Evidence based medicine

The New York Times magazine’s headline story this Sunday is on evidence-based medicine.  It talks about how a physician, Brent James, has been developing objective empirical means to measure outcomes and use the data to design medical protocols.  This is a perfect example of the migration from a highly skilled and paid profession (what I called an NP job in a recent post) to a more algorithmic and mechanical one (a P job).  Here are some excerpts from the story:

For the past decade or so, a loose group of reformers has been trying to do precisely this. They have been trying to figure out how to improve health care while also holding down the growth in costs. The group includes Dr. John Wenn­berg and his protégés at Dartmouth, whose research about geographic variation in care has received a lot of attention lately, as well as Dr. Mark McClellan, who ran Medicare in the Bush administration, and Dr. Donald Berwick, a Boston pediatrician who has become a leading advocate for patient safety. These reformers tend to be an optimistic bunch. It’s probably a necessary trait for anyone trying to overturn an entrenched status quo. When I have asked them whether they have any hope that medicine will change, they have tended to say yes. When I have asked them whether anybody has already begun to succeed, they have tended to mention the same name: Brent James.

…In the late 1980s, a pulmonologist at Intermountain named Alan Morris received a research grant to study whether a new approach to ventilator care could help treat a condition called acute respiratory distress syndrome. The condition, which is known as ARDS, kills thousands of Americans each year, many of them young men. (It can be a complication of swine flu.) As Morris thought about the research, he became concerned that the trial might be undermined by the fact that doctors would set ventilators at different levels for similar patients. He knew that he himself sometimes did so. Given all the things that the pulmonologists were trying to manage, it seemed they just could not set the ventilator consistently.

Working with James, Morris began to write a protocol for treating ARDS. Some of the recommendations were based on solid evidence. Many were educated guesses. The final document ran to 50 pages and was left at the patients’ bedsides in loose-leaf binders. Morris’s colleagues were naturally wary of it. “I thought there wasn’t anybody better in the world at twiddling the knobs than I was,” Jim Orme, a critical-care doctor, told me later, “so I was skeptical that any protocol generated by a group of people could do better.” Morris helped overcome this skepticism in part by inviting his colleagues to depart from the protocol whenever they wanted. He was merely giving them a set of defaults, which, he emphasized, were for the sake of a research trial.

… While the pulmonologists were working off of the protocol, Intermountain’s computerized records system was tracking patient outcomes. A pulmonology team met each week to talk about the outcomes and to rewrite the protocol when it seemed to be wrong. In the first few months, the team made dozens of changes. Just as the pulmonologists predicted, the initial protocol was deeply flawed. But it seemed to be successful anyway. One widely circulated national study overseen by doctors at Massachusetts General Hospital had found an ARDS survival rate of about 10 percent. For those in Intermountain’s study, the rate was 40 percent.

Hurdles for mathematical thinking

From my years as both a math professor and observer of people, I’ve come up with a list of  hurdles for mathematical thinking.  These are what I believe to be the essential set of skills  a  person must have if they want to understand and do mathematics.  They don’t need to have all these skills to use mathematics but would need most of them if they want to progress far in mathematics.  Identifying what sorts of conceptual barriers people may have could help in improving mathematics education.

I’ll first give the list and then explain what I mean by them.

1. Context dependent rules

2. Equivalence classes

3. Limits and infinitesimals

4. Formal  logic

5. Abstraction

Darts and Diophantine equations

Darts is a popular spectator sport in the UK. I had access to cable television recently so I was able to watch a few games.  What I find interesting about professional darts is that the players must solve a Diophantine equation to win.  For those who know nothing of the game, it involves throwing a small pointed projectile at an enumerated target board that looks like this:

A dart that lands on a given sector on the board obtains that score.  The center circle of the board called the bulls eye is worth 50 points.  The ring around the bulls eye is worth 25 points.  The wedges are worth the score ascribed by the number on the perimeter.  However, if you land in the inner ring then you get triple the score of the wedge and if you land in the outer ring you get double the score.  Hence, the maximum number of points for one dart is the triple twenty worth 60 points.

The NP economy

I used to believe that one day all human labour would be automated (e.g. see here).  Upon further reflection, I realize that I am wrong.  The question of whether or not machines will someday replace all humans depends crucially on whether or not P is equal to NP.   Jobs that will eventually be automated will be the ones that can be solved easily with an algorithm.  In computer science parlance, these are problems in the computational complexity class P (solvable in polynomial time).   For example, traditional travel agents have disappeared faster than bluefin tuna because their task is pretty simple to automate.  However, not all travel agents will disappear.  The ones that survive will be more like concierges that put together complex travel arrangements or require negotiating with many parties.

Eventually, the jobs that humans will hold (barring a collapse of civilization as we know it) will involve solving problems in the complexity class NP (or harder).  That is not to say that machines won’t be doing some of these jobs, only that the advantage of machines over humans will not be as clear cut.  While it is true that if we could fully reproduce a human and make it faster and bigger then it could do everything that a human could do better but as I blogged about before, I think it will be difficult to exactly reproduce humans.  Additionally, for some very hard problems that don’t even have any good approximation schemes, blind luck will play an important role in coming up with solutions.  Balancing different human centric priorities will also be important and that may be best left for humans to do.   Even if it turns out that P=NP there could still be some jobs that humans can do like working on undecidable problems.

So what are some jobs that will be around in the NP economy?  Well, I think mathematicians will still be employed. Theorems can be verified in polynomial time but there are no known algorithms in P to generate them.   That is not to say that there won’t be robot mathematicians and mathematicians will certainly use automated theorem proving programs to help them (e.g. see here). However, I think the human touch will always have some use.  Artists and comedians will also have jobs in the future.  These are professions that require intimate knowledge of  what it is like to be human .  Again, there will be machine comics and artists but they won’t fully replace humans.  I also think that craftsmen like carpenters, stone masons, basket weavers and so forth could also make a comeback.  They will have to exhibit some exceptional artistry to survive but the demand for them could increase since some people will always long for the human touch in their furniture and houses.

The question then is whether or not there will be enough NP jobs to go around and whether or not everyone is able and willing to hold one.  To some, an NP economy will be almost Utopian – everyone will have interesting jobs.    However, there may be some people who simply don’t want or can’t do an NP job.   What will happen to them?  I think that will be a big (probably undecidable) problem that will face society in the not too distant future, provided we make it that far.

Arts and Crafts

There is an opinion piece by  Denis Dutton in the New York Times today on Conceptual Art, which presents some views that I am very sympathetic to.   All creative endeavours involve some inspiration and perspiration – There is the idea and then there is the execution of that idea.  Conceptual art essentially removes the execution aspect of art and makes it a pure exercise in cleverness.  In some sense it does crystallize the essence of art but I’ve always found it lacking.   I just can’t get that inspired by a medicine cabinet.  I’ve always found that the craft of a work of art to be as compelling (if not more) as the idea itself.  In many cases the two are inseparable.  Dutton argues that the craft aspect of art will never disappear because people intrinsically enjoy witnessing virtuosity.  I’m inclined to agree.  So while Vermeer or Caravaggio will remain timeless Damien Hurst may just fade away in time.

Retire the Nobel Prize

I’ve felt for sometime now that perhaps we should retire the Nobel Prize.  The money could be used to fund grants, set up an institute for peace and science, or even have a Nobel conference like TED.  The prize puts too much emphasis on individual achievement and in many instances misplaced emphasis.  The old view of science involving the lone explorer seeking truth in the wilderness needs to be updated to a new metaphor of the sandpile, as used to described self-organized criticality by Per Bak, Chao Tang, and Kurt Wiesenfeld.  In the sandpile model, individual grains of sand are dropped on the pile and every once in awhile there are “avalanches” where a bunch of grains cascade down.  The distribution of avalanche sizes is a power law.  Hence, there is no scale to avalanches and there is no grain that is more special than any other.

This is just like science.  The contributions of scientists and nonscientists are like grains of sand dropping on the sandpile of knowledge and every once in awhile a big scientific avalanche is triggered.  The answer to the question of who triggered the avalanche is that everyone contributed to it.  The Noble Prize rewards a few of the grains of sand that happend to be proximally located to some specific avalanche (and sometimes not) but the rewarded work always depended on something else.

Talk at MBI

I’m currently at the Mathematical Biosciences Institute for a workshop on Computational challenges in integrative biological modeling.  The slides for my talk on using Bayesian methods for parameter estimation and model comparison are here.

Title: Bayesian approaches for parameter estimation and model evaluation of dynamical systems

Abstract: Differential equation models are often used to model biological systems. An important and difficult problem is how to estimate parameters and decide which model among possible models is the best. I will argue that Bayesian inference provides a self-consistent framework to do both tasks. In particular, Bayesian parameter estimation provides a natural measure of parameter sensitivity and Bayesian model comparison automatically evaluates models by rewarding fit to the data while penalizing the number of parameters. I will give examples of employing these approaches on ODE and PDE models.

Human scale

I’ve always been intrigued by how long we live compared to the age of the universe.  At 14 billion years, the universe is only a factor of older than a long-lived human.  In contrast, it is immensely bigger than us.  The nearest star is 4 light years away, which is a factor of larger than a human, and the observable universe is about 25 billion times bigger than that.    The size scale of the universe is partly dictated by the speed of light which at m/s is coincidentally (or not) the same order of magnitude faster than we can move as the universe is older than we live.

Although we are small compared to the universe, we are also exceedingly big compared to our constituents. We are comprised of about cells, each of which are about m in diameter.  If we assume that the density of the cell is about that of water () then that roughly amounts to molecules.  So a human is comprised of something like molecules, most of it being water which has an atomic weight of 18.  Given that proteins and organic molecules can be much larger than that a lower bound on the number of atoms in the body is .

The speed at which we can move is governed by the reaction rates of metabolism.  Neurons fire at an average of approximately 10 Hz, so that is why awareness operates on a time scale of a few hundred milliseconds.  You could think of a human moment as being one tenth of a second.  There are 86,400 seconds in a day so we have close to a million moments in a day although we are a sleep for about a third of them.  That leads to about 20 billion moments in a lifetime. Neural activity also sets the scale for how fast we can move our muscles, which is a few metres per second.  If we consider a movement every second then that implies about a billion twitches per lifetime.  Our hearts beat about once a second so that is also the number of heart beats in a lifetime.

The average thermal energy at body temperature is about Joules, which is not too far below the binding energies of protein-DNA and protein-protein interactions required for life.   Each of our  cells can translate about 5 amino acids per second, which is a lot of proteins in our lifetime.  I find it completely amazing that  a bag of or more things, incessantly buffeted by noise, can stay coherent for a hundred years.  There is no question that evolution is the world’s greatest engineer.  However, for those that are interested in artificial life this huge expanse of scale does pose a question -  What is the minimal computational requirement to simulate life and in particular something as complex as a mammal?  Even if you could do a simulation with say or more objects,  how would you even know that there was something living in it?

The numbers came from Wolfram Alpha and Bionumbers.

Are mass extinctions inevitable?

It is well known from the fossil record that there have been a large number of extinction events of various magnitudes.  Some famous examples include the Cretaceous-Tertiary extinction that killed off the dinosaurs 65 million years ago and the Great Dying 250 million years ago where almost everything died.  It has been postulated that mass extinctions occur every ~30 or ~60 million years.  Most explanations for these events are exogenous – some external astrophysical or geological cataclysm like an asteroid slamming into the Yucatan 65 million years ago or large scale volcanic eruptions.  However, as I watch the news every night, I’m beginning to wonder if life itself is unstable and prone to wild fluctuations.  We are currently in the midst of a mass extinction and it is being caused by us.  However, we are not separate from the ecosystem so in effect, the system is causing it’s own extinction.

I listen to a number of podcasts of science radio shows (e.g. CBC’s Quirks and Quarks, ABC’s The Science Show, BBC’s The Naked Scientists, …) on my long drive home from work each day.  Each week I hear stories and interviews of scientists finding that climate change is worse than they predicted and we’re nearing a point of no return.  (Acidification of the oceans is what scares me the most.)  However, in all of these shows there is always an optimistic undertone that implores us do something about this, under the assumption that we have a choice in what we do.   It is at this point that I can’t help but to smirk because we really don’t have a choice. We’re just a big dynamical (probably stochastic) system that is plunging along.  We may have the capability to experience and witness what is happening (a mystery of which I actually have the privilege to think about for a living) but we don’t have control per se as I wrote about recently.

Seeing red

This week’s Nature has a fascinating article where gene therapy was used to reverse colour blindness in monkeys.  The remarkable thing is that the monkeys were red-green colour blind from birth because they lacked a long wavelength (L-opsin) gene.   A virus containing the human L-opsin gene was injected into the monkey’s eyes.  The virus inserted the gene into some of the medium wavelength cones.  It took about 20 weeks for the inserted gene to be expressed robustly. The amazing thing is that almost immediately after robust expression the treated monkeys were able to discern the frequencies that were missing before in behavioural tests.  In essence, they could now see the colour red when they couldn’t before.

The rapidity in which the behavioural effect occured implies that the neural plasticity required to adopt a new colour was minor.  It could be possible that the neural mechanisms for the missing colours already exists since only the males of the species are colour blind (the females are not) and could thus be tapped into immediately.  However, the gene was inserted randomly into the cones and developmentally it takes a few months before babies can distinguish colours so it is not obvious at all as to how the circuits could be idle for so long and suddenly be activated.

I think understanding how a new colour can suddenly pop into existence may be the avenue to investigate the neural basis of qualia.  The researchers of the study are conducting human trials now on patients that have retinal degeneration.  If it works, then it is only a matter of time before they try it on healthy humans with colour blindness.  We can then ask them what they actually experience when they see red for the first time.

Energy efficiency and boiling water

I’ve noticed that my last few posts have been veering towards the metaphysical so I thought today I would talk about some kitchen science, literally. The question is what is the most efficient way to boil water.  Should one turn the heat on the stove to the maximum or is there some mid-level that should be used?  I didn’t know what the answer was so I tried to calculate it.  The answer turned out to be more subtle than I anticipated.

Reframing the evolution debate

I firmly believe that given the way our brains work, some arguments can never be resolved. This includes political and economic issues (e.g. efficient markets) and also the debate between evolution and creationism.  I think many scientists feel that the way to fight creationists is to challenge them at every level and try to win the debate using reason and overwhelming evidence.  If that doesn’t work then creationists should be shut down by legal and other means because they might take over and send us back to the Dark Ages. Unfortunately, if a creationist has a prior with zero support over the possibility that the earth is 4.5 billion years old then no amount of evidence can ever change their opinion.  That is why I think the Richard Dawkins strategy of equating science with atheism may not be a winning one.  I think there is a different approach that may even get creationists interested in modern biology and science as a way for them to get closer to God.

The ontological argument

An ontological argument is an attempt to prove the existence of God using logic alone. It is one of those things that I had come across a few times in the past but  never took the time to understand.  So, when a blog post by Nathan Schneider on this topic appeared last week in the New York Times, I finally tried to follow the argument.  There have been many attempts at an ontological proof throughout history.  Schneider wrote about an early one from the eleventh century by an English Catholic Bishop named St. Anslem of Canterbury.  I couldn’t really understand Schneider’s somewhat poetic version of the proof but after reading several other versions on the web I think I finally get it.  It is actually quite clever although it obviously must make some assumptions that are not self-evident.

Here’s the proof:  The first assumption is that God is the greatest possible being that can be conceived.  The second assumption is that existing and being conceived is greater than not existing and being conceived.  Hence, God must exist, since a God that exists is greater than a God that doesn’t exist.  Another way of saying this is that the fact that I can think of a God implies that she must exist.  In some sense, this is a precursor to modal realism.

There have been many historical criticisms of this proof.  Kant’s critique is that existence is not a predicate.  By this he means that existence is not a property of an object.  For example, a unicorn has properties such as having a horn, looks like a horse and so forth.  But a unicorn could exist or not exist and that doesn’t change what a unicorn is. So existence is something that must be inferred empirically and can never be deduced a priori.  I think Kant effectively kills Anslem’s proof. However, another weakness in the argument is that Anslem assumes that the set of all conceived beings has an upper bound.  This may not be true as well.  There could be an infinite hierarchy of Gods, a possibility that has interesting philosophical consequences as well.

Life without free will

Given that a materialistic theory of mind is becoming more and more mainstream, we must face the prospect of living our lives without free will.  That is not to say that our lives will be predictable or even determined.  Given what we know about dynamical systems, computer science and quantum mechanics it is almost certain that life is completely unpredictable and undetermined.  However, there is no “you” or “me to make decisions about what we do.  Results from neuroscience (e.g. Bill Newsome’s lab at Stanford) show that there are neurons in cortex that fire before a monkey makes a decision and the simulation of some of these neurons can influence a monkey’s choice.  We too are at the mercy of our neurons.

So the question I have is once a large fraction of the population believes that free will does not exist,  will that change society.   Although this is a dynamical systems question where the belief of free will is some aspect of the state of the system and what I ask is how the system evolves subsequent to reaching a state of no belief in free will, I will address it using language that still connotes some sense of agency or directed action since it is more convenient to do so.  However, keep in mind that everything I say is with respect to how  society will evolve after it attains a state where there is no longer a belief in free will.

Being wrong may be rational

This past Sunday, economist Paul Krugman was lamenting in a book review of Justin Fox’s book “Myth of the Rational Market” (which he liked very much) that despite this current financial crisis and previous crises, like the failure of the hedge fund Long Term Capital Management, people still believe in efficient markets as strongly as ever. The efficient market hypothesis is the basis of most of modern finance and assumes that the price of a security is always correct and that you can never beat the market.  So artificial bubbles should never occur.  Krugman wonders what it will take to ever change people’s minds.

I want to show here that there might be no amount of evidence that will ever change their minds and they can still be perfectly rational in the Bayesian sense.  The argument can also apply to all other controversial topics.  I think it is generally believed in intellectual circles that the reason there is so much disagreement on these issues is that the other side is either stupid, deluded or irrational.   I want to point out that believing in something completely wrong even in the face of overwhelming evidence may arise in perfectly rational beings.  That is not to say that faulty reasoning does not exist and can be dangerous.  It just explains why two perfectly reasonable and intelligent people can disagree so alarmingly.

Ecosystem ghosts

Olivia Judson’s blog post in the New York times today talks about the fragility and robustness of ecosystems.  She talks about how we really don’t know what happens to an ecosystem when a single species goes extinct.  Can that species be restored or has another species taken over its niche?  Also, when an invasive species arrives, it can thrive or not thrive.  Mathematical models have found that the perturbation induced by such an event can cause another species to go extinct even if the invasive species also goes extinct.  These transient invaders are called ghosts. She also talks about experimental ecosystems with single-cell organisms.  In these artificial settings, the equilibrium states are generally composed of a small number of organisms and ghosts can cause established species to disappear.

Now, this brings me to something that has always puzzled me, which is why are natural ecosystems so varied and relatively robust when they are at the same time so susceptible to invasive species?  Examples being rabbits and cane toads ravaging Australia, zebra mussels clogging up the North American Great Lakes, and Kudzu taking over the American southwest.  Clearly, these examples show that there were niches in the ecosystems that were not being exploited.  My guess is that if we wait long enough, the these invaded ecosystems will eventually adjust and become varied again.  After all, these invasive species are held in check in their native habitats. Thus, ecosystems may tend to evolve to a state with wide variety but also one that always leaves them vulnerable to attack.  Can we mathematically prove this? The really interesting thing is that this fragile stability seems to require a large number of species since experiments with small numbers tend to evolve to small communities.  Why is that? What is the difference between a large system and a small system?  Is there a bifurcation or phase transition as you increase the size of the ecosystem?  Is there an analogy to economics or the brain?  This is why I’m so interested in large but finite interacting systems.  There seems to be something there that I just don’t understand.

Information theory

It took me a very long time to develop an intuitive feel for information theory and Shannon entropy.  In fact, it was only when I had to use it for an application that it finally fell together and made visceral sense.  Now, I understand fully why people, especially in the neural coding field, are so focused on it.  I also think that the concepts are actually very natural and highly useful in a wide variety of applications.  I now think in terms of entropy and mutual information all the time.

Our specific application was to develop a scheme to find important amino acid positions in families of proteins called GPCRs, which I wrote about recently.  Essentially, we have a matrix of letters from an alphabet of twenty letters.  Each row of the matrix corresponds to a protein and each column of the matrix corresponds to a specific position on the protein.  Each column is a vector of letters.  Conserved columns are those which have very little variation in the letters and these positions are thought to be functionally important.   They are also relatively easy to find.

What we were interested in was finding pairs of columns that are correlated in some way. For example, suppose whenever column 1 had the letter A (in a given row), column 2 was more likely to have the letter W, whereas when column 1 had the letter C, column 2 was less likely to have the letter P but more likely to have R and D.  You can appreciate how hard it would be to spot these correlations visually.  This is confounded by the fact that if the two columns have high variability then there will be random coincidences from time to time.  So what we really want to know is the amount of correlation that exceeds randomness. As I show below, this is exactly what mutual information quantifies.

Incentives in health care

The American health care system relies on a “fee for service” model, in which physicians are reimbursed for the procedures they perform.  I think this is a perfect example of how organizational structure and in particular incentives can affect outcomes.  Free market proponents argue that the only system that can optimally distribute goods and services is a free market.  I tangentially posted on efficient markets a short time ago.  However, even with a free market, the rules of the game determine what it means to win.  For example, when physicians are reimbursed for procedures then it makes sense for them to perform as many procedures as possible.  If it is the choice between an inexpensive therapy and an expensive one and there is no clear cut evidence for the benefit of either then why choose the inexpensive option.  A provocative article in the New Yorker by Atul Gawande  shows what can happen when this line of thought is taken to the extreme.  Another unintended consequence of the fee for service model may be that there is no incentive to recruit individuals for clinical studies as detailed in this article by Gina Kolata  in the New York Times.  The interesting thing about both of these examples is that they are independent of whether health insurance is private,  public or single payer.  Gawande’s article was mostly about Medicare, which is government run. An alternative to fee for service is  “fee for outcome”, where physicians are rewarded for having healthier patients.  Gawande favours the Mayo Clinic model where the physicians have a fixed salary and focus on maximizing patient care.  There must be a host of different possible compensation models that are possible, which I’m sure economists have explored. However, perhaps this is also a (critically important) problem where ideas from physics and applied math might be useful.

Persistent activity

Whenever I think about the recession and the stimulus package, I’m reminded of the phenomenon of working memory and persistent activity in the brain, which I’ve worked on in the past.  I’ll explain the connection at the end of the post. Working memory is the short term memory we use when we remember a phone number just long enough to call someone and then forget shortly afterward.  Neuroscientists have found neurons in the pre-frontal cortex of monkeys that are correlated with the memory.  So when you present the monkey a transient stimulus that it must remember, these neurons start firing  and remain activated until the memory is no longer needed.  This is a neural correlate of working memory.  This implies that there must be bistability (or multistability) in the firing state of a neuron.

More on Feynman

It had been many years since I last read any books by or about Feynman.  Unfortunately, I never had the chance to hear him speak in person.  I also had never read the book version of “The character of physical law” before so there were several things that struck me after watching some of the lectures.  The first was that Feynman was extremely philosophical and cultured.  This was somewhat surprising because the mythology surrounding Feynman, promoted by his own autobiographies, is that he was the no-nonsense street-smart kid from Brooklyn who used common sense and cunning to outsmart the so-called intellectuals with highfalutin ideas.  I never fully bought into that myth but now  after watching three of the lectures I feel as if they can be completely dispelled.  Feynman was extremely intellectual and very interested in the humanities. He just disagreed with how they were being carried out and done at that time.