Posts Tagged ‘mortality’

Asher Peres was a physicist, an expert in information theory who died in 2005 and was remembered for his scientific contributions as well as for his iconoclastic wit and ironic aphorisms. One of his witticisms was that “unperformed research has no results ”  Peres had undoubtedly never heard of intention-to-treat (ITT), the strange statistical method that has appeared recently, primarily in the medical literature.  According to ITT, the data from a subject assigned at random to an experimental group must be included in the reported outcome data for that group even if the subject does not follow the protocol, or even if they drop out of the experiment.  At first hearing, the idea is counter-intuitive if not completely idiotic  – why would you include people who are not in the experiment in your data? – suggesting that a substantial burden of proof rests with those who want to employ it.  No such obligation is usually met and particularly in nutrition studies, such as comparisons of isocaloric weight loss diets, ITT is frequently used with no justification and sometimes demanded by reviewers.   Not surprisingly, there is a good deal of controversy on this subject.  Physiologists or chemists, hearing this description usually walk away shaking their head or immediately come up with one or another obvious reductio ad absurdum, e.g. “You mean, if nobody takes the pill, you report whether or not they got better anyway?” That’s exactly what it means.

On the naive assumption that some people really didn’t understand what was wrong with ITT — I’ve been known to make a few elementary mistakes in my life — I wrote a paper on the subject.  It received negative, actually hostile. reviews from two public health journals — I include an amusing example at the end of this post.  I even got substantial grief from Nutrition & Metabolism, where I was the editor at the time, but where it was finally published.  The current post will be based on that paper and I will provide a couple of interesting cases from the medical literature.  In the next post I will discuss a quite remarkable new instance — Foster’s two year study of low carbohydrate diets — of the abuse of common sense that is the major alternative to ITT.

To put a moderate spin on the problem, there is nothing wrong with ITT, if you explicitly say what the method shows — the effect of assigning subjects to an experimental protocol; the title of my paper was Intention-to-treat.  What is the question? If you are very circumspect about that question, then there is little problem.  It is common, however, for the Abstract of a paper to correctly state that patients “were assigned to a diet” but by the time the Results are presented, the independent variable has become, not “assignment to the diet,” but “the diet” which most people would assume meant what people ate, rather than what they were told to eat. Caveat lector.  My paper was a kind of over-kill and I made several different arguments but the common sense argument gets to the heart of the problem in a practical way.  I’ll describe that argument and also give a couple of real examples.

Common sense argument against intention-to-treat

Consider an experimental comparison of two diets in which there is a simple, discrete outcome, e.g. a threshold amount of weight lost or remission of an identifiable symptom. Patients are randomly assigned to two different diets: diet group A or diet group B and a target of, say, 5 kg weight loss is considered success. As shown in the table above, in group A, half of the subject are able to stay on the diet but, for whatever reason, half are not. The half of the patients in group A who did stay on the diet, however, were all able to lose the target 5 kg.  In group B, on the other hand, everybody is able to stay on the diet but only half are able to lose the required amount of weight. An ITT analysis shows no difference in the two outcomes, while just looking at those people who followed the diet shows 100 % success.  This is one of the characteristics of ITT: it always makes the better diet look worse than it is.

         Diet A         Diet B
Compliance (of 100 patients)   50   100
Success (reached target)   50    50
ITT success   50/100 = 50%   50/100 = 50%
“per protocol” (followed diet) success   50/50 = 100%   50/100 = 50%

Now, you are the doctor.  With such data in hand should you advise a patient: “well, the diets are pretty much the same. It’s largely up to you which you choose,” or, looking at the raw data (both compliance and success), should the recommendation be: “Diet A is much more effective than diet B but people have trouble staying on it. If you can stay on diet A, it will be much better for you so I would encourage you to see if you could find a way to do so.” Which makes more sense? You’re the doctor.

I made several arguments trying to explain that there are two factors, only one of which (whether it works) is clearly due to the diet. The other (whether you follow the diet) is under control of other factors (whether WebMD tells you that one diet or the other will kill you, whether the evening news makes you lose your appetite, etc.)  I even dragged in a geometric argument because Newton had used one in the Principia: “a 2-dimensional outcome space where the length of a vector tells how every subject did…. ITT represents a projection of the vector onto one axis, in other words collapses a two dimensional vector to a one-dimensional vector, thereby losing part of the information.” Pretentious? Moi?

Why you should care.  Case I. Surgery or Medicine?

Does your doctor actually read these academic studies using ITT?  One can only hope not.  Consider the analysis by Newell  of the Coronary Artery Bypass Surgery (CABS) trial.  This paper is astounding for its blanket, tendentious insistence on what is correct without any logical argument.  Newell considers that the method of

 “the CABS research team was impeccable. They refused to do an ‘as treated’ analysis: ‘We have refrained from comparing all patients actually operated on with all not operated on: this does not provide a measure of the value of surgery.”

Translation: results of surgery do not provide a measure of the value of surgery.  So, in the CABS trial, patients were assigned to Medicine or Surgery. The actual method used and the outcomes are shown in the Table below. Intention-to-treat analysis was, as described by Newell, “used, correctly.” Looking at the table, you can see that a 7.8% mortality was found in those assigned to receive medical treatment (29 people out of 373 died), and a 5.3% mortality (21 deaths out of 371) for assignment to surgery.  If you look at the outcomes of each modality as actually used, it turns out that that medical treatment had a 9.5% (33/349) mortality rate compared with 4.1% (17/419) for surgery, an analysis that Newell says “would have wildly exaggerated the apparent value of surgery.”

Survivors and deaths after allocation to surgery or medical treatment
Allocated medicine Allocated surgery
  Received surgery     Received medicine   Received surgery     Received medicine
Survived 2 years   48   296   354   20
Died    2    27    15    6
Total   50   323   369   26

Common sense suggests that appearances are not deceiving. If you were one of the 33-17 = 16 people who were still alive, you would think that it was the potential report of your death that had been exaggerated.  The thing that is under the control of the patient and the physician, and which is not a feature of the particular modality, is getting the surgery implemented. Common sense dictates that a patient is interested in surgery, not the effect of being told that surgery is good.  The patient has a right to expect that if they comply, the physician would avoid conditions where, as stated by Hollis,  “most types of deviations from protocol would continue to occur in routine practice.” The idea that “Intention to treat analysis is … most suitable for pragmatic trials of effectiveness rather than for explanatory investigations of efficacy” assumes that practical considerations are the same everywhere and that any practitioner is locked into the same abilities or lack of abilities as the original experimenter.

What is the take home message.  One general piece of advice that I would give based on this discussion in the medical literature: don’t get sick.

Why you should care.  Case II. The effect of vitamin E supplementation

A clear cut case of how off-the-mark ITT can be is a report on the value of antioxidant supplements. The Abstract of the paper concluded that “there were no overall effects of ascorbic acid, vitamin E, or beta carotene on cardiovascular events among women at high risk for CVD.” The study was based on an ITT analysis but,on the fourth page of the paper, it turns out that removing subjects due to

“noncompliance led to a significant 13% reduction in the combined end point of CVD morbidity and mortality… with a 22% reduction in MI …, a 27% reduction in stroke …. a 23% reduction in the combination of MI, stroke, or CVD death (RR (risk ratio), 0.77; 95% CI, 0.64–0.92 [P = 005]).”

The media universally reported the conclusion from the Abstract, namely that there was no effect of vitamin E. This conclusion is correct if you think that you can measure the effect of vitamin E without taking the pill out of the bottle.  Does this mean that vitamin E is really of value? The data would certainly be accepted as valuable if the statistics were applied to a study of the value of replacing barbecued pork with whole grain cereal. Again, “no effect” was the answer to the question: “what happens if you are told to take vitamin E” but it still seems is reasonable that the effect of a vitamin means the effect of actually taking the vitamin.

The ITT controversy

Advocates of ITT see its principles as established and may dismiss a common sense approach as naïve. The issue is not easily resolved; statistics is not axiomatic: there is no F=ma, there is no zeroth law.  A good statistics book will tell you in the Introduction that what we do in statistics is to try to find a way to quantify our intuitions. If this is not appreciated, and you do not go back to consideration of exactly what the question is that you are asking, it is easy to develop a dogmatic approach and insist on a particular statistic because it has become standard.

As I mentioned above, I had a good deal of trouble getting my original paper published and one  anonymous reviewer said that “the arguments presented by the author may have applied, maybe, ten or fifteen years ago.” This criticism reminded me of Molière’s Doctor in Spite of Himself:

Sganarelle is disguised as a doctor and spouts medical double-talk with phony Latin, Greek and Hebrew to impress the client, Geronte, who is pretty dumb and mostly falls for it but:

Geronte: …there is only one thing that bothers me: the location of the liver and the heart. It seemed to me that you had them in the wrong place: the heart is on the left side but the liver is on the right side.

Sgnarelle: Yes. That used to be true but we have changed all that and medicine uses an entirely new approach.

Geronte: I didn’t know that and I beg your pardon for my ignorance.

 In the end, it is reasonable that scientific knowledge be based on real observations. This has never before been thought to include data that was not actually in the experiment. I doubt that nous avons changé tout cela.

“Dost thou think, because thou art virtuous, there shall be no more cakes and ale?”

— William Shakespeare, Twelfth Night.

Experts on nutrition are like experts on sexuality.  No matter how professional they are in general, in some way they are always trying to justify their own lifestyle.  Theyo share a tendency to think that their own lifestyle is the one that everybody else should follow and they are always eager to save us from our own sins, sexual or dietary. The new puritans want to save us from red meat. It is unknown whether Michael Pollan’s In Defense of Food was reporting the news or making the news but it’s coupling of not eating too much and not eating meat is common.  More magazine’s take on saturated fat was very sympathetic to my own point of view and I probably shouldn’t complain that tacked on at the end was the conclusion that “most physicians will probably wait for more research before giving you carte blanche to order juicy porterhouse steaks.” I’m not sure that my physician knows about the research that already exists or that I am waiting for his permission on a zaftig steak.

Daily Red Meat Raises Chances Of Dying Early” was the headline in the Washington Post last year. This scary story was accompanied by the photo below. The gloved hand slicing roast beef with a scalpel-like instrument was probably intended to evoke CSI autopsy scenes, although, to me, the beef still looked pretty good if slightly over-cooked.  I don’t know the reporter, Rob Stein, but I can’t help feeling that we’re not talking Woodward and Bernstein here.  For those too young to remember Watergate, the reporters from the Post were encouraged to “follow the money” by Deep Throat, their anonymous whistle-blower. A similar character, claiming to be an insider and  identifying himself or herself as “Fat Throat,” has been sending intermittent emails to bloggers, suggesting that they “follow the data.”

The Post story was based on a research report “Meat Intake and Mortality” published in the medical journal, Archives of Internal Medicine by Sinha and coauthors.  It got a lot of press and had some influence and recently re-surfaced in the Harvard Men’s Health Watch in a two part article called, incredibly enough, “Meat or beans: What will you have?” (The Health Watch does admit that “red meat is a good source of iron and protein and…beans can trigger intestinal gas” and that they are “very different foods”) but somehow it is assumed that we can substitute one for the other.

Let me focus on Dr. Sinha’s article and try to explain what it really says.  My conclusion will be that there is no reason to think that any danger of red meat has been demonstrated and I will try to point out some general ways in which one can deal with these kinds of reports of scientific information.

A few points to remember first.  During the forty years that we describe as the obesity and diabetes epidemic, protein intake has been relatively constant; almost all of the increase in calories has been due to an increase in carbohydrates; fat, if anything, went down. During this period, consumption of almost everything increased.  Wheat and corn, of course went up.  So did fruits and vegetables and beans.  The two things whose consumption went down were red meat and eggs.  In other words there is some a priori reason to think that red meat is not a health risk and that the burden of proof should be on demonstrating harm.  Looking ahead, the paper, like analysis of the population data, will rely entirely on associations.

The conclusion of the study was that “Red and processed meat intakes were associated with modest increases in total mortality, cancer mortality, and cardiovascular disease mortality.”  Now, modest increase in mortality is a fairly big step down from “Dying Early,” and surely a step-down from the editorial quoted in the Washington Post.  Written by Barry Popkin, professor of global nutrition at the University of North Carolina it said: “This is a slam-dunk to say that, ‘Yes, indeed, if people want to be healthy and live longer, consume less red and processed meat.'” Now, I thought that the phrase “slam-dunk” was pretty much out after George Tenet, head of the CIA, told President Bush that the Weapons of Mass Destruction in Iraq was a slam-dunk.  I found an interview after his resignation quite disturbing; when the director of the CIA can’t lie convincingly, we are in big trouble.  And quoting Barry Popkin is like getting a second opinion from a member of the “administration.” It’s definitely different from investigative reporting like, you know, reading the article.

So what does the research article really say?  As I mentioned in my blog on eggs, when I read a scientific paper, I look for the pictures. The figures in a scientific paper usually make clear to the reader what is going on — that is the goal of scientific communication.  But there are no figures.  With no figures, Dr. Sinha’s research paper has to be analyzed for what it does have: a lot of statistics.  Many scientists share Mark Twain’s suspicion of statistics, so it is important to understand how it is applied.  A good statistics book will have an introduction that says something like “what we do in statistics, is try to put a number on our intuition.”  In other words, it is not really, by itself, science.  It is, or should be, a tool for the experimenter’s use. The problem is that many authors of papers in the medical literature allow statistics to become their master rather than their servant: numbers are plugged into a statistical program and the results are interpreted in a cut-and-dried fashion with no intervention of insight or common sense. On the other hand, many medical researchers see this as an impartial approach. So let it be with Sinha.

What were the outcomes? The study population of 322, 263 men and 223, 390 women was broken up into five groups (quintiles) according to meat consumption, the highest taking in about 7 times as much as the lower group (big differences).  The Harvard News Letter says that the men who ate the most red meat had a 31 % higher death rate than the men who ate the least meat.  This sounds serious but does it tell you what you want to know? In the media, scientific results are almost universally reported this way but it is entirely misleading.  To be fair, the Abstract of the paper itself reported this as a hazard ratio of 1.31 which, while still misleading, is less prejudicial. Hazard ratio is a little bit complicated but, in the end, it is similar to odds ratio or risk ratio which is pretty much what you think: an odds ratio of 2 means you’re twice as likely to win with one strategy as compared to the other.  A moment’s thought tells you that this is not good information because you can get an odds ratio of 2, that is, you can double your chances of winning the lottery, by buying two tickets instead of one.  You need to know the actual odds of each strategy.  Taking the ratio hides information.  Do reporters not know this?  Some have told me they do but that their editors are trying to gain market share and don’t care.  Let me explain it in detail.  If you already understand, you can skip the next paragraph.

A trip to Las Vegas

Taking the hazard ratio as more or less the same as odds ratio or risk ratio, let’s consider applying odds.  We are in Las Vegas and it turns out that there are two black-jack tables and, for some reason (different number of decks or something), the odds are different at the two tables.  Table 1 pays out on average once every 100 hands.  Table 2 pays out once in 67 hands. The odds are 1/100 or one in a hundred at the first table and 1/67 at the second.  The odds ratio is, obviously the ratio of the two odds or 1/67 divided by 1/00 or about 1.31.  (The odds ratio would be 1 if there were no difference between the two tables).

Right off, something is wrong: if you were just given the odds ratio you would have lost some important  information.  The odds ratio tells you that one gambling table is definitely better than the other but you need additional information to find out that the odds aren’t particularly good at either table: technically, information about the absolute risk was lost.

So knowing the odds ratio by itself is not much help.  But since we know the absolute risk of each table, does that help you decide which table to play?  Well, it depends who you are. For the guy who is at the blackjack table when you go up to your room to go to sleep and who is still sitting there when you come down for the breakfast buffet, things are going to be much better off at the second table.  He will play hundreds of hands and the better odds ratio of 1.31 will pay off in the long run.  Suppose, however, that you are somebody who will take the advice of my cousin the statistician who says to just go and play one hand for the fun of it, just to see if the universe really loves you (that’s what gamblers are really trying to find out).  You’re going to play the hand and then, win or lose, you are going to go do something else.  Does it matter which table you play at?  Obviously it doesn’t.  The odds ratio doesn’t tell you anything useful because you know that your chances of winning are pretty slim either way.

Now going over to the Red Meat article the hazard ratio (again, roughly the odds ratio) between high and low red meat intakes for all-cause mortality for men, for example, is 1.31 or, as they like to report in the media 31 % higher risk of dying which sounds pretty scary.  But what is the absolute risk?  To find that we have to find the actual number of people who died in the high red meat quintile and the low end quintile.  This is easy for the low end: 6,437 people died from the group of  64,452, so the odds of  dying are 6,437/64,452 or just about 0.10 or 10 %.  It’s a little trickier for the high red meat consumers.  There, 13,350 died.  Again,  dividing that by the number in that group, we find an absolute risk of 0.21 or 21 % which seems pretty high and the absolute difference in risk is an increase of 10 % which still seems pretty significant.  Or is it?  In these kinds of studies, you have to ask about confounders, variables that might bias the results.  Well, here, it is not hard to find.  Table 1 reveals that the high red meat group had 3 times the number of smokers. (Not 31 % more but 3 times more).  So the authors corrected the data for this and other effects (education, family history of cancer, BMI, etc.) which is how the final a value of 1.31 was obtained.  Since we know the absolute value of risk in the lowest red meat group, 0.1 we can calculate the risk in the highest red meat group which will be 0.131.  The absolute increase in risk from eating red meat, a lot more red meat, is then 0.131 – 0.10 = 0.031 or 3.1 % which is quite a bit less than we thought.

Now, we can see that the odds ratio of 1.31 is not telling us much — and remember this is for big changes, like 6 or 7 times as much meat; doubling red meat intake (quintiles 1 and 2) leads to a hazard ratio of 1.07.  What is a meaningful odds ratio?  For comparison, the odds ratio for smoking vs not smoking for incidence of lung disease is about 22.

Well, 3.1 % is not much but it’s something.  Are we sure?  Remember that this is a statistical outcome and that means that some people in the high red meat group had lower risk, not higher risk.  In other words, this is what is called statistically two-tailed, that is, the statistics reflect changes that go both ways.  What is the danger in reducing meat intake.  The data don’t really tell you that.  Unlike cigarettes, where there is little reason to believe that anybody’s lungs really benefit from cigarette smoke (and the statistics are due to random variation), we know that there are many benefits to protein especially if it replaces carbohydrate in the diet, that is, the variation may be telling us something real.  With odds ratios around 1.31 — again, a value of 1 means that there is no difference — you are almost as likely to benefit from adding red meat as you are reducing it.  The odds still favor things getting worse but it really is a risk in both directions. You are at the gaming tables.  You don’t get your chips back. If reducing red meat does not reduce your risk, it may increase it.  So much for the slam dunk.

What about public health? Many people would say that for a single person, red meat might not make a difference but if the population reduced meat by half, we would save thousands of lives.  The authors do want to do this.  At this point, before you and your family take part in a big experiment to save health statistics in the country, you have to ask how strong the relations are.  To understand the quality of the data, you must look for things that would not be expected to have a correlation.  “There was an increased risk associated with death from injuries and sudden death with higher consumption of red meat in men but not in women.”  The authors dismiss this because the numbers were smaller (343 deaths) but the whole study is about small differences and it sounds like we are dealing with a good deal of randomness.  Finally, the authors set out from the start to investigate red meat.  To be fair, they also studied white meat which was slightly beneficial. But what are we to compare the meat results to? Why red meat?  What about potatoes?  Cupcakes?   Breakfast cereal?  Are these completely neutral? If we ran these through the same computer, what would we see?  And finally there is the elephant in the room: carbohydrate. Basic biochemistry suggests that a roast beef sandwich may have a different effect than roast beef in a lettuce wrap.

So I’ve given you the perspective of a biochemistry professor.  This was a single paper and surely not the worst, but I think it’s not really about science.  It’s about sin.

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Nutrition & Metabolism Society