cut off for athletic events was March 31st, so by being born on March 12th I was one of the oldest in my year, while he, being born on April 7th, was one of the youngest in his.
The following year I entered the hurdles myself. I still had not had my growth spurt. The height of the hurdles astonished me. They were about a foot higher than when he had won. Of course, I fell at the first and suffered the ignominy of the headmaster rushing over and disentangling me from the broken hurdle (they were constructed by the woodworking class and looked like proper sheep hurdles rather than the ones you see nowadays in Track and Field. Thus ended my athletic career.
After puberty I did feature in the school first XI for both cricket and football, but aged 17 I snapped my anterior cruciate and had to give up all thoughts of a career in professional sport!
I have been reading a book called Outliers by Malcolm Gladwell. He makes a similar point about the month you are born in affecting sporting success. A survey of Canadian Ice Hockey players shows that the most successful players are born in the winter months: January, February and March. The simple explanation for this is that the cut-off date for age-class hockey is January 1st. so that those who are older in their year at the age of 10, say, have an enormous physical advantage over those born in December. At this age boys get selected for representative teams and thus benefit from the extra coaching and practice that they receive, so that the age bias becomes set in stone.
This same effect is seen in soccer in the UK, where it is always the bigger boys that get selected for representative teams. I remember a couple of lads in my class who were selected for the English under-15 squad. they were large boys who had an early puberty and could kick a football a long way (these were the days of heavy leather boots and heavy leather balls that got water-sodden when it rained).
Although this was a grammar school with high academic achievement, neither lad was a star in the classroom. Neither progressed in professional sport and one became a hod-carrier and the other left school after becoming a father at the age of 16.
The book is a fascinating read and I may quote from it again. After last week finding that statistics perform better than experts, you won't be surprised to find that succes is related less to ability than to happenstance.
Friday, July 30, 2010
Super Crunchers
I have been reading the book Super Crunchers by Ian Ayres. The bottom line is that statistics can do better than experts.
We have been living this reality in medicine for the best part of 20 years. Want advice on how to treat a rare disease? We used to go to an expert at one of the great teaching hospitals, but now we are more likely to use the Internet. On PubMed we can search for Randomized Controlled Trials in that disease and discover that treatment A is significantly better than treatment B.
It isn't only in medicine that the figures outperform the expert. Ayres begins by telling the story of Orley Ashenfelter who was sceptical about wine experts. Looking back over successful vintages and the weather at the time of their growth, he produced a regression formula based on high average summer temperature and low harvest-time rainfall that correlated with a good vintage. When he made predictions for the 1989 and 1990 vintages based on his formula, the experts scoffed. But he was proved correct, and today most wine investors follow his formula.
Bill James did the same for baseball. Baseball scouts claim to have an eye for a good player and watch hundreds of high school and college games to identify a future star. James derived a formula that he said would predict who would succeed in major league baseball. Once again statistics beat the experts.
What has changed is the availability of huge databases to guide decision making. The size of these databases is enormous. They are not measured in gigabytes but in terabytes or even petabytes (a million gigabytes). The entire Library of Congess consists of 20 terabytes of text. In contrast, Wal-Mart's data warehouse comprises 570 terabytes. Data mining is able to produce business decisions like the refusal rental car companies to offer a service to people with poor credit scores because they are more likely to have an accident. Airlines, when a fight is cancelled, no longer offer the next seat to frequent flyers as a reward for loyalty, but to the customer whose continued business is calculated to be at greatest risk. The "No Child Left Behind" Act requires schools to adopt teaching methods supported by rigorous data analysis. In some cases this means adopting lessons where every word is scripted and statistically vetted.
Apart from just analysing correlations, the super crunchers have introduced the randomized controlled trial into business. Without consent, you may be taking part in one right now. Say a manufacturer of cornflakes is concerned about packet design. He might produce the identical product save for "More Fiber" printed in red at the top left hand corner. Packets are sent out randomly to different stores and the manufacturer can compare how quickly each disappears from the shelf.
It gets more complicated, but the next thing is for consumers to game the system. Once we are aware of what is going on we should be able to turn the thing to our advantage.
Is there no place for the expert then? The wise expert will use this new technology and add value to it, by recognizing the flaws in clinical trials, just as I have in pointing out how the manufacturers cheat in their trials of supposedly new drugs against chlorambucil in CLL. You have to be aware of the tricks that are played in RCTs. However, gone are the days when we can just say, "Lies, damned lies and statistics." We need to understand statistics and make them work for us rather than the opposition.
We have been living this reality in medicine for the best part of 20 years. Want advice on how to treat a rare disease? We used to go to an expert at one of the great teaching hospitals, but now we are more likely to use the Internet. On PubMed we can search for Randomized Controlled Trials in that disease and discover that treatment A is significantly better than treatment B.
It isn't only in medicine that the figures outperform the expert. Ayres begins by telling the story of Orley Ashenfelter who was sceptical about wine experts. Looking back over successful vintages and the weather at the time of their growth, he produced a regression formula based on high average summer temperature and low harvest-time rainfall that correlated with a good vintage. When he made predictions for the 1989 and 1990 vintages based on his formula, the experts scoffed. But he was proved correct, and today most wine investors follow his formula.
Bill James did the same for baseball. Baseball scouts claim to have an eye for a good player and watch hundreds of high school and college games to identify a future star. James derived a formula that he said would predict who would succeed in major league baseball. Once again statistics beat the experts.
What has changed is the availability of huge databases to guide decision making. The size of these databases is enormous. They are not measured in gigabytes but in terabytes or even petabytes (a million gigabytes). The entire Library of Congess consists of 20 terabytes of text. In contrast, Wal-Mart's data warehouse comprises 570 terabytes. Data mining is able to produce business decisions like the refusal rental car companies to offer a service to people with poor credit scores because they are more likely to have an accident. Airlines, when a fight is cancelled, no longer offer the next seat to frequent flyers as a reward for loyalty, but to the customer whose continued business is calculated to be at greatest risk. The "No Child Left Behind" Act requires schools to adopt teaching methods supported by rigorous data analysis. In some cases this means adopting lessons where every word is scripted and statistically vetted.
Apart from just analysing correlations, the super crunchers have introduced the randomized controlled trial into business. Without consent, you may be taking part in one right now. Say a manufacturer of cornflakes is concerned about packet design. He might produce the identical product save for "More Fiber" printed in red at the top left hand corner. Packets are sent out randomly to different stores and the manufacturer can compare how quickly each disappears from the shelf.
It gets more complicated, but the next thing is for consumers to game the system. Once we are aware of what is going on we should be able to turn the thing to our advantage.
Is there no place for the expert then? The wise expert will use this new technology and add value to it, by recognizing the flaws in clinical trials, just as I have in pointing out how the manufacturers cheat in their trials of supposedly new drugs against chlorambucil in CLL. You have to be aware of the tricks that are played in RCTs. However, gone are the days when we can just say, "Lies, damned lies and statistics." We need to understand statistics and make them work for us rather than the opposition.
Thursday, December 03, 2009
Cancer statistics
It is probably easier to lie with statistics than in any other way. If you put a number to your lie and draw a graph you bully people into believing you. The truth is that many people are afraid of figures.
That is what is currently happening over health service statistics. Let us consider the case of cancer survival. It seems as though it should be simple to compare whether patients with cancer who attend different hospitals survive for longer or shorter periods. If you look carefully you should be able to find out what is wrong with the system and put it right.
Recent statistics demonstrate that the UK is doing particularly poorly when it comes to cancer patients surviving the first year. There are several possible explanations. One is that NICE prevents patients getting access to the latest drugs that would help people to live longer. Another possibility is that the European Working Time Directive, which restricts junior doctors' hours to 48 hours a week means that our surgeons and oncologists are not properly trained when they are let loose on the public. Or it could be that we have too many immigrant doctors, whose training is not up to Western standards, but because of political correctness we cannot say so. Or perhaps it is the nurses' fault, or the managers', or the government's.
But generally I find that when there are marked differences it is because we are comparing apples and oranges.
Although we have quite good measurements for when a patient dies of cancer, we have pretty poor measurements of when a patient contracts cancer. I say quite good measurements of deaths, because quite a lot of patients with cancer die undiagnosed, especially among the poorer members of the community. If you can't afford healthcare insurance then you don't seek out a physician for minor symptoms. You certainly don't buy into executive screening programs. How do you get diagnosed? You die and during your terminal illness your cancer is diagnosed. Or not. This lack of medical attention can have two effects. If you are diagnosed, the diagnosis is too late and you make the figures worse, but if you aren't diagnosed, then you don't get into the cancer statistics which are consequently improved.
Because we don't know when cancer starts, people who are picked up earlier in their cancer journey have better survival figures than those who are diagnosed late. Their longer survival may have nothing to do with better treatment and everything to do with being picked up earlier in the natural history of the disease. One sure way of diagnosing people earlier is by cancer screening of well people. Take prostate cancer. Routinely measuring serum PSA will pick up most cases of prostate cancer (not all because some cancers don't secrete very much). Of course it will also pick up a lot of people with benign enlarged prostates, who will have to undergo an unnecessary prostate biopsy. It will also diagnose many patients who have a well differentiated, slowly growing tumor which would not have presented clinically in the patient's lifetime. These patients will have long survivals, though if they are treated they are exposed to the hazards of treatment that include incontinence and impotence.
It follows then, that if you want to improve your one-year cancer survival statistics you should be a hawk for screening, even though this might not be the best way to benefit patients.
The same is probably true also for breast screening with mammograms. We know that patients are picked up earlier in the natural history of the disease; we do not know that it saves lives. Regular chest X-rays for lung cancer, gastroscopies for stomach cancer, colonoscopies for bowel cancer all have the same result. Does early diagnosis mean that cancer patients live longer? Certainly they live longer than patients who are diagnosed late, but do they live longer than they would have done had their cancer not been diagnosed? The answer is surely yes for some types of cancer, but it is not a given for all types.
That is what is currently happening over health service statistics. Let us consider the case of cancer survival. It seems as though it should be simple to compare whether patients with cancer who attend different hospitals survive for longer or shorter periods. If you look carefully you should be able to find out what is wrong with the system and put it right.
Recent statistics demonstrate that the UK is doing particularly poorly when it comes to cancer patients surviving the first year. There are several possible explanations. One is that NICE prevents patients getting access to the latest drugs that would help people to live longer. Another possibility is that the European Working Time Directive, which restricts junior doctors' hours to 48 hours a week means that our surgeons and oncologists are not properly trained when they are let loose on the public. Or it could be that we have too many immigrant doctors, whose training is not up to Western standards, but because of political correctness we cannot say so. Or perhaps it is the nurses' fault, or the managers', or the government's.
But generally I find that when there are marked differences it is because we are comparing apples and oranges.
Although we have quite good measurements for when a patient dies of cancer, we have pretty poor measurements of when a patient contracts cancer. I say quite good measurements of deaths, because quite a lot of patients with cancer die undiagnosed, especially among the poorer members of the community. If you can't afford healthcare insurance then you don't seek out a physician for minor symptoms. You certainly don't buy into executive screening programs. How do you get diagnosed? You die and during your terminal illness your cancer is diagnosed. Or not. This lack of medical attention can have two effects. If you are diagnosed, the diagnosis is too late and you make the figures worse, but if you aren't diagnosed, then you don't get into the cancer statistics which are consequently improved.
Because we don't know when cancer starts, people who are picked up earlier in their cancer journey have better survival figures than those who are diagnosed late. Their longer survival may have nothing to do with better treatment and everything to do with being picked up earlier in the natural history of the disease. One sure way of diagnosing people earlier is by cancer screening of well people. Take prostate cancer. Routinely measuring serum PSA will pick up most cases of prostate cancer (not all because some cancers don't secrete very much). Of course it will also pick up a lot of people with benign enlarged prostates, who will have to undergo an unnecessary prostate biopsy. It will also diagnose many patients who have a well differentiated, slowly growing tumor which would not have presented clinically in the patient's lifetime. These patients will have long survivals, though if they are treated they are exposed to the hazards of treatment that include incontinence and impotence.
It follows then, that if you want to improve your one-year cancer survival statistics you should be a hawk for screening, even though this might not be the best way to benefit patients.
The same is probably true also for breast screening with mammograms. We know that patients are picked up earlier in the natural history of the disease; we do not know that it saves lives. Regular chest X-rays for lung cancer, gastroscopies for stomach cancer, colonoscopies for bowel cancer all have the same result. Does early diagnosis mean that cancer patients live longer? Certainly they live longer than patients who are diagnosed late, but do they live longer than they would have done had their cancer not been diagnosed? The answer is surely yes for some types of cancer, but it is not a given for all types.
Saturday, August 29, 2009
CCTV cameras
It keeps coming up in the press. I heard it on the radio. Big Brother is watching us. A story the other day about how few crimes are solved by them. Watch 'Spooks' the TV spy program and you would think that your every movement was observed by them. We are told that a third of all the CCTV cameras in the world are concentrated in Britain.
Let me let you into a secret. It ain't true.
What is true is that no-one knows how many CCTV cameras there are in the UK. They are mostly put up by private individuals or firms to protect their property. So where does this paranoia come from.
It comes from a survey done 7 years ago in Putney, south-west London. Observers walked up two streets in Putney, which is an affluent area of London, and counted the number of CCTV cameras they could spot. Then they worked out how many people there were in those streets - about a couple of hundred - divided that number into 60 million, and then multiplied the answer by the number of cameras they spotted.
As an exercise in statistics it was ludicrous, about as silly as a newspaper poll that claimed that more than 50% of doctors approved of something or other. It turned out that the newspaper asked 15 doctors their opinion and extrapolated from that.
It used to be said that 90% of statistics were made up on the spot. That probably isn't true, but the abuse of statistics is very common perpetrated by people who ought to know better.
One site to visit if you want to know more about statistics is this
I listen to the pod cast regularly and it never fails to explode silly statistics.
Let me let you into a secret. It ain't true.
What is true is that no-one knows how many CCTV cameras there are in the UK. They are mostly put up by private individuals or firms to protect their property. So where does this paranoia come from.
It comes from a survey done 7 years ago in Putney, south-west London. Observers walked up two streets in Putney, which is an affluent area of London, and counted the number of CCTV cameras they could spot. Then they worked out how many people there were in those streets - about a couple of hundred - divided that number into 60 million, and then multiplied the answer by the number of cameras they spotted.
As an exercise in statistics it was ludicrous, about as silly as a newspaper poll that claimed that more than 50% of doctors approved of something or other. It turned out that the newspaper asked 15 doctors their opinion and extrapolated from that.
It used to be said that 90% of statistics were made up on the spot. That probably isn't true, but the abuse of statistics is very common perpetrated by people who ought to know better.
One site to visit if you want to know more about statistics is this
I listen to the pod cast regularly and it never fails to explode silly statistics.
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