Archive for the ‘Association and Causality’ Category

“…789 deaths were reported in Doll and Hill’s original cohort. Thirty-six of these were attributed to lung cancer. When these lung cancer deaths were counted in smokers versus non-smokers, the correlation virtually sprang out: all thirty-six of the deaths had occurred in smokers. The difference between the two groups was so significant that Doll and Hill did not even need to apply complex statistical metrics to discern it. The trial designed to bring the most rigorous statistical analysis to the cause of lung cancer barely required elementary mathematics to prove his point.”

Siddhartha Mukherjee —The Emperor of All Maladies.

 Scientists don’t like philosophy of science. It is not just that pompous phrases like hypothetico-deductive systems are such a turn-off but that we rarely recognize it as what we actually do. In the end, there is no definition of science and it is hard to generalize about actual scientific behavior. It’s a human activity and precisely because it puts a premium on creativity, it defies categorization. As the physicist Steven Weinberg put it, echoing Justice Stewart on pornography:

“There is no logical formula that establishes a sharp dividing line between a beautiful explanatory theory and a mere list of data, but we know the difference when we see it — we demand a simplicity and rigidity in our principles before we are willing to take them seriously [1].”

A frequently stated principle is that “observational studies only generate hypotheses.” The related idea that “association does not imply causality” is also common, usually cited by those authors who want you to believe that the association that they found does imply causality. These ideas are not right or, at least, they insufficiently recognize that scientific experiments are not so easily wedged into categories like “observational studies.”  The principles are also invoked by bloggers and critics to discredit the continuing stream of observational studies that make an association between their favorite targets, eggs, red meat, sugar-sweetened soda and a metabolic disease or cancer. In most cases, the studies are getting what they deserve but the bills of indictment are not quite right.  It is usually not simply that they are observational studies but rather that they are bad observational studies and, in any case, the associations are so weak that it is reasonable to say that they are an argument for a lack of causality. On the assumption that good experimental practice and interpretation can be even roughly defined, let me offer principles that I think are a better representation, insofar as we can make any generalization, of what actually goes on in science:

 Observations generate hypotheses. 

Observational studies test hypotheses.

Associations do not necessarily imply causality.

In some sense, all science is associations. 

Only mathematics is axiomatic.

 If you notice that kids who eat a lot of candy seem to be fat, or even if you notice that candy makes you yourself fat, that is an observation. From this observation, you might come up with the hypothesis that sugar causes obesity. A test of your hypothesis would be to see if there is an association between sugar consumption and incidence of obesity. There are various ways — the simplest epidemiologic approach is simply to compare the history of the eating behavior of individuals (insofar as you can get it) with how fat they are. When you do this comparison you are testing your hypothesis. There are an infinite number of things that you could have measured as an independent variable, meat, TV hours, distance from the French bakery but you have a hypothesis that it was candy. Mike Eades described falling asleep as a child by trying to think of everything in the world. You just can’t test them all. As Einstein put it “your theory determines the measurement you make.”

Associations predict causality. Hypotheses generate observational studies, not the other way around.

In fact, association can be strong evidence for causation and frequently provide support for, if not absolute proof, of the idea to be tested. A correct statement is that association does not necessarily imply causation. In some sense, all science is observation and association. Even thermodynamics, that most mathematical and absolute of sciences, rests on observation. As soon as somebody observes two systems in thermal equilibrium with a third but not with each other (zeroth law), the jig is up. When somebody builds a perpetual motion machine, that’s it. It’s all over.

Biological mechanisms, or perhaps any scientific theory, are never proved. By analogy with a court of law, you cannot be found innocent, only not guilty. That is why excluding a theory is stronger than showing consistency. The grand epidemiological study of macronutrient intake vs diabetes and obesity shows that increasing carbohydrate is associated with increased calories even under conditions where fruits and vegetables also went up and fat, if anything went down. It is an observational study but it is strong because it gives support to a lack of causal effect of increased carbohydrate and decreased fat on outcome. The failure of total or saturated fat to have any benefit is the kicker here. It is now clear that prospective experiments have, in the past, and will continue to show, the same negative outcome. Of course, in a court of law, if you are found not guilty of child abuse, people may still not let you move into their neighborhood. It is that saturated fat should never have been indicted in the first place.

An association will tell you about causality 1) if the association is strong and 2) if there is a plausible underlying mechanism and 3) if there is no more plausible explanation — for example, countries with a lot of TV sets have modern life styles that may predispose to cardiovascular disease; TV does not cause CVD.

Re-inventing the wheel. Bradford Hill and the history of epidemiology.

Everything written above is true enough or, at least, it seemed that way to me. I thought of it as an obvious description of what everybody knows. The change to saying that “association does not necessarily imply causation” is important but not that big a deal. It is common sense or logic and I had made it into a short list of principles. It was a blogpost of reasonable length. I described it to my colleague Gene Fine. His response was “aren’t you re-inventing the wheel?” Bradford Hill, he explained, pretty much the inventor of modern epidemiology, had already established these and a couple of other principles. Gene cited The Emperor of All Maladies, an outstanding book on the history of cancer.  I had read The Emperor of All Maladies on his recommendation and I remembered Bradford Hill and the description of the evolution of the ideas of epidemiology, population studies and random controlled trials. I also had a vague memory, of reading the story in James LeFanu’s The Rise and Fall of Modern Medicine, another captivating history of medicine. However, I had not really absorbed these as principles. Perhaps we’re just used to it, but saying that an association implies causality only if it is a strong association is not exactly a scientific breakthrough. It seems an obvious thing that you might say over coffee or in response to somebody’s blog. It all reminded me of learning, in grade school, that the Earl of Sandwich had invented the sandwich and thinking “this is an invention?”  Woody Allen thought the same thing and wrote the history of the sandwich and the Earl’s early failures — “In 1741, he places bread on bread with turkey on top. This fails. In 1745, he exhibits bread with turkey on either side. Everyone rejects this except David Hume.”

At any moment in history our background knowledge — and accepted methodology —  may be limited. Some problems seem to have simple solutions. But simple ideas are not always accepted. The concept of the random controlled trial (RCT), obvious to us now, was hard won and, proving that any particular environmental factor — diet, smoking, pollution or toxic chemicals was the cause of a disease and that, by reducing that factor, the disease could be prevented, turned out to be a very hard sell, especially to physicians whose view of disease may have been strongly colored by the idea of an infective agent.

Hill_CausationThe Rise and Fall of Modern Medicine describes Bradford Hill’s two demonstrations that streptomycin in combination with PAS (para-aminosalicylic acid) could cure tuberculosis and that tobacco causes lung cancer as one of the Ten Definitive Moments in the history of modern medicine (others shown in the textbox). Hill was Professor of Medical Statistics at the London School of Hygiene and Tropical Medicine but was not formally trained in statistics and, like many of us, thought of proper statistics as common sense. An early near fatal case of tuberculosis also prevented formal medical education. His first monumental accomplishment was, ironically, to demonstrate how tuberculosis could be cured with the combination of streptomycin and PAS.  In 1941, Hill and co-worker Richard Doll undertook a systematic investigation of the risk factors for lung cancer. His eventual success was accompanied by a description of the principles that allow you to say when association can be taken as causation.

 Ten Definitive Moments from Rise and Fall of Modern Medicine.

1941: Penicillin

1949: Cortisone

1950: streptomycin, smoking and Sir Austin Bradford Hill

1952: chlorpromazine and the revolution in psychiatry

1955: open-heart surgery – the last frontier

1963: transplanting kidneys

1964: the triumph of prevention – the case of strokes

1971: curing childhood cancer

1978: the first ‘Test-Tube’ baby

1984: Helicobacter – the cause of peptic ulcer

Wiki says: “in 1965, built  upon the work of Hume and Popper, Hill suggested several aspects of causality in medicine and biology…” but his approach was not formal — he never referred to his principles as criteria — he recognized them as common sense behavior and his 1965 presentation to the Royal Society of Medicine, is a remarkably sober, intelligent document. Although described as an example of an article that, as here, has been read more often in quotations and paraphrases, it is worth reading the original even today.

Note: “Austin Bradford Hill’s surname was Hill and he always used the name Hill, AB in publications. However, he is often referred to as Bradford Hill. To add to the confusion, his friends called him Tony.” (This comment is from Wikipedia, not Woody Allen).

The President’s Address

Bradford Hill’s description of the factors that might make you think an association implied causality:

Hill_Environment1965

1. Strength. “First upon my list I would put the strength of the association.” This, of course, is exactly what is missing in the continued epidemiological scare stories. Hill describes

“….prospective inquiries into smoking have shown that the death rate from cancer of the lung in cigarette smokers is nine to ten times the rate in non-smokers and the rate in heavy cigarette smokers is twenty to thirty times as great.”

But further:

“On the other hand the death rate from coronary thrombosis in smokers is no more than twice, possibly less, the death rate in nonsmokers. Though there is good evidence to support causation it is surely much easier in this case to think of some features of life that may go hand-in-hand with smoking – features that might conceivably be the real underlying cause or, at the least, an important contributor, whether it be lack of exercise, nature of diet or other factors.”

Doubts about an odds ratio of two or less. That’s where you really have to wonder about causality. The progression of epidemiologic studies that tell you red meat, HFCS, etc. will cause diabetes, prostatic cancer, or whatever, these rarely hit an odds ratio of 2.  While the published studies may contain disclaimers of the type in Hill’s paper, the PR department of the university where the work is done, and hence the public media, show no such hesitation and will quickly attribute causality to the study as if the odds ratio were 10 instead of 1.2.

2. Consistency: Hill listed the repetition of the results in other studies under different circumstances as a criterion for considering how much an association implied causality. Not mentioned but of great importance, is that this test cannot be made independent of the first criterion. Consistently weak associations do not generally add up to a strong association. If there is a single practice in modern medicine that is completely out of whack with respect to careful consideration of causality, it is the meta-analysis where studies with no strength at all are averaged so as to create a conclusion that is stronger than any of its components.

3. Specificity. Hill was circumspect on this point, recognizing that we should have an open mind on what causes what. On specificity of cancer and cigarettes, Hill noted that the two sites in which he showed a cause and effect relationship were the lungs and the nose.

4. Temporality: Obviously, we expect the cause to precede the effect or, as some wit put it “which got laid first, the chicken or the egg.”  Hill recognized that it was not so clear for diseases that developed slowly. “Does a particular diet lead to disease or do the early stages of the disease lead to those peculiar dietetic habits?” Of current interest are the epidemiologic studies that show a correlation between diet soda and obesity which are quick to see a causal link but, naturally, one should ask “Who drinks diet soda?”

5. Biological gradient:  the association should show a dose response curve. In the case of cigarettes, the death rate from cancer of the lung increases linearly with the number of cigarettes smoked. A subset of the first principle, that the association should be strong, is that the dose-response curve should have a meaningful slope and, I would add, the numbers should be big.

6. Plausibilityy: On the one hand, this seems critical — the association of egg consumption with diabetes is obviously foolish — but the hypothesis to be tested may have come from an intuition that is far from evident. Hill said, “What is biologically plausible depends upon the biological knowledge of the day.”

7. Coherence: “data should not seriously conflict with the generally known facts of the natural history and biology of the disease”

8. Experiment: It was another age. It is hard to believe that it was in my lifetime. “Occasionally it is possible to appeal to experimental, or semi-experimental, evidence. For example, because of an observed association some preventive action is taken. Does it in fact prevent?” The inventor of the random controlled trial would be amazed how many of these are done, how many fail to prevent. And, most of all, he would have been astounded that it doesn’t seem to matter. However, the progression of failures, from Framingham to the Women’s Health Initiative, the lack of association between low fat, low saturated fat and cardiovascular disease, is strong evidence for the absence of causation.

9. Analogy: “In some circumstances it would be fair to judge by analogy. With the effects of thalidomide and rubella before us we would surely be ready to accept slighter but similar evidence with another drug or another viral disease in pregnancy.”

Hill’s final word on what has come to be known as his criteria for deciding about causation:

“Here then are nine different viewpoints from all of which we should study association before we cry causation. What I do not believe — and this has been suggested — is that we can usefully lay down some hard-and-fast rules of evidence that must be obeyed before we accept cause and effect. None of my nine viewpoints can bring indisputable evidence for or against the cause-and-effect hypothesis and none can be required as a sine qua non. What they can do, with greater or less strength, is to help us to make up our minds on the fundamental question – is there any other way of explaining the set of facts before us, is there any other answer equally, or more, likely than cause and effect?” This may be the first critique of the still-to-be-invented Evidence-based Medicine.

Nutritional Epidemiology.

The decision to say that an observational study implies causation is equivalent to an assertion that the results are meaningful, that it is not a random association at all, that it is scientifically sound. Critics of epidemiological studies have relied on their own perceptions and appeal to common sense and when I started this blogpost, I was one of them, and I had not appreciated the importance of Bradford Hill’s principles. The Emperor of All Maladies described Hill’s strategies for dealing with association and causation “which have remained in use by epidemiologists to date.”  But have they? The principles are in the texts. Epidemiology, Biostatistics, and Preventive Medicine has a chapter called “The study of causation in Epidemiologic Investigation and Research” from which the dose-response curve was modified. Are these principles being followed? Previous posts in this blog and others have have voiced criticisms of epidemiology as it’s currently practiced in nutrition but we were lacking a meaningful reference point. Looking back now, what we see is a large number of research groups doing epidemiology in violation of most of Hill’s criteria.

The red meat scare of 2011 was Pan, et al and I described in a previous post, the remarkable blog from Harvard . Their blog explained that the paper was unnecessarily scary because it had described things in terms of “relative risks, comparing death rates in the group eating the least meat with those eating the most. The absolute risks… sometimes help tell the story a bit more clearly. These numbers are somewhat less scary.”  I felt it was appropriate to ask “Why does Dr. Pan not want to tell the story as clearly as possible?  Isn’t that what you’re supposed to do in science? Why would you want to make it scary?” It was, of course, a rhetorical question.

Looking at Pan, et al. in light of Bradford Hill, we can examine some of their data. Figure 2 from their paper shows the risk of diabetes as a function of red meat in the diet. The variable reported is the hazard ratio which can be considered roughly the same as the odds ratio, that is, relative odds of getting diabetes. I have indicated, in pink, those values that are not statistically significant and I grayed out the confidence interval to make it easy to see that these do not even hit the level of 2 that Bradford Hill saw as some kind of cut-off.

TheBlog_Cause_Pan_Fig2_

The hazard ratios for processed meat are somewhat higher but still less than 2. This is weak data and violates the first and most important of Hill’s criteria. As you go from quartile 2 to 3, there is an increase in risk, but at Q4, the risk goes down and then back up at Q5, in distinction to principle 5 which suggests the importance of dose-response curves. But, stepping back and asking what the whole idea is, asking why you would think that meat has a major — and isolatable role separate from everything else — in a disease of carbohydrate intolerance, you see that this is not rational, this is not science. And Pan is not making random observations. This is a test of the hypothesis that red meat causes diabetes. Most of us would say that it didn’t make any sense to test such a hypothesis but the results do not support the hypothesis.

What is science?

Science is a human activity and what we don’t like about philosophy of science is that it is about the structure and formalism of science rather than what scientists really do and so there aren’t even any real definitions. One description that I like, from a colleague at the NIH: “What you do in science, is you make a hypothesis and then you try to shoot yourself down.” One of the more interesting sidelights on the work of Hill and Doll, as described in Emperor, was that during breaks from the taxing work of analyzing the questionnaires that provided the background on smoking, Doll himself would step out for a smoke. Doll believed that cigarettes were unlikely to be a cause — he favored tar from paved highways as the causative agent — but as the data came in, “in the middle of the survey, sufficiently alarmed, he gave up smoking.” In science, you try to shoot yourself down and, in the end, you go with the data.

Doctor:    Therein the patient

  Must minister to himself.

Macbeth: Throw physic [medicine] to the dogs; I’ll none of it.

— William Shakespeare, Macbeth

The quality of nutrition papers even in the major scientific and medical journals is so variable and the lack of restraint in the popular media is so great that it is hard to see how the general public or even scientists can find out anything at all. Editors and reviewers are the traditional gate-keepers in science but in an area where rigid dogma has reached Galilean proportions, it is questionable that any meaningful judgement was made: it is easy to publish papers that conform to the party line (“Because of the deleterious effects of dietary fructose, we hypothesized that…”) and hard to publish others: when JAMA published George Bray’s “calorie-is-a-calorie” paper and I pointed out that the study more accurately supported the importance of carbohydrate as a controlling variable, the editor declined to publish my letter.  In this, the blogs have performed a valuable service in providing an alternative POV but if the unreliability is a problem in the scientific literature, that problem is multiplied in internet sources. In the end, the consumer may feel that they are pretty much out there on their own. I will try to help.  The following was posted on FatHead’s Facebook page:

 How does one know if a study is ‘flawed’? I see a lot of posts on here that say a lot of major studies are flawed. How? Why? What’s the difference if I am gullible and believe all the flawed studies, or if I (am hopefully not a sucker) believe what the Fat Heads are saying and not to believe the flawed studies — eat bacon.

Where are the true studies that are NOT flawed…. and how do I differentiate? : /

 My comment was that it was a great question and that it would be in the next post so I will try to give some of the principles that reviewers should adhere to.  Here’s a couple of guides to get started. More in future posts:

 1“Healthy” (or “healthful”) is not a scientific term. If a study describes a diet as “healthy,” it is almost guaranteed to be a flawed study.  If we knew which diets were “healthy,” we wouldn’t have an obesity epidemic. A good example is the paper by Appel, et al. (2005). “Effects of protein, monounsaturated fat, and carbohydrate intake on blood pressure and serum lipids: results of the OmniHeart randomized trial,” whose conclusion is:

“In the setting of a healthful diet, partial substitution of carbohydrate with either protein or monounsaturated fat can further lower blood pressure, improve lipid levels, and reduce estimated cardiovascular risk.”

 It’s hard to know how healthful the original diet, a “carbohydrate-rich diet used in the DASH trials … currently advocated in several scientific reports” really is if removing carbohydrate improved everything.

Generally, understatement  is good.  One of the more famous is from Watson & Cricks’s 1953 paper in which they proposed the DNA double helix structure. They said “It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material.”  A study with the word “healthy” is an infomercial.

2. Look for the pictures (figures).  Presentation in graphic form usually means the author wants to explain things to you, rather than snow you.  This is part of the Golden Rule of Statistics that I mentioned in my blogpost “The Seventh Egg”  which discusses a very flawed study from Harvard on egg consumption. The rule comes from the book PDQ Statistics:

“The important point…is that the onus is on the author to convey to the reader an accurate impression of what the data look like, using graphs or standard measures, before beginning the statistical shenanigans.  Any paper that doesn’t do this should be viewed from the outset with considerable suspicion.”

The Watson-Crick  paper cited above had the diagram of the double-helix  which essentially became the symbol of modern biology.  It was drawn by Odile, Francis’s wife, who is described as being famous for her nudes, only one of which I could find on the internet.

Krauss, et. al. Separate effects of reduced carbohydrate intake and weight loss on atherogenic dyslipidemia.

The absence of a figure may indicate that the authors are not giving you a chance to actually see the results, that is, the experiment may not be flawed but the interpretation may be misleading, intentionally or otherwise.  An important illustration of the principle is a paper published by Krauss. It is worth looking at this paper in detail because the experimental work is very good and the paper directly — or almost directly — confronts a big question in diet studies: when you reduce calories by cutting out carbohydrate, is the effect due simply  to lowering calories or is there a specific effect of carbohydrate restriction.  The problem is important since many studies compare low-carbohydrate and low-fat diets where calories are reduced on both. Because the low-carbohydrate diet generally has the better weight loss and better improvement in HDL and triglycerides, it is said that it was the weight loss that caused the lipid improvements.

So Krauss compared the effects of carbohydrate restriction and weight loss on the collection of lipid markers known collectively as atherogenic dyslipidemia.  The markers of atherogenic dyslipidemia, which are assumed to predispose to cardiovascular disease, include high triglycerides (triacylglycerol), low HDL and high concentrations of the small dense LDL.

Here is how the experiment was set up: subjects first consumed a baseline diet of  54% of energy as carbohydrate, for 1 week. They were then assigned to one of four groups.  Either they continued the baseline diet, or they kept calories constant but reduced carbohydrate by putting fat in its place.  The three lower carbohydrate diets had 39 % or 26 % carbohydrate or 26 % carbohydrate with higher saturated fat.  After 3 weeks on constant calories but reduced carbohydrate, calories were decreased by 1000 kcal/d for 5 week and, finally, energy was stabilized for 4 weeks and the features of atherogenic dyslidemia were measured at week 13.  The protocol is shown in the figure from Krauss’s paper:

The Abstract of the paper describes the outcomes and the authors’ conclusions.

Results: The 26%-carbohydrate, low-saturated-fat diet reduced [atherogenic dylipidemia]. These changes were significantly different from those with the 54%-carbohydrate diet. After subsequent weight loss, the changes in all these variables were significantly greater…(my italics)

 Conclusions: Moderate carbohydrate restriction and weight loss provide equivalent but non-additive approaches to improving atherogenic dyslipidemia. Moreover, beneficial lipid changes resulting from a reduced carbohydrate intake were not significant after weight loss.

Now there is something odd about this.  It is the last line of the conclusion that is really weird. If you lose weight, the effect of carbohydrate is not significant?  As described below, Jeff Volek and I re-analyzed this paper so I have read that line a dozen times and I have no idea what it means.  In fact, the whole abstract is strange.  It will turn out that the lower (26 %) is certainly “significantly different from.. the 54%-carbohydrate diet” but it is not just different but much better. Why would you not say that?  The Abstract is generally written so that it sounds negative about low carbohydrate effects but it is already known from Krauss’s previous work and others that carbohydrate restriction has a beneficial effect on lipids and the improvements in lipid markers occur on low-carbohydrate diets whether weight is lost or not.  The last sentence doesn’t seem to make any sense at all.    For one thing, the experiment wasn’t done that way.  As set up, weight loss came after carbohydrate restriction.  So, let’s look at the data in the paper.  There are few figures in the paper and Table 2 in the paper presents the results in a totally mind-numbing layout.  Confronted with data like this, I sometimes stop reading.  After all, if the author doesn’t want to conform to the Golden Rule of Statistics, if they don’t want to really explain what they accomplished, how much impact is the paper going to have.  In this case, however, it is clear that the experiment was designed correctly and it just seems impossible from previous work that this wouldn’t support the benefits of carbohydrate restriction and the negative tone of the Abstract needs to be explained.  So we all had to slog through those tables.  Let’s just look at the triglycerides since this is one of the more telling attributes of atherogenic dyslpidemia.  Here’s the section from the Table:

Well this looks odd in that the biggest change is in the lowest carb group with high SF but it’s hard to tell what the data look like.  First it is reported as logarithms. You sometime take logs of your data in order to do a statistical determination but that doesn’t change the data and it is better to report the actual value.  In any case, it’s easy enough to take antilogs and we can plot the data.  This is what it looks like:

It’s not hard to see what the data really show: Reducing carbohydrate has an overwhelming effect on triglycerides even without weight loss.  When weight loss is introduced, the high carbohydrate diets still can’t equal the performance of the carbohydrate reduction phase.  (The dotted line in the figure are data from Volek’s earlier work which Krauss forgot to cite).

The statements in the Conclusion from the Abstract are false and totally misrepresent the data.  It is not true as it says “carbohydrate restriction and weight loss provide equivalent…” effects. The carbohydrate-reduction phase is dramatically better than the calorie restriction phase and it is not true that they are “non-additive”  Is this an oversight?  Poor writing?  Well, nobody knows what Krauss’s motivations were but Volek and I plotted all of the data from Krauss’s paper and we published a paper in Nutrition & Metabolism providing an interpretation of Krauss’s work (with pictures).  Our conclusion:

Summary Although some effort is required to disentangle the data and interpretation, the recent publication from Krauss et al. should be recognized as a breakthrough. Their findings… make it clear that the salutary effects of CR on dyslipidemia do not require weight loss, a benefit that is not a feature of strategies based on fat reduction. As such, Krauss et al.  provides one of the strongest arguments to date for CR as a fundamental approach to diet, especially for treating atherogenic dyslipidemia.

An important question in this experiment, however, is whether even in the calorie reduction phase, calories are actually the important variable.  This is a general problem in calorie restriction studies if for no other reason than that there is no identified calorie receptor.  When we published this data, Mike Eades pointed out that in the phase in which Krauss reduced calories, it was done by reducing macronutrients across the board so carbohydrate was also reduced and that might be the actual controlling variable so we plotted the TAG against carbohydrate in each phase (low, medium and high carb (LC, MC, HC) without or with weight loss (+WL) and the results are shown below

This is remarkably good agreement for a nutrition study. When you consider carbohydrates as the independent variable, you can see what’s going on.  Or can you?  After all, by changing the variables you have only made an association between carbohydrate and outcome  of an experiment. So does this imply a causal relation between carbohydrate and triglycerides or not?  It is widely said that observational studies do not imply causality, that observational studies can only provide hypothesis for future testing. It certainly seems like causality is implied here.  It will turn out that a more accurate description is that observational studies do not necessarily imply causality and I will discuss that in the next posts.  The bottom line will be that there is flaw in grand principles like “Random controlled trials are the gold standard.” “Observational studies are only good for generating hypotheses,”  “Metabolic Ward Studies are the gold standard.” Science doesn’t run on such arbitrary rules.

TIME: You’re partnering with, among others, Harvard University on this. In an alternate Lady Gaga universe, would you have liked to have gone to Harvard?

Lady Gaga: I don’t know. I am going to Harvard today. So that’ll do.

— Belinda Luscombe, Time Magazine, March 12, 2012

There was a sense of déja-vu about the latest red meat scare and I thought that my previous post as well as those of others had covered the bases but I just came across a remarkable article from the Harvard Health Blog. It was entitled “Study urges moderation in red meat intake.” It describes how the “study linking red meat and mortality lit up the media…. Headline writers had a field day, with entries like ‘Red meat death study,’ ‘Will red meat kill you?’ and ‘Singing the blues about red meat.”’

What’s odd is that this is all described from a distance as if the study by Pan, et al (and likely the content of the blog) hadn’t come from Harvard itself but was rather a natural phenomenon, similar to the way every seminar on obesity begins with a slide of the state-by-state development of obesity as if it were some kind of meteorologic event.

When the article refers to “headline writers,” we are probably supposed to imagine sleazy tabloid publishers like the ones who are always pushing the limits of first amendment rights in the old Law & Order episodes.  The Newsletter article, however, is not any less exaggerated itself. (My friends in English Departments tell me that self-reference is some kind of hallmark of real art). And it is not true that the Harvard study was urging moderation. In fact, it is admitted that the original paper “sounded ominous. Every extra daily serving of unprocessed red meat (steak, hamburger, pork, etc.) increased the risk of dying prematurely by 13%. Processed red meat (hot dogs, sausage, bacon, and the like) upped the risk by 20%.” That is what the paper urged. Not moderation. Prohibition. Who wants to buck odds like that? Who wants to die prematurely?

It wasn’t just the media. Critics in the blogosphere were also working over-time deconstructing the study.  Among the faults that were cited, a fault common to much of the medical literature and the popular press, was the reporting of relative risk.

The limitations of reporting relative risk or odds ratio are widely discussed in popular and technical statistical books and I ran through the analysis in the earlier post. Relative risk destroys information.  It obscures what the risks were to begin with.  I usually point out that you can double your odds of winning the lottery if you buy two tickets instead of one. So why do people keep doing it?  One reason, of course, is that it makes your work look more significant.  But, if you don’t report the absolute change in risk, you may be scaring people about risks that aren’t real. The nutritional establishment is not good at facing their critics but on this one, they admit that they don’t wish to contest the issue.

Nolo Contendere.

“To err is human, said the duck as it got off the chicken’s back”

 — Curt Jürgens in The Devil’s General

Having turned the media loose to scare the American public, Harvard now admits that the bloggers are correct.  The Health NewsBlog allocutes to having reported “relative risks, comparing death rates in the group eating the least meat with those eating the most. The absolute risks… sometimes help tell the story a bit more clearly. These numbers are somewhat less scary.” Why does Dr. Pan not want to tell the story as clearly as possible?  Isn’t that what you’re supposed to do in science? Why would you want to make it scary?

The figure from the Health News Blog:

Deaths per 1,000 people per year

    1 serving unprocessed meat a week   2 servings unprocessed meat a day
    Women    

7.0

8.5
    3 servings unprocessed meat a week   2 servings unprocessed meat a day
    Men

12.3

13.0

Unfortunately, the Health Blog doesn’t actually calculate the  absolute risk for you.  You would think that they would want to make up for Dr. Pan scaring you.   Let’s calculate the absolute risk.  It’s not hard.Risk is usually taken as probability, that is, number cases divided by total number of participants.  Looking at the men, the risk of death with 3 servings per week is equal to the 12.3 cases per 1000 people = 12.3/1000 = 0.1.23 = 1.23 %. Now going to 14 servings a week (the units in the two columns of the table are different) is 13/1000 = 1.3 % so, for men, the absolute difference in risk is 1.3-1.23 = 0.07, less than 0.1 %.  Definitely less scary. In fact, not scary at all. Put another way, you would have to drastically change the eating habits (from 14 to 3 servings) of 1, 429 men to save one life.  Well, it’s something.  Right? After all for millions of people, it could add up.  Or could it?  We have to step back and ask what is predictable about 1 % risk. Doesn’t it mean that if a couple of guys got hit by cars in one or another of the groups whether that might not throw the whole thing off? in other words, it means nothing.

Observational Studies Test Hypotheses but the Hypotheses Must be Testable.

It is commonly said that observational studies only generate hypotheses and that association does not imply causation.  Whatever the philosophical idea behind these statements, it is not exactly what is done in science.  There are an infinite number of observations you can make.  When you compare two phenomena, you usually have an idea in mind (however much it is unstated). As Einstein put it “your theory determines the measurement you make.”  Pan, et al. were testing the hypothesis that red meat increases mortality.  If they had done the right analysis, they would have admitted that the test had failed and the hypothesis was not true.  The association was very weak and the underlying mechanism was, in fact, not borne out.  In some sense, in science, there is only association. God does not whisper in our ear that the electron is charged. We make an association between an electron source and the response of a detector.  Association does not necessarily imply causality, however; the association has to be strong and the underlying mechanism that made us make the association in the first place, must make sense.

What is the mechanism that would make you think that red meat increased mortality.  One of the most remarkable statements in the original paper:

“Regarding CVD mortality, we previously reported that red meat intake was associated with an increased risk of coronary heart disease2, 14 and saturated fat and cholesterol from red meat may partially explain this association.  The association between red meat and CVD mortality was moderately attenuated after further adjustment for saturated fat and cholesterol, suggesting a mediating role for these nutrients.” (my italics)

This bizarre statement — that saturated fat played a role in increased risk because it reduced risk— was morphed in the Harvard News Letters plea bargain to “The authors of the Archives paper suggest that the increased risk from red meat may come from the saturated fat, cholesterol, and iron it delivers;” the blogger forgot to add “…although the data show the opposite.” Reference (2) cited above had the conclusion that “Consumption of processed meats, but not red meats, is associated with higher incidence of CHD and diabetes mellitus.” In essence, the hypothesis is not falsifiable — any association at all will be accepted as proof. The conclusion may be accepted if you do not look at the data.

The Data

In fact, the data are not available. The individual points for each people’s red meat intake are grouped together in quintiles ( broken up into five groups) so that it is not clear what the individual variation is and therefore what your real expectation of actually living longer with less meat is.  Quintiles are some kind of anachronism presumably from a period when computers were expensive and it was hard to print out all the data (or, sometimes, a representative sample).  If the data were really shown, it would be possible to recognize that it had a shotgun quality, that the results were all over the place and that whatever the statistical correlation, it is unlikely to be meaningful in any real world sense.  But you can’t even see the quintiles, at least not the raw data. The outcome is corrected for all kinds of things, smoking, age, etc.  This might actually be a conservative approach — the raw data might show more risk — but only the computer knows for sure.

Confounders

“…mathematically, though, there is no distinction between confounding and explanatory variables.”

  — Walter Willett, Nutritional Epidemiology, 2o edition.

You make a lot of assumptions when you carry out a “multivariate adjustment for major lifestyle and dietary risk factors.”   Right off , you assume that the parameter that you want to look at — in this case, red meat — is the one that everybody wants to look at, and that other factors can be subtracted out. However, the process of adjustment is symmetrical: a study of the risk of red meat corrected for smoking might alternatively be described as a study of the risk from smoking corrected for the effect of red meat. Given that smoking is an established risk factor, it is unlikely that the odds ratio for meat is even in the same ballpark as what would be found for smoking. The figure below shows how risk factors follow the quintiles of meat consumption.  If the quintiles had been derived from the factors themselves we would have expected even better association with mortality.

The key assumption is that the there are many independent risk factors which contribute in a linear way but, in fact, if they interact, the assumption is not appropriate.  You can correct for “current smoker,” but biologically speaking, you cannot correct for the effect of smoking on an increased response to otherwise harmless elements in meat, if there actually were any.  And, as pointed out before, red meat on a sandwich may be different from red meat on a bed of cauliflower puree.

This is the essence of it.  The underlying philosophy of this type of analysis is “you are what you eat.” The major challenge to this idea is that carbohydrates, in particular, control the response to other nutrients but, in the face of the plea of nolo contendere,  it is all moot.

Who paid for this and what should be done.

We paid for it. Pan, et al was funded in part by 6 NIH grants.  (No wonder there is no money for studies of carbohydrate restriction).  It is hard to believe with all the flaws pointed out here and, in the end, admitted by the Harvard Health Blog and others, that this was subject to any meaningful peer review.  A plea of no contest does not imply negligence or intent to do harm but something is wrong. The clear attempt to influence the dietary habits of the population is not justified by an absolute risk reduction of less than one-tenth of one per cent, especially given that others have made the case that some part of the population, particularly the elderly may not get adequate protein. The need for an oversight committee of impartial scientists is the most important conclusion of Pan, et al.  I will suggest it to the NIH.

The King in Hamlet says “you cannot speak of reason to the Dane and lose your voice” and most Americans do feel good about the Danes. We hold to the stereotype that they are friendly folk with a dry sense of humor like Victor Borge.  That is why Reuben and Rose Mattus, the Polish-Jewish immigrant ice-cream makers from the Bronx who tried to find an angle that would allow them to compete with Sealtest® and other big guns, picked Häagen-Dazs® as the name for their up-scale ice cream, even including a map of Denmark on the early packaging. (Never mind that there is no Scandinavian language that has the odd-ball collection of foreign-looking spelling; Danish does not have an umlaut and I don’t think any Indo-European language has the combination “zs;” there is Zsa Zsa Gabor, of course, but Hungarian is a Uralic language related only to languages that you never heard of).

Jakob Axel Nielsen

The original post here held that the Mattuses would have been very surprised to see that products like their high-butterfat ice cream are now a target of the Danish government which instituted a tax on foods containing saturated fat on October 1 of 2011. The tax, I am happy to say has since been repealed.  In a brilliant turn-around that gives a great insight into the mind of the tax man, the Times reported that ” the tax raised $216 million in new revenue. To offset the loss of that money, the Legislature plans a small increase in income taxes and the elimination of some deductions.” Get it? They are going to increase taxes to cover the money that they hoped to have, never mind, that the intention was to stop people from buying the stuff that would bring in the revenue.

The original idea for collecting taxes on a number of items including “sugar, fat and tobacco,” came from  Jakob Axel Nielsen (right), then Sundhedsminister.  A graduate of the law school at Aarhus, Nielsen is reputed to know even more about science than Hizzona’ Michael Bloomberg.  The LA Times points out, however, that “for those who may be tempted to call for Nielsen’s job, please note that he stepped down…last year.”

One of the things that is surprising about all this is that, in  2009, a combined Danish and American research group whose senior author was Dr. Marianne Jakobsen of Copenhagen University Hospital published a paper showing that there was virtually no effect of dietary saturated fatty acids (SFAs) on cardiovascular disease.  The study was a meta-analysis which means a re-evaluation of many previous studies. The authors concluded that the results “suggest that replacing SFA intake with PUFA (polyunsaturated fatty acid) intake rather than MUFA (monounsaturated fatty acids) or carbohydrate intake prevents CHD (coronary heart disease) over a wide range of intakes.”

As in many nutritional papers, it is worthwhile to actually look at the data.  The figure below, from Jakobsen’s paper shows the results from several studies in which the effect of substituting 5 % of energy from SFA with either carbohydrate (CHO) or PUFA or MUFA (not shown here) was measured.  The outcome variable is the hazard ratio for incidence of coronary events (heart attack, sudden death).  You can think of the hazard ratio as similar to an odds ratio which is what it sounds like: the comparative odds of different possible outcomes. The basic idea is that if 10 people in a group of 100 have a heart attack with saturated fat in their diet, the odds = 10 out of 100 or 1/10.  If you now replace 5 % of energy with PUFAs for a different group of 100 and find only 8 people have an event, then the odds for the second group is 8/100 and the odds ratio is 0.8 (8/100 divided by 10/100).  If the odds ratio were 1.0, then there would be no benefit either way, no difference if you keep SFAs or replace.  So in the first figure below, most of the points are to the left of the point 1.0, suggesting that PUFA is better than SFA but the figure on the right suggests that SFA is better than CHO.  But is this real?

You probably noticed that you would have the same odds ratio if the sample sizes were 1000.  In other words, a ratio gives relative values and obscures some information. If there were a large number of people and the real numbers were actually 8 and 10, you wouldn’t put much stock in the hazard ratio; decreasing your chances of a low probability event is not a big deal; you double your chances of winning the lottery by buying two tickets.  In fact, whereas heart disease is a big killer, if you study a thousand people for 5 years there will be only a small number of coronary events. I discussed this in a previous post, but giving Jakobsen the benefit of the doubt that there were really differences on outcomes, we need to know whether the hazard ratios are really reliable.  In this case, Jakobsen showed the variability in the results with “95% confidence intervals,” which are represented by the horizontal bars in the figure.

The 95% confidence interval (95% CI) is a measure of the spread of values around the average. It tells you how reliable the data is. Technically, the term means that if you calculate the size of the interval over and over, 95% of the time the interval will contain the true value. Although not technically precise, you could think of it as meaning that there is a 95% chance of the interval containing the true value.

There is one important point here. It is a statistical rule that if the 95% CI bar crosses the line for hazard ratio = 1.0 then this is taken as indiction that there is no significant difference between the two conditions, in this case, SFAs or a replacement.  Looking at the figure from Jakobsen, we are struck by the fact that, in the list of 15 different studies for two replacements, all but one cross the hazard ratio = 1.0 line; one study found that keeping SFAs in the diet provides a lower risk than replacement with carbohydrate. For all the others it was a wash.  At this point, one has to ask why a combined value was calculated.  How could 15 studies that show nothing add up to a new piece of information. Who says two wrongs, or even 15, can’t make a right?  The remarkable thing is that some of the studies in this meta-analysis are more than 20 years old. How could these have had so little impact?  Why did we keep believing that saturated fat was bad?

Taxing Saturated Fat.

Now the main thing that taxes do is bring in money.   That’s why it is not a good idea to tie it to a health strategy unless you are really sure (as in the case of cigarettes). For one thing, there is something contradictory (or pessimistic) about trying to raise money from a behavior that you want people to stop doing.   In any case, given that during the epidemic of obesity and diabetes, saturated fat intake went down (for men, the absolute amount went down by 14%), and that there was no effect on the incidence of heart disease (although survival was better due to treatment), there is every reason to consider  the possibility of unexpected negative outcomes (think margarine and trans-fat).  Although now repealed, it is worth considering possible unintended consequences (since the sugar tax is still alive).  Suppose that the Danes had reduced consumption of saturated fat but still ate enough to bring in money. And suppose that this had the opposite effect — after all, if you believe the Jakobsen study, substituting carbohydrate for saturated fat will increase cardiovascular risk.  So now there would be a revenue stream that was associated with an increase in cardiovascular disease.  What would they have done?  What would we do? Well, we’d stop it, of course.  Yeah, right.

“These results suggest that there is no superior long-term metabolic benefit of a high-protein diet over a high-carbohydrate in the management of type 2 diabetes.”  The conclusion is from a paper by Larsen, et al. [1] which, based on that statement in the Abstract, I would not normally bother to read; it is good that you have to register trials and report failures but from a broader perspective, finding nothing is not great news and just because Larsen couldn’t do it, doesn’t mean it can’t be done.  However, in this case, I received an email from International Diabetes published bilingually in Beijing: “Each month we run a monthly column where choose a hot-topic article… and invite expert commentary opinion about that article” so I agreed to write an opinion. The following is my commentary:

“…no superior long-term metabolic benefit of a high-protein diet over a high-carbohydrate ….” A slightly more positive conclusion might have been that “a high-protein diet is as good as a high carbohydrate diet.”  After all, equal is equal. The article is, according to the authors, about “high-protein, low-carbohydrate” so rather than describing a comparison of apples and pears, the conclusion should emphasize low carbohydrate vs high carbohydrate.   It is carbohydrate, not protein, that is the key question in diabetes but clarity was probably not the idea. The paper by Larsen, et al. [1] represents a kind of classic example of the numerous studies in the literature whose goal is to discourage people with diabetes from trying a diet based on carbohydrate restriction, despite its intuitive sense (diabetes is a disease of carbohydrate intolerance) and despite its established efficacy and foundations in basic biochemistry.  The paper is characterized by blatant bias, poor experimental design and mind-numbing statistics rather than clear graphic presentation of the data. I usually try to take a collegial approach in these things but this article does have a unique and surprising feature, a “smoking gun” that suggests that the authors were actually aware of the correct way to perform the experiment or at least to report the data.

Right off, the title tells you that we are in trouble. “The effect of high-protein, low-carbohydrate diets in the treatment…” implying that all such diets are the same even though  there are several different versions, some of which (by virtue of better design) will turn out to have had much better performance than the diet studied here and, almost all of which are not “high protein.” Protein is one of the more stable features of most diets — the controls in this experiment, for example, did not substantially lower their protein even though advised to do so –and most low-carbohydrate diets advise only carbohydrate restriction.  While low-carbohydrate diets do not counsel against increased protein, they do not necessarily recommend it.  In practice, most carbohydrate-restricted diets are hypocaloric and the actual behavior of dieters shows that they generally do not add back either protein or fat, an observation first made by LaRosa in 1980.

Atkins-bashing is not as easy as it used to be when there was less data and one could run on “concerns.” As low-fat diets continue to fail at both long-term and short-term trials — think Women’s Health Initiative [2] — and carbohydrate restriction continues to show success and continues to bear out the predictions from the basic biochemistry of the insulin-glucose axis  [3], it becomes harder to find fault.  One strategy is to take advantage of the lack of formal definitions of low-carbohydrate diets to set up a straw man.  The trick is to test a moderately high carbohydrate diet and show that, on average, as here, there is no difference in hemoglobin A1c, triglycerides and total cholesterol, etc. when compared to a higher carbohydrate diet as control —  the implication is that in a draw, the higher carbohydrate diet wins.  So, Larsen’s low carbohydrate diet contains 40 % of energy as carbohydrate.  Now, none of the researchers who have demonstrated the potential of carbohydrate restriction would consider 40 % carbohydrate, as used in this study, to be a low-carbohydrate diet. In fact, 40 % is close to what the American population consumed before the epidemic of obesity and diabetes. Were we all on a low carbohydrate diet before Ancel Keys?

What happened?  As you might guess, there weren’t notable differences on most outcomes but like other such studies in the literature, the authors report only group statistics so you don’t really know who ate what and they use an intention-to-treat (ITT) analysis. According to ITT, a research report should include data from those subjects that dropped out of the study (here, about 19 % of each group). You read that correctly.  The idea is based on the assumption (insofar as it has any justification at all) that compliance is an inherent feature of the diet (“without carbs, I get very dizzy”) rather than a consequence of bias transmitted from the experimenter, or distance from the hospital, or any of a thousand other things.  While ITT has been defended vehemently, the practice is totally counter-intuitive, and has been strongly attacked on any number of grounds, the most important of which is that, in diet experiments, it makes the better diet look worse.  Whatever the case that can be made, however, there is no justification for reporting only intention-to-treat data, especially since, in this paper, the authors consider as one of the “strengths of the study … the measurement of dietary compliance.”

The reason that this is all more than technical statistical detail, is that the actual reported data show great variability (technically, the 95 % confidence intervals are large).  To most people, a diet experiment is supposed to give a prospective dieter information about outcome.  Most patients would like to know: if I stay on this diet, how will I do.  It is not hard to understand that if you don’t stay on the diet, you can’t expect good results.  Nobody knows what 81 % staying on the diet could mean.  In the same way, nobody loses an average amount of weight. If you look at  the spread in performance and in what was consumed by individuals on this diet, you can see that there is big individual variation Also, being “on a diet”, or being “assigned to a diet” is very different than actually carrying out dieting behavior, that is, eating a particular collection of food.  When there is wide variation, a person in the low-carb group may be eating more carbs than some person in the high-carb group.  It may be worth testing the effect of having the doctor tell you to eat fewer carbs, but if you are trying to lose weight, you want them to test the effect of actually eating fewer carbs.

When I review papers like this for a journal I insist that the authors present individual data in graphic form.  The question in low-carbohydrate diets is the effect of amount of carbohydrate consumed on the outcomes.  Making a good case to the reader involves showing individual data.  As a reviewer, I would have had the authors plot each individual’s consumption of carbohydrate vs for example, individual changes in triglyceride and especially HbA1c.  Both of these are expected to be dependent on carbohydrate consumption.  In fact, this is the single most common criticism I make as reviewer or that I made when I was co-editor-in chief at Nutrition and Metabolism.

So what is the big deal?  This is not the best presentation of the data and it is really hard to tell what the real effect of carbohydrate restriction is. Everybody makes mistakes and few of my own papers are without some fault or other. But there’s something else here.  In reading a paper like this, unless you suspect that something wasn’t done correctly, you don’t tend to read the Statistical analysis section of the Methods very carefully (computers have usually done most of the work).  In this paper, however, the following remarkable paragraph jumps out at you.  A real smoking gun:

  • “As this study involved changes to a number of dietary variables (i.e. intakes of calories, protein and carbohydrate), subsidiary correlation analyses were performed to identify whether study endpoints were a function of the change in specific dietary variables. The regression analysis was performed for the per protocol population after pooling data from both groups. “

What?  This is exactly what I would have told them to do.  (I’m trying to think back. I don’t think I reviewed this paper).  The authors actually must have plotted the true independent variable, dietary intake — carbohydrate, calories, etc. — against the outcomes, leaving out the people who dropped out of the study.  So what’s the answer?

  • “These tests were interpreted marginally as there was no formal adjustment of the overall type 1 error rate and the p values serve principally to generate hypotheses for validation in future studies.”

Huh?  They’re not going to tell us?  “Interpreted marginally?”  What the hell does that mean?  A type 1 error refers to a false positive, that is, they must have found a correlation between diet and outcome in distinction to what the conclusion of the paper is.  They “did not formally adjust for” the main conclusion?  And “p values serve principally to generate hypotheses?”  This is the catch-phrase that physicians are taught to dismiss experimental results that they don’t like.  Whether it means anything or not, in this case there was a hypothesis, stated right at the beginning of the paper in the Abstract: “…to determine whether high-protein diets are superior to high-carbohydrate diets for improving glycaemic control in individuals with type 2 diabetes.”

So somebody — presumably a reviewer — told them what to do but they buried the results.  My experience as an editor was, in fact, that there are people in nutrition who think that they are beyond peer review and I had had many fights with authors.  In this case, it looks like the actual outcome of the experiment may have actually been the opposite of what they say in the paper.  How can we find out?  Like most countries, Australia has what are called “sunshine laws,” that require government agencies to explain their actions.  There is a Australian Federal Freedom of Information Act (1992) and one for the the state of Victoria (1982). One of the authors is supported by NHMRC (National Health and Medical Research Council)  Fellowship so it may be they are obligated to share this marginal information with us.  Somebody should drop the government a line.

Bibliography

1. Larsen RN, Mann NJ, Maclean E, Shaw JE: The effect of high-protein, low-carbohydrate diets in the treatment of type 2 diabetes: a 12 month randomised controlled trial. Diabetologia 2011, 54(4):731-740.

2. Tinker LF, Bonds DE, Margolis KL, Manson JE, Howard BV, Larson J, Perri MG, Beresford SA, Robinson JG, Rodriguez B et al: Low-fat dietary pattern and risk of treated diabetes mellitus in postmenopausal women: the Women’s Health Initiative randomized controlled dietary modification trial. Arch Intern Med 2008, 168(14):1500-1511.

3. Volek JS, Phinney SD, Forsythe CE, Quann EE, Wood RJ, Puglisi MJ, Kraemer WJ, Bibus DM, Fernandez ML, Feinman RD: Carbohydrate Restriction has a More Favorable Impact on the Metabolic Syndrome than a Low Fat Diet. Lipids 2009, 44(4):297-309.

…the association has to be strong and the causality has to be plausible and consistent. And you have to have some reason to make the observation; you can’t look at everything.  And experimentally, observation may be all that you have — almost all of astronomy is observational.  Of course, the great deconstructions of crazy nutritional science — several from Mike Eades blog and Tom Naughton’s hysterically funny-but-true course in how to be a scientist —  are still right on but, strictly speaking, it is the faulty logic of the studies and the whacko observations that is the problem, not simply that they are observational.  It is the strength and reliability of the association that tells you whether causality is implied.  Reducing carbohydrates lowers triglycerides.  There is a causal link.  You have to be capable of the state of mind of the low-fat politburo not to see this (for example, Circulation, May 24, 2011; 123(20): 2292 – 2333).

It is frequently said that observational studies are only good for generating hypotheses but it is really the other way around.  All studies are generated by hypotheses.  As Einstein put it: your theory determines what you measure.  I ran my post on the red meat story passed April Smith  and her reaction was “why red meat? Why not pancakes” which is exactly right.  Any number of things can be observed. Once you pick, you have a hypothesis.

Where did the first law of thermodynamics come from?

Thermodynamics is an interesting case.  The history of the second law involves a complicated interplay of observation and theory.  The idea that there was an absolute limit to how efficient you could make a machine and by extension that all real processes were necessarily inefficient largely comes from the brain power of Carnot. He saw that you could not extract as work all of the heat you put into a machine. Clausius encapsulated it into the idea of the entropy as in my Youtube video.

©2004 Robin A. Feinman

 The origins of the first law, the conservation of energy, are a little stranger.  It turns out that it was described more than twenty years after the second law and it has been attributed to several people, for a while, to the German physicist von Helmholtz.  These days, credit is given to a somewhat eccentric German physician named Robert Julius Mayer. Although trained as a doctor, Mayer did not like to deal with patients and was instead more interested in physics and religion which he seemed to think were the same thing.  He took a job as a shipboard physician on an expedition to the South Seas since that would give him time to work on his main interests.  It was in Jakarta where, while treating an epidemic with the practice then of blood letting, that he noticed that the venous blood of the sailors was much brighter than when they were in colder climates as if “I had struck an artery.” He attributed this to a reduced need for the sailors to use oxygen for heat and from this observation, he somehow leapt to the grand principle of conservation of energy, that the total amount of heat and work and any other forms of energy does not change but can only be interconverted. It is still unknown what kind of connections in his brain led him to this conclusion.  The period (1848) corresponds to the point at which science separated from philosophy. Mayer seems to have had one foot in each world and described things in the following incomprehensible way:

  • If two bodies find themselves in a given difference, then they could remain  in a state of rest after the annihilation of [that] difference if the  forces that were communicated to them as a result of the leveling of  the difference could cease to exist; but if they are assumed to be indestructible,  then the still persisting forces, as causes of changes in relationship,  will again reestablish the original present difference.

(I have not looked for it but one can only imagine what the original German was like). Warmth Disperses and Time Passes. The History of Heat, Von Baeyer’s popular book on thermodynamics, describes the ups and downs of Mayer’s life, including the death of three of his children which, in combination with rejection of his ideas, led to hospitalization but ultimate recognition and knighthood.  Surely this was a great observational study although, as von Baeyer put it, it did require “the jumbled flashes of insight in that sweltering ship’s cabin on the other side of the world.”

It is also true that association does imply causation but, again, the association has to have some impact and the proposed causality has to make sense.  In some way, purely observational experiments are rare.  As Pasteur pointed out, even serendipity is favored by preparation.  Most observational experiments must be a reflection of some hypothesis. Otherwise you’re wasting tax-payer’s money; a kiss of death on a grant application is to imply that “it would be good to look at.…”  You always have to have something in mind.  The great observational studies like the Framingham Study are bad because they have no null hypothesis. When the Framingham study first showed that there was no association between dietary total and saturated fat or dietary cholesterol, the hypothesis was quickly defended. The investigators were so tied to a preconceived hypothesis, that there was hardly any point in making the observations.

In fact, a negative result is always stronger than one showing consistency; consistent sunrises will go by the wayside if the sun fails to come up once.  It is the lack of an association between the decrease in fat consumption during the epidemic of obesity and diabetes that is so striking.  The figure above shows that the  increase in carbohydrate consumption is consistent with the causal role of dietary carbohydrate in creating anabolic hormonal effects and with the poor satiating effects of carbohydrates — almost all of the increase of calories during the epidemic of obesity and diabetes has been due to carbohydrates.  However, this observation is not as strong as the lack of an identifiable association of obesity and diabetes with fat consumption.  It is the 14 % decrease in the absolute amount of saturated fat for men that is the problem.  If the decrease in fat were associated with decrease in obesity, diabetes and cardiovascular disease, there is little doubt that the USDA would be quick to identify causality.  In fact, whereas you can find the occasional low-fat trial that succeeds, if the diet-heart hypothesis were as described, they should not fail. There should not be a single Women’s Health Initiative, there should not be a single Framingham study, not one.

Sometimes more association would be better.  Take intention-to-treat. Please. In this strange statistical idea, if you assign a person to a particular intervention, diet or drug, then you must include the outcome data (weight loss, change in blood pressure) for that person even if the do not comply with the protocol (go off the diet, stop taking the pills).  Why would anybody propose such a thing, never mind actually insist on it as some medical journals or granting agencies do?  When you actually ask people who support ITT, you don’t get coherent answers.  They say that if you just look at per protocol data (only from people who stayed in the experiment), then by excluding the drop-outs, you would introduce bias but when you ask them to explain that you get something along the lines of Darwin and the peas growing on the wrong side of the pod. The basic idea, if there is one, is that the reason that people gave up on their diet or stopped taking the pills was because of an inherent feature of the intervention: made them sick, drowsy or something like that.  While this is one possible hypothesis and should be tested, there are millions of others — the doctor was subtly discouraging about the diet, or the participants were like some of my relatives who can’t remember where they put their pills, or the diet book was written in Russian, or the diet book was not written in Russian etc. I will discuss ITT in a future post but for the issue at hand:  if you do a per-protocol you will observe what happens to people when stay on their diet and you will have an association between the content of the diet and performance.  With an ITT analysis, you will be able to observe what happens when people are told to follow a diet and you will have an association between assignment to a diet and performance.  Both are observational experiments with an association between variables but they have different likelihood of providing a sense of causality.

“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