Saturday, April 5, 2008
The Linear Hypothesis
That is a pretty kludgy method, of course, but all the methods are pretty kludgy. Using longer-lived animals also has problems, not least being that you have to wait much longer for results. Moreover, the lower the general exposure, the fewer responses you are likely to get, statistically speaking, so the use of realistic exposures and exposure times becomes prohibitively expensive. Also, longer-lived animals tend to be more "charismatic" in the sense that people like them more and animal rights activists pay them more attention, sometimes to the detriment of the researchers.
For the purposes of this little essay, I'm going to use radiation as the example, mostly because there are so many places to get information on the radiation/cancer debate, but also because the chemical/cancer debate gets even more arcane in spots, and I'm doing a once-over-lightly here.
The main alternative to the "linear hypothesis" is the "threshold hypothesis," the idea that a toxin or radiation does not overwhelm the body's cellular defenses until it gets above a certain level, or threshold. There are clearly many, many cases where such thresholds exist; "the dose makes the poison" as Paracelsus claimed, and there are few things that don't become poisonous at a high enough concentration.
There is a variation of the threshold hypothesis, which is called the "hormesis model." This is a somewhat more extreme version of the threshold model, and postulates that low doses of radiation are good for you. This isn't an entirely loopy suggestion; after all, radiation is used to treat some kinds of cancer, because cancer cells are more susceptible to dying from radiation than most body cells. It does, however, contain echoes of the early days of radiation, when things like radium were used as "invigorating" tonics, and that didn't work out well.
There are a variety of arguments and observations made to support both alternatives to the linear model. One of my favorite involves studies that create biological systems that lack the naturally occurring radioisotope potassium-40 and include only potassium-39. This apparently leads to birth defects. However, a high concentration of deuterium in the body (i.e. biological systems using heavy water) also produces severe-to-lethal effects, with no radiation involvement whatsoever. It's not out of the question to suggest that our bodies' enzymes are "tuned" to a particular isotopic weight of the elements involved, and that even relatively small changes in these elements can cause problems. To the best of my knowledge, the potassium isotope experiment has never been performed with some external source substituting for the missing radiation. The result would need to be normal development, obviously, for hormesis to be validated.
Other observations that seem to support various versions of threshold or hormesis include epidemiology in areas of high natural background radiation, which seem to show no excess cancers. Again, matters of the adaptation of local populations, questions of whether or not differences in infant mortality create a "harvesting effect" (where susceptible individuals die before they reach the age where cancers would present), or even simple things like actually getting the exposure levels correctly measured, become important. I've seen claims that the linear hypothesis cannot explain the epidemiology of the Japanese atom bomb survivors, for example, but I know for a fact that the actual radiation exposure to these individuals is a matter of estimation and guesswork, so the "failure" may simply be a matter of not knowing what the true exposure was.
Then there is the fact that when we talk of "radiation" we're not talking about a unitary subject. There are many different kinds of radiation, and many different ways of being exposed to it. These "hypotheses" and "models" that we are talking about are just that: models. A lot of different phenomena are being compressed onto a single, seemingly authoritative graph, but the real, underlying situation is complex and complicated. It's entirely possible that some forms of radiation show some hormesis effect, while others are linear, with no safe levels. The science necessary to make these distinctions is lacking.
Ultimately, however, these models are not some abstract scientific question, but rather, they are used to sort out issues of regulatory policy. And there is where the rubber meets the road. Advocates of threshold and hormesis models are invariably proponents of nuclear power (the reverse is not necessarily true, since there are nuclear power advocates to have no problem with the linearity regulations). There are claims that the public is "radiophobic," which may be true, but then again, that is the public's right. It is not as if there has been a consistent policy of telling the public the truth about these matters, and people tend to get a bit antsy when they know they've been lied to.
Ultimately, the linear hypothesis is the easiest to administer and produces the most clear-cut regulatory framework. It is conservative. Threshold standards tend to create situations where pollutant releases go right up to the threshold and bump against the standard, usually exceeding it from time to time. Linear standards say, "Reduce your impact to the lowest possible level." I find this to be a useful first (and usually second and third) approximation to regulation. But then I am what used to be called a conservative.
Tuesday, February 12, 2008
It's Always about the Blood
Bone marrow makes blood cells. More specifically, it contains various "uncommitted" stem cells that remain in the marrow while splitting off cells that then are "committed" to maturing into cells that circulate in the blood.
The biggie is the red blood cells, without which you and I would die in seconds, since they are what convey oxygen from the lungs to everywhere else. The fancy term for red blood cells is erythrocytes, which has the interesting characteristic of being not only less informative than "red blood cells" but also has more syllables.
The lab measurement for red blood cells is called "hematocrit," and 35% to 55% is considered normal. Less, and you have anemia. More, and you may have a blood disease, live at a high altitude, have dengue fever, or are taking a performance enhancing drug, like EPO.
White blood cells are "leukocytes," or ""lymphocytes" (hooray! same number of syllables, plus there's a differentiation in kind. That's what technical terms should be about). There's an entire menagerie of white blood cells, having to do with which part of the immune system is in play.
Then there are platelets, aka thrombocytes, which aren't exactly cells, but I'll get to that. A normal platelet count is between 150,000 and 400,000 per cubic millimeter of blood, but the ",000" is usually dropped in reporting, so a person with a platelet count of 200,000 is usually said to have a platelet count of 200. A low platelet count is called thrombocytopenia, and may create problems with bruising, bleeding, etc. although there are other factors involved. A count of 120, for example, is not considered that big a deal, but if the count drops below 20, the risk of spontaneous bleeding becomes very high.
Platelets aren't cells, per se; they are more akin to cell walls, hence the "plate" part of the name. Platelets are formed in the cytoplasm of a very large cell, the megakaryocyte. Megakaryocytes mature in about 10 days, from a large stem cell, the megakaryoblast. The cytoplasm of the megakaryocyte fragments at the edge of the cell. This is called platelet budding. The spleen serves as a holding tank for platelets, and contains about a third of the blood's platelets at any given time. Platelets are destroyed by macrophages, and have a lifetime of between 8 and 12 days in the blood, so the full life cycle of a platelet is on the order of about 20 days.
Platelets are necessary but not sufficient for blood clotting. A blood clot consists of a mass of platelets enmeshed in a lattice of insoluble fibrin molecules. Platelet aggregation and fibrin formation both require the proteolytic enzyme thrombin, plus calcium ions and about a dozen other protein clotting factors. Most of these circulate in the blood as inactive precursors until they are activated by trigger enzymes that form when blood vessels are ruptured or something else unpleasant happens.
So, basically, platelets are the bricks and the aggregation factors are the mortar, glue, etc, that hold them together to form blood clots. This entire process is pretty much unique to mammals, incidentally.
There are a number of drugs that will reduce platelet count, including the aspirin-like drugs, ibuprofen and naproxen. I was taking prescription-level amounts of naproxen until recently, owing to the practice of Aikido, and this did lower my platelet levels to somewhat below the lower level of normal, which is to say 100-150, but I did not seem to have any clotting problems, so big deal, was my opinion. However, a few months ago, I began a series of encounters with a fine (intentional irony here) drug called Temodar, which really slams the platelet count, so I had to give up the naproxen. I now report that this made me feel roughly 10-15 years older on the Aikido mat.
A fellow Aikido student recently underwent a root planing, a dental procedure that removes accumulated plaque from below the gum line. After finishing one side, the dentists said, "There's too much bleeding here. I'm not going to do the other side without a doctor's release." So, said student went to his doctor, who sent him to get the requisite blood test.
Upon receipt of the results, the doctor called and told him, "I want you to immediately go to the nearest hospital and check yourself in." The student then called a friend of his, also a physician, for advice. Upon reading his friend the blood test results over the phone, the friend said, "What are you doing talking to me? Go to the nearest hospital and check yourself in immediately."
Our boy did not quite follow the advice. He first wrote up a list of things that needed doing at his job, then he went, not to the nearest hospital, but to San Francisco General. This was actually a good move, because they immediately sent him over to UCSF Hospital, where they could make a proper diagnosis, and where he is now just about done with the chemotherapy for the rare (and, fingers crossed for the happy ending) and very curable form of leukemia that he had developed. Upon admission, he was immediately given a transfusion, and has since had 6-8 "platelet packs," which consist of platelets that have been centrifuged out of whole blood.
He is 36.
His blood test platelet count was 11.
Wednesday, October 31, 2007
Significant
Over on Mark Thoma's Economist's View blog, there were a couple of discussions about a, well, let's call it a "raging debate," albeit one in fairly slow motion. The backstory papers are here:
McCloskey and Ziliak, "The Standard Error of Regressions," Journal of Economic Literature 1996.
Ziliak and McCloskey, "Size Matters: The Standard Error of Regressions in the American Economic Review," Journal of Socio-Economics 2004.
Hoover and Siegler, "Sound and Fury: McCloskey and Significance Testing in Economics," Journal of Economic Methodology, 2008.
McCloskey and Ziliak, "Signifying Nothing: Reply to Hoover and Siegler."
These papers were pulled from an entry on "Significance Testing in Economics" by Andrew Gelman, and there followed two discussions at Economist's View:
"Tests of Statistical Significance in Economics" and later, a response by one of the main players (McCloskey), followed by my arguing with a poster named notsneaky. That led to my essay, "The Authority of Science."
Okay, you are allowed to say, "Yeesh."
So let me boil down some of this. McCloskey published a book in 1985, entitled, The Rhetoric of Economics, in which she argued that the term "Statistical Significance" occupied a pernicious position in economics, and some other sciences. The 1996 paper by McCloskey and Ziliak (M&Z) continued this argument, and the 2004 paper documented a quantitative method for illustrating the misuse of statistics that derived from what was, basically, an error in rhetoric, the connecting the word "significant" to certain sorts of statistical tests. The forthcoming (to be published in 2008, the link is to a draft) paper by Hoover and Siegler (H&S) finally rises to the bait, and presents a no-holds-barred critique of M&Z. Then M&Z reply, etc.
Any of my readers who managed to slog through my criticisms of the use of the word "rent" (See "Playing the Rent" and subsequent essays) in economics (as in "rent-seeking behavior"), will understand that I start off on the side of the rhetoriticians. When a technical subject uses a word in a special, technical sense that is substantially different from its common language use, there is trouble to be had. "Significant" carries the meaning of "important," or "substantial" around with it, but something that is "statistically significant" is simply something that is statistically different from the "null hypothesis" at some level of probability. Often, that level of probability is arbitrarily set to a value like 95%, or two standard deviations, two sigma, which is about 98% for a normal distribution.
(I'll note here that in statistical sampling, one usually uses something like the t-distribution, which only turns into the normal distribution when the number of samples is infinite, so it adds additional uncertainty for the size of the sample. The t-distribution also assumes that the underlying distribution being sampled is normal, which is rarely a good assumption at the levels of reliability that are being demanded, so the assumption train has run off the rails pretty early on).
But some differences make no difference. Given precise enough measurements, one can certain establish that one purchased pound of ground beef is actually one and one thousandths of a pound, but no one who purchased it would feel that they were getting a better deal than if they'd gotten a package that was one thousandth of a pound light. We just don't care about that small a difference; some of the beef is going to stick to the package.
I saw something written recently that referred to something as "statistically reliable," and on the face of it, that would be a much better phrase than "statistically significant," and I will use it hereafter, except when writing about the misused phrase, which I will put in quotes.
So, okay, "statistically significant" is not necessarily "significant." Furthermore, everyone agrees that this is so. But one disagreement is whether or not everyone acts as if this were so. And that is where M&Z's second criticism comes in: that many economics journals (plus some other sciences) simply reject any paper that does not show results at greater than 95% reliability, i.e. the results must be "statistically significant." M&Z say outright that the level of reliability should adapt to the actual importance of the question at hand.
The flip side of this is that, in presenting their work, authors sometimes use "statistically significant" as if it really mean "significant" or "important," rather than just reliable.
Alternately, one can simply report the reliability statistic, the so-called "p value," which is a measure of how likely the result is to have come about simply because of sampling error. I have, for example, published results with p values of 10%, meaning that there was one chance in 10 of the result being just coincidence. I've seen some other p values that were much lower, and those are usually given in the spirit of "there might be something here worth knowing, so maybe someone should do some further work."
In fact, this giving lower p values, or using error bars at the single sigma level, is fairly standard practice is some sciences, like physics, chemistry, geology, and so forth. Engineers usually present things that way as well. On the other hand, the vague use of "significant" that M&Z criticize is often used in social sciences other than economics, e.g. psychology and sociology, as well as some of the biological sciences, including especially, medicine.
It's in medicine where all this begins to get a tad creepy. In one of their papers, M&Z refer to a study (of small doses of aspirin on cardiovascular diseases like heart attack and stroke) as having been cancelled, for ethical reasons, before the results reached "statistical significance." "Ha!" exclaim H&S (I am paraphrasing for dramatic effect). "You didn't read the study, merely a comment on it from elsewhere! In fact, when the study was terminated, the aspirin was found to be beneficial to myocardial infarction (both lethal and non-lethal) at the level of p=0.00001, well past the level of statistical significance! It was only stroke deaths and total mortality that had not reached the level of p=0.05!"
Well, that would surely score points in a high school debate, but let's unpack that argument a bit. M&Z say that the phrase "statistically significant" is used as a filter for results, and what do H&S do? They concentrate on the results that were found to be statistically reliable at a high level. How about the stroke deaths? What was the p value? H&S do not even mention it.
(As an aside, I will note that the very concept of a p value of 0.00001 is pretty ridiculous. Here we have an example of the concept of statistical reliability swamping actual reliability. The probability of any distribution perfectly meeting the underlying statistical assumptions of the t-distrubution is indistinguishable from zero, and the likelihood of some other confounding factor intervening at a level of more than once per hundred thousand is nigh onto one).
Furthermore, H&S use a little example involving an accidental coincidence of jellybeans seeming to cure migraines to show why one must use "statistical significance." Then, when discussing the aspirin study, they invoke the jellybean example. On the face of it, this looks like they are equating migraines with heart attacks and strokes, again, completely ignoring the context in which samples are taken, in order to focus on the statistics. In many ways, it looks like H&S provide more in the way of confirming examples of M&Z's hypothesis than good arguments against it.
Also consider what H&S are saying about the aspirin study, that there was a period of time when members of the control group were dying, when the statistical reliability of the medication had been demonstrated, but the study had yet to be terminated. Possibly the study did not have an ongoing analysis, and depended upon certain predetermined analysis and decision points. But how would such points be selected? By estimating how long it would take for the numbers to be "statistically significant?"
Some studies definitely do use ongoing statistical analyses. Are there really studies where a medication has be been shown to be life-saving, to a statistical reliability of 90%, where patients are still dying while the analysts are waiting for the numbers to exceed 95%? How about cases where medications are found to have lethal side effects, but remain on the market until the evidence exceeds "statistical significance?"
The blood runs a little cold at that, doesn't it?
Tuesday, June 12, 2007
Funny As a Heart Attack
Of the various stories I bring from my 35 year college reunion, none are funnier than the defibrillator story.
One of my college buddies had a heart attack a few years ago (see the laughs start coming right off the bat). It was a fairly major one, though he says that the lasting heart damage was not too great. He had total blockage in one of the coronary arteries, etc., and now he has a stent, plus some other stuff, including a personal defibrillator that he wears on chest.
But the story isn’t about him. Having had a heart attack, plus wearing a defib, makes my college chum a magnet for others’ stories about heart attacks and defibrillators, just like I now know a lot of cancer stories I wouldn’t have otherwise heard.
Anyway, this is a defibrillation story. The defib scene is now a staple of medical drama, what with the rising tone and the barked “Clear!” letting the EMT guys look and sound so cool and macho. Defibrillation is used essentially to “reboot” a cardiac control system that has gang agley, where an “arrhythmia” has become a “seizure.” This tends to happen most often in a rapidly beating heart, where, in fact, the heart is trying to beat so rapidly that it begins to lose pumping efficiency. In the extreme, the poor organ is just quivering, unable to deliver blood to the body, including itself, so it begins to die. The quicker defibrillation is applied, the better the outcome, hence personal, implantable defibs.
The personal devices constantly monitor a person’s heart rate, ready to apply the electric shock if the rate gets too high. The problem for the guy in this story was two-fold. First, he had a tendency for a runaway heart rate in the first place, some form of tachycardia, though I don’t know which kind. Second, his personal defibrillator had been set a little two low.
Ah, you can see this coming, can’t you?
It happened while he was playing softball, maybe not the best recreational activity for someone with a heart condition, but who am I to make that particular call? The way I heard the story was that there was a thunderstorm brewing, but you play until the rain begins, that’s part of the deal. Let’s say also that our protagonist was chasing a fly ball in the outfield under a darkening sky.
Then, suddenly, wham! He’s now flat on his back, his defibrillator having kicked in, its tiny little microchip brain sure that it was needed to save his life.
Now here’s the thing: being zapped with an electrical current to stop and restart your heart is not a window into sartori. No, it’s quite scary, and will do a good job of accelerating your heart rate. So our protagonist gets several seconds of an adrenal rush with a soundtrack of his own heartbeat in his ears, said heartbeat going faster and faster, then…wham! Yes, Our Friend the Defibrillator has come to the rescue once again.
Okay, now he’s both scared and angry, because this was not in the sales brochure. He struggles a bit, trying to maybe get up, or at least lift his head to call for help and wham! Another reboot.
So now he’s just stuck on his back, realizing he’s completely helpless, in the grip of a deranged robot that’s smaller than a pack of cigarettes, but it’s got a couple of electrodes jammed into his chest, and it’s gonna keep zapping him until help arrives, or it runs out of juice, whichever comes first. And maybe by now the lightning from the thunderstorm is beginning to light things up, and he is trying everything he can to CALM DOWN DAMMIT! But all he can do is listen to his own heartbeat accelerate, punctuated every now and then by another zap.
He went through the entire cycle maybe five or six times before the EMT guys got there and either switched off the defib or gave him something to calm down the tachychardia. What lets the whole thing be funny, of course, is that he lived to tell the tale. In fact, it’s probably the funniest story he knows, and he can probably dine out on it for the rest of his (and I do fervently wish it to be long) life.
You know, Dick Cheney has an implanted defibrillator. I’m absolutely sure you can’t hack one of those things, but still, it’s a funny thought.