Archive for the ‘misuse of statistics’ Category

The attack was quite sudden although it appeared to have been planned for many years. The paper was published last week (Augustin LS, Kendall CW, Jenkins DJ, Willett WC, Astrup A, Barclay AW, Bjorck I, Brand-Miller JC, Brighenti F, Buyken AE et al: Glycemic index, glycemic load and glycemic response: An International Scientific Consensus Summit from the International Carbohydrate Quality Consortium (ICQC). Nutr Metab Cardiovasc Dis 2015, 25(9):795-815.


As indicated by the title, responsibility was taken by the self-proclaimed ICQC.  It turned out to be a continuation of the long-standing attempt to use the glycemic index to co-opt the obvious benefits in control of the glucose-insulin axis while simultaneously attacking real low-carbohydrate diets. The authors participated in training in Stresa, Italy.

The operation was largely passive aggressive. While admitting the importance of dietary carbohydrate in controlling post-prandial glycemic,  low-carbohydrate diets were ignored. Well, not exactly. The authors actually had a strong attack.  The Abstract of the paper said (my emphasis):

Background and aims: The positive and negative health effects of dietary carbohydrates are of interest to both researchers and consumers.”

Methods: International experts on carbohydrate research held a scientific summit in Stresa, Italy, in June 2013 to discuss controversies surrounding the utility of the glycemic index (GI), glycemic load (GL) and glycemic response (GR).”

So, for the record, the paper is about dietary carbohydrate and about controversies.

The Results in Augustin, et al were simply

“The outcome was a scientific consensus statement which recognized the importance of postprandial glycemia in overall health, and the GI as a valid and reproducible method of classifying carbohydrate foods for this purpose…. Diets of low GI and GL were considered particularly important in individuals with insulin resistance.”

A definition is always a reproducible way of classifying things, and the conclusion is not controversial: glycemia is important.  Low-GI diets are a weak form of low-carbohydrate diet and they are frequently described as a politically correct form of carbohydrate restriction. It is at least a subset of carbohydrate restriction and one of the “controversies” cited in the Abstract is sensibly whether it is better or worse than total carbohydrate restriction. Astoundingly, this part of the controversy was ignored by the authors.  Our recent review of carbohydrate restriction in diabetes had this comparison:




A question of research integrity.

It is considered normal scientific protocol that, in a scientific field, especially one that is controversial, that you consider and cite alternative or competing points of view. So how do the authors see low-carbohydrate diets fitting in? If you search the pdf of Augustin, et al on “low-carbohydrate” or “low carbohydrate,” there are only two in the text:

“Very low carbohydrate-high protein diets also have beneficial effects on weight control and some cardiovascular risk factors (not LDL-cholesterol) in the short term, but are associated with increased mortality in long term cohort studies [156],”


“The lowest level of postprandial glycemia is achieved using very low carbohydrate-high protein diets, but these cannot be recommended for long term use.”

There are no references for the second statement but very low carbohydrate diets can be and frequently are recommended for long term use and have good results. I am not aware of “increased mortality in long term cohort studies” as in the first statement. In fact, low-carbohydrate diets are frequently criticized for not being subjected to long-term studies. So it was important to check out the studie(s) in reference 156:

[156] Pagona L, Sven S, Marie L, Dimitrios T, Hans-Olov A, Elisabete W. Low carbohydrate-high protein diet and incidence of cardiovascular diseases in Swedish women: prospective cohort study. BMJ 2012;344.

Documenting increased mortality.

The paper is not about mortality but rather about cardiovascular disease and, oddly, the authors are listed by their first names. (Actual reference: Lagiou P, Sandin S, Lof M, Trichopoulos D, Adami HO, Weiderpass E: . BMJ 2012, 344:e4026). This minor error probably reflects the close-knit “old boys” circle that functions on a first name basis although it may also indicate that the reference was not actually read so it was not discovered what the reference was really about.

Anyway, even though it is about cardiovascular disease, it is worth checking out. Who wants increased risk of anything. So what does Lagiou, et al say?

The Abstract of Lagiou says (my emphasis) “Main outcome measures: Association of incident cardiovascular diseases … with decreasing carbohydrate intake (in tenths), increasing protein intake (in tenths), and an additive combination of these variables (low carbohydrate-high protein score, from 2 to 20), adjusted for intake of energy, intake of saturated and unsaturated fat, and several non-dietary variables.”

Low-carbohydrate score? There were no low-carbohydrate diets. There were no diets at all. This was an analysis of “43, 396 Swedish women, aged 30-49 years at baseline, [who] completed an extensive dietary questionnaire and were followed-up for an average of 15.7 years.” The outcome variable, however, was only the “score” which the authors made up and which, as you might guess, was not seen and certainly not approved, by anybody with actual experience with low-carbohydrate diets. And, it turns out that “Among the women studied, carbohydrate intake at the low extreme of the distribution was higher and protein intake at the high extreme of the distribution was lower than the respective intakes prescribed by many weight control diets.” (In social media, this is called “face-palm”).

Whatever the method, though, I wanted to know how bad it was? The 12 years or so that I have been continuously on a low-carbohydrate diet might be considered pretty long term. What is my risk of CVD?

Results: A one tenth decrease in carbohydrate intake or increase in protein intake or a 2 unit increase in the low carbohydrate-high protein score were all statistically significantly associated with increasing incidence of cardiovascular disease overall (n=1270)—incidence rate ratio estimates 1.04 (95% confidence interval 1.00 to 1.08), 1.04 (1.02 to 1.06), and 1.05 (1.02 to 1.08).”

Rate ratio 1.04? And that’s an estimate.  That’s odds of 51:49.  That’s what I am supposed to be worried about. But that’s the relative risk. What about the absolute risk? There were 43 396 women in the study with 1270 incidents, or 2.9 % incidence overall.  So the absolute difference is about 1.48-1.42% = 0.06 % or less than 1/10 of 1 %.

Can such low numbers be meaningful? The usual answers is that if we scale them up to the whole population, we will save thousands of lives. Can we do that? Well, you can if the data are strong, that is, if we are really sure of the reliability of the independent variable. The relative risk in the Salk vaccine polio trial, for example, was in this ballpark but scaling up obviously paid off. In the Salk vaccine trial, however, we knew who got the vaccine and who didn’t. In distinction, food questionnaire’s have a bad reputation. Here is Lagiou’s description (you don’t really have to read this):

“We estimated the energy adjusted intakes of protein and carbohydrates for each woman, using the ‘residual method.’ This method allows evaluation of the “effect” of an energy generating nutrient, controlling for the energy generated by this nutrient, by using a simple regression of that nutrient on energy intake.…” and so on. I am not sure what it means but it certainly sounds like an estimate. So is the data itself any good? Well,

“After controlling for energy intake, however, distinguishing the effects of a specific energy generating nutrient is all but impossible, as a decrease in the intake of one is unavoidably linked to an increase in the intake of one or several of the others. Nevertheless, in this context, a low carbohydrate-high protein score allows the assessment of most low carbohydrate diets, which are generally high protein diets, because it integrates opposite changes of two nutrients with equivalent energy values.”

And “The long interval between exposure and outcome is a source of concern, because certain participants may change their dietary habits during the intervening period.”

Translation: we don’t really know what we did here.

In the end, Lagiou, et al admit “Our results do not answer questions concerning possible beneficial short term effects of low carbohydrate or high protein diets in the control of body weight or insulin resistance. Instead, they draw attention to the potential for considerable adverse effects on cardiovascular health of these diets….” Instead? I thought insulin resistance has an effect on CVD but if less than 1/10 of 1 % is “considerable adverse effects” what would something “almost zero” be.?

Coming back to the original paper by Augustin, et al, what about the comparison between low-GI diets and low-carbohydrate diets. The comparison in the figure above comes from Eric Westman’s lab. What do they have to say about that?


They missed this paper. Note: a comment I received suggested that I should have searched on “Eric” instead of “Westman.” Ha.

Overall, this is the evidence used by ICQC to tell you that low-carbohydrate diets would kill you. In the end, Augustin, et al is a hatchet-job, citing a meaningless paper at random. It is hard to understand why the journal took it. I will ask the editors to retract it.

As the nutrition world implodes, there are a lot of accusations about ulterior motives and personal gain. (A little odd, that in this period of unbelievable greed — CEO’s ripping off public companies for hundreds of millions of dollars, congress trying to give tax breaks to billionaires — book authors are upbraided for trying to make money). So let me declare that I am not embarrassed to be an author for the money — although the profits from my book do go to research, it is my own research and the research of my colleagues. So beyond general excellence (not yet reviewed by David Katz), I think “World Turned Upside Down” does give you some scientific information about red meat and cancer that you can’t get from the WHO report on the subject.

The WHO report has not yet released the evidence to support their claim that red meat will give you cancer but it is worth going back to one of the previous attacks.  Chapters 18 and 19 discussed a paper by Sinha et al, entitled “Meat Intake and Mortality.”    The Abstract says “Conclusion: Red and processed meat intakes were associated with modest increases in total mortality, cancer mortality, and cardiovascular disease mortality,” I had previously written a blogpost about the study indicating how weak the association was. In that post, I had used the data on men but when I incorporated the information into the book, I went back to Sinha’s paper and analyzed the original data. For some reason, I also checked the data on women. That turned out to be pretty surprising:


I described on Page 286: “The population was again broken up into five groups or quintiles. The lower numbered quintiles are for the lowest consumption of red meat. Looking at all cause mortality, there were 5,314 deaths [in lowest quintile] and when you go up to quintile 05, highest red meat consumption, there are 3,752 deaths. What? The more red meat, the lower the death rate? Isn’t that the opposite of the conclusion of the paper? And the next line has [calculated] relative risk which now goes the other way: higher risk with higher meat consumption. What’s going on? As near as one can guess, “correcting” for the confounders changed the direction….” They do not show most of the data or calculations but I take this to be equivalent to a multivariate analysis, that is, red meat + other things gives you risk. If they had broken up the population by quintiles of smoking, you would see that that was the real contributor. That’s how I interpreted it but, in any case, their conclusion is about meat and it is opposite to what the data say.

So how much do you gain from eating red meat? “A useful way to look at this data is from the standpoint of conditional probability. We ask: what is the probability of dying in this experiment if you are a big meat‑eater? The answer is simply the number of people who both died during the experiment and were big meat‑eaters …. = 0.0839 or about 8%. If you are not a big meat‑eater, your risk is …. = 0.109 or about 11%.” Absolute gain is only 3 %. But that’s good enough for me.

Me, at Jubilat, the Polish butcher in the neighborhood: “The Boczak Wedzony (smoked bacon). I’ll take the whole piece.”


Boczak Wedzony from Jubilat Provisions

Rashmi Sinha is a Senior Investigator and Deputy Branch Chief and Senior at the NIH. She is a member of the WHO panel, the one who says red meat will give you cancer (although they don’t say “if you have the right confounders.”)

So, buy my book: AmazonAlibris, or

Direct:  Personalized, autographed copy $ 20.00 free shipping USA only.  Use coupon code: SEPT16


…what metaphysics is to physics. The old joke came to mind when a reporter asked me yesterday to comment on a paper published in the BMJ. “Intake of saturated and trans unsaturated fatty acids and risk of all cause mortality, cardiovascular disease, and type 2 diabetes: systematic review and meta-analysis of observational studies” by de Souza, et al.

Now the title ““Intake of saturated and trans unsaturated fatty acids…” tells you right off that this is not good news; lumping together saturated fat and trans-fat is an indication of bias. A stand-by of Atkins-bashers, it is a way of vilifying saturated fat when the data won’t fit.  In the study that the reporter asked about, the BMJ provided a summary:

“There was no association between saturated fats and health outcomes in studies where saturated fat generally replaced refined carbohydrates, but there was a positive association between total trans fatty acids and health outcomes Dietary guidelines for saturated and trans fatty acids must carefully consider the effect of replacement nutrients.”

“But?” The two statements are not really connected. In any case the message is clear: saturated fat is Ok. Trans-fat is not Ok. So, we have to be concerned about both  saturated fat and trans-fat. Sad.

And “systematic” means the system that the author wants to use. This usually means a meta-analysis. Explained by the overly optimistic “What is …?” series:


The jarring notes are “precise estimate” in combination with “combining…independent studies.” In practice, you usually only repeat an experiment exactly if you suspect that something was wrong with the original study or if the result is sufficiently outside expected values that you want to check it. Such a systematic examination involves an analysis of the experimental details. The idea underlying the meta-analysis, however, usually unstated is that the larger the number of subjects in a study, the more compelling the conclusion. One might make the argument, instead, that if you have two or more studies which are imperfect, combining them is likely to lead to greater uncertainty and more error, not less.  I am one who would make such an argument. So where did meta-analysis come from and what, if anything, is it good for?

I am trained in enzyme and protein chemistry but I have worked in a number of different  fields including invertebrate animal behavior. I never heard of meta-analysis until very recently, that is, until I started doing research in nutrition. In fact, in 1970 there weren’t any meta-analyses, at least not with that phrase in the title, or at least not as determined by my PubMed search. By 1990, there were about a 100 and by 2014, there were close to 10, 000 (Figure 1).

Meta-anal_Year_Mar9Figure 1. Logarithm of the number of papers in PubMed search with the title containing “meta-analysis” vs. Year of publication

This exponential growth suggests that the technique grew by reproducing itself. It suggests, in fact, that its origins are in spontaneous generation. In other words, it is popular because it is popular. (It does have obvious advantages; you don’t have to do any experiments). But does it give any useful information?


If you have a study that is under-powered, that is, if you only have a small number of subjects, and you find a degree of variability in the outcome, then combining the results from your experiment with another small study may point you to a consistent pattern. As such, it is a last-ditch, Hail-Mary kind of method. Applying it to large studies that have statistically meaningful results, however, doesn’t make sense, because:

  1. If all of the studies go in the same direction, you are unlikely to learn anything from combining them. In fact, if you come out with a value for the output that is different from the value from the individual studies, in science, you are usually required to explain why your analysis improved things. Just saying it is a larger n won’t cut it, especially if it is my study that you are trying to improve on.
  2. In the special case where all the studies show no effect and you come up with a number that is statistically significant, you are, in essence saying that many wrongs can make a right as described in a previous blog post on abuse of meta-analyses.  In that post, I re-iterated the statistical rule that if the 95% CI bar crosses the line for hazard ratio = 1.0 then this is taken as an indication that there is no significant difference between the two conditions that are being compared. The example that I gave was the meta-analysis by Jakobsen, et al. on the effects of SFAs or a replacement on CVD outcomes (Figure 2). Amazingly, in the list of 15 different studies that she used, all but one cross the hazard ratio = 1.0 line. In other words, only one study found that keeping SFAs in the diet provides a lower risk than replacement with carbohydrate. For all the others there was no significant difference.  The question is why an analysis was done at all.  What could we hope to find? How could 15 studies that show nothing add up to a new piece of information? Most amazing is that some of the studies are more than 20 years old. How could these have had so little impact on our opinion of saturated fat?  Why did we keep believing that it was bad?


Figure 2. Hazard ratios and 95% confidence intervals for coronary events and deaths in the different studies in a meta-analysis from Jakobsen, et al.Major types of dietary fat and risk of coronary heart disease: a pooled analysis of 11 cohort studies. Am J Clin Nutr 2009, 89(5):1425-1432.

3. Finally, suppose that you are doing a meta-analysis on several studies and that they have very different outcomes, showing statistically significant associations in different directions. For example, if some studies showed substituting saturated fat for carbohydrate increased risk while some showed that it decreased risk. What will you gain by averaging them? I don’t know about you but it doesn’t sound good to me. It makes me think of the old story of the emerging nation that was planning to build a railroad and didn’t know whether to use a gauge that matched the country to the north or the gauge of the country to the south. The parliament voted to use a gauge that was the average of the two.


I was walking on a very dark street and I assumed that the voice I heard was a guy talking on a cell phone. Apparently about a dinner party, he was saying “Remember, I don’t eat red meat.” Only a few years ago, that would have sounded strange. Of course, a few years ago a man talking to himself on the street would have been strange. He would have been assumed to be deranged, more so if he told you that he was talking on the telephone. But yesterday’s oddity pops up everywhere today. Neo-vegetarianism affects us all. It’s all described very well by Jane Kramer’s excellent review of veggie cookbooks in the April 14 New Yorker,

“…from one chili party to the next, everything changed. Seven formerly enthusiastic carnivores called to say they had stopped eating meat entirely…. Worse, on the night of that final party, four of the remaining carnivores carried their plates to the kitchen table, ignoring the cubes of beef and pancetta, smoky and fragrant in their big red bean pot, and headed for my dwindling supply of pasta. “Stop!” I cried. “That’s for the vegetarians!”

Illustration by Robin Feinman. Reference:


“…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:


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.


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.

Everybody has their favorite example of how averages don’t really tell you what you want to know or how they are inappropriate for some situations. Most of these are funny because they apply averages to cases where single events are important. I’ll list a couple in the text boxes in this post. From the title:

If Bill Gates walks into a bar, on average, everybody in the bar is a millionaire.

Technically speaking, averages start with the assumption that deviations are due to random error, that is, that there is a kind of “true” value if we could only control things well — if there were no wind resistance and all balls were absolutely uniform, they would always fall in the same place; any spread in values is random rather than systematic.