Aging and cancer: The importance of taking a hard look at the numbers

The table below is from a study by Hayat and colleagues (). It illustrates one common trend regarding cancer – it increases dramatically in incidence among those who are older. With some exceptions, such as Hodgkin's lymphoma, there is a significant increase in risk particularly after 50 years of age.



So I decided to get state data from the US Census web site (), on the percentage of seniors (age 65 or older) by state and cancer diagnoses per 1,000 people. I was able to get some recent data, for 2011.

I analyzed the data with WarpPLS (version 4.0 has been just released: ), generating the types of coefficients that would normally be reported by researchers who wanted to make an effect appear very strong.

In this case, the effect would be essentially of population aging on cancer incidence (assessed indirectly), summarized in the graph below. The graph was generated by WarpPLS. The scales are standardized, and so are the coefficients of association in the two segments shown. As you can see, the coefficients of association increase as we move along the horizontal scale, because this is a nonlinear relationship. The overall coefficient of association, which is a weighted average of the two betas shown, is 0.84. The probability that this is a false positive is less than 1 percent.



A beta coefficient of 0.84 essentially means that a 1 standard deviation variation in the percentage of seniors in a state is associated with an overall 84 percent increase in cancer diagnoses, taking the standardized unit of the number of cancer diagnoses as the baseline. This sounds very strong and would usually be presented as an enormous effect. Since the standard deviation for the percentage of seniors in various states is 1.67, one could say that for each 1.67 increment in the percentage of seniors in a state the number of cancer diagnoses goes up by 84 percent.

Effects expressed in percentages can sometimes give a very misleading picture. For example, let us consider an increase in mortality due to a disease from 1 to 2 cases for each 1 million people. This essentially is a 100 percent increase! Moreover, the closer the baseline is from zero, the more impressive the effect becomes, since the percentage increase is calculated by dividing the increment by the baseline number. As the baseline number approaches zero, the percentage increase from the baseline approaches infinity.

Now let us take a look at the graph below, also generated by WarpPLS. Here the scales are unstandardized, which means that they refer to the original measures in their respective original scales. (Standardization makes the variables dimensionless, which is sometimes useful when the original measurement scales are not comparable – e.g., dollars vs. meters.) As you can see here, the number of cancer diagnoses per 1,000 people goes from a low of 3.74 in Utah to a high of 6.64 in Maine.



One may be tempted to explain the increase in cancer diagnoses that we see on this graph based on various factors (e.g., lifestyle), but the percentage of seniors in a state seems like a very good and reasonable predictor. You may say: This is very depressing. You may be even more depressed if I tell you that controlling for state obesity rates does not change this picture at all.

But look at what these numbers really mean. What we see here is an increase in cancer diagnoses per 1,000 people of less than 3. In other words, there is a minute increase of less than 3 diagnoses for each group of 1,000 people considered. It certainly feels terrible if you are one of the 3 diagnosed, but it is still a minute increase.

Also note that one of the scales, for diagnoses, refers to increments of 1 in 1,000; while the other, for seniors, refers to increments of 1 in 100. This leads to an interesting effect. If you move from Alaska to Florida you will see a significant increase in the number of seniors around, as the difference in the percentage of seniors between these two states is about 10. However, the difference in the number of cancer diagnoses will not be even close to the difference in the presence of seniors.

The situation above is very common in medical research. An effect that is fundamentally tiny is stated in such a way that the general public has the impression that the effect is enormous. Often the reason is not to promote a drug, but to attract media attention to a research group or organization.

When you look at the actual numbers, the magnitude of the effect is such that it would go unnoticed in real life. By real life I mean: John, since we moved from Alaska to Maine I have been seeing a lot more people of my age being diagnosed with cancer. An effect of the order of 3 in 1,000 would not normally be noticed in real life by someone whose immediate circle of regular acquaintances included fewer than 333 people (about 1,000 divided by 3).

But thanks to Facebook, things are changing … to be fair, the traditional news media (particularly television) tends to increase perceived effects a lot more than social media, often in a very stressful way.

We share an ancestor who probably lived no more than 640 years ago

This post is a revised version of a previous post. The original post has been or will be deleted, with the comments preserved. Typically this is done with posts that attract many visits at the time they are published, and whose topics become particularly relevant or need to be re-addressed at a later date.

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We all evolved from one single-celled organism that lived billions of years ago. I don’t see why this is so hard for some people to believe, given that all of us also developed from a single fertilized cell in just 9 months.

However, our most recent common ancestor is not that first single-celled organism, nor is it the first Homo sapiens, or even the first Cro-Magnon.

The majority of the people who read this blog probably share a common ancestor who lived no more than 640 years ago. Genealogical records often reveal interesting connections - the figure below has been cropped from a larger one from Pinterest.

You and I, whoever you are, have each two parents. Each of our parents have (or had) two parents, who themselves had two parents. And so on.

If we keep going back in time, and assume that you and I do not share a common ancestor, there will be a point where the theoretical world population would have to be impossibly large.

Assuming a new generation coming up every 20 years, and going backwards in time, we get a theoretical population chart like the one below. The theoretical population grows in an exponential, or geometric, fashion.

As we move back in time the bars go up in size. Beyond a certain point their sizes go up so fast that you have to segment the chart. Otherwise the bars on the left side of the chart disappear in comparison to the ones on the right side (as several did on the chart above). Below is the section of the chart going back to the year 1371.

The year 1371 is a mere 640 years ago. And what is the theoretical population in that year if we assume that you and I have no common ancestors? The answer is: more than 8.5 billion people. We know that is not true.

Admittedly this is a somewhat simplistic view of this phenomenon, used here primarily to make a point. For example, it is possible that a population of humans became isolated 15 thousand years ago, remained isolated to the present day, and that one of their descendants just happened to be around reading this blog today.

Perhaps the most widely cited article discussing this idea is this one by Joseph T. Chang, published in the journal Advances in Applied Probability. For a more accessible introduction to the idea, see this article by Joe Kissell.

Estimates vary based on the portion of the population considered. There are also assumptions that have to be made based on migration and mating patterns, as well as the time for each generation to emerge and the stability of that number over time.

Still, most people alive today share a common ancestor who lived a lot more recently than they think. In most cases that common ancestor probably lived less than 640 years ago.

And who was that common ancestor? That person was probably a man who, due to a high perceived social status, had many consorts, who gave birth to many children. Someone like Genghis Khan.

The 2013 PLoS ONE sugar and diabetes study: Sugar from fruits is harmless

A new study linking sugar consumption with diabetes prevalence has gained significant media attention recently. The study was published in February 2013 in the journal PLoS ONE (). The authors are Sanjay Basu, Paula Yoffe, Nancy Hills and Robert H. Lustig.

Among the claims made by the media is that “… sugar consumption — independent of obesity — is a major factor behind the recent global pandemic of type 2 diabetes” (). As it turns out, the effects revealed by the study seem to be very small, which may actually be a side effect of data aggregation; I will discuss this further below.

Fruits are exonerated

Let me start by saying that this study also included in the analysis the main natural source of sugar, fruit, as a competing variable (competing with the effects of sugar itself), and found it to be unrelated to diabetes. As the authors note: “None of the other food categories — including fiber-containing foods (pulses, nuts, vegetables, roots, tubers), fruits, meats, cereals, and oils — had a significant association with diabetes prevalence rates”.

This should not surprise anyone who has actually met and talked with Dr. Lustig, the senior author of the study and a very accessible man who has been reaching out to the public in a way that few in his position do. He is a clinician and senior researcher affiliated with a major university; public outreach, in the highly visible way that he does it, is probably something that he does primarily (if not solely) to help people. Dr. Lustig was at the 2012 Ancestral Health Symposium, and he told me, and anyone who asked him, that sugar in industrialized foods was his target, not sugar in fruits.

As I noted here before, the sugar combination of fruits, in their natural package, may in fact be health-promoting (). The natural package probably promotes enough satiety to prevent overconsumption.

Both (unnatural) sugar and obesity have effects, but they are tiny in this study

The Diabetes Report Card 2012 () provides a wealth of information that can be useful as a background for our discussion here.

In the USA, general diabetes prevalence varies depending on state, with some states having higher prevalence than others. The vast majority of diabetes cases are of type 2 diabetes, which is widely believed to be strongly associated with obesity.

In 2012, the diabetes prevalence among adults (aged 20 years or older) in Texas was 9.8 percent. This rate is relatively high compared to other states, although lower than in some. So, among a random group of 1,000 adult Texans, you would find approximately 98 with diabetes.

Prevalence increases with age. Among USA adults in general, prevalence of diabetes is 2.6 percent within ages 20–44, 11.7 percent within ages 45–64, and 18.9 percent at age 64 or older. So the numbers above for Texas, and prevalence in almost any population, are also a reflection of age distribution in the population.

According to the 2013 study published in PLoS ONE, a 1 percent increase in obesity prevalence is associated with a 0.081 percent increase in diabetes prevalence. This comes directly from the table below, fifth column on the right. That is the column for the model that includes all of the variables listed on the left.



We can translate the findings above in more meaningful terms by referring to hypothetical groups of 1,000 people. Let us say we have two groups of 1,000 people. In one of them we have 200 obese people (20 percent); and no obese person in the other. We would find only between 1 and 2 people with diabetes in the group with 200 obese people.

The authors also considered overweight prevalence as a cause of diabetes prevalence. A section of the table with the corresponding results in included below. They also found a significant effect, of smaller size than for obesity – which itself is a small effect.



The study also suggests that consumption of the sugar equivalent of a 12 oz. can of regular soft drink per person per day was associated with a 1.1 percent rise in diabetes prevalence. The effect here is about the same as that of a 1 percent increase in obesity.

That is, let us say we have two groups of 1,000 people. In one of them we have 200 people (20 percent) consuming one 12 oz. can of soft drink per day; and no one consuming sugar in the other. (Sugar from fruits is not considered here.) We would find only about 2 people with diabetes in the group with 200 sugary soda drinkers.

In other words, the effects revealed by this study are very small. They are so small that their corresponding effect sizes make them borderline irrelevant for predictions at the individual level. Based on this study, obesity and sugar consumption combined would account for no more than 5 out of each 100 cases of diabetes (a generous estimate, based on the results discussed above).

Even being weak, the effects revealed by this study are not irrelevant for policy-making, because policies tend to influence the behavior of very large numbers of people. For example, if the number of people that could be influenced by policies to curb consumption of refined sugar were 100 million, the number of cases of diabetes that could be prevented would be 200 thousand, notwithstanding the weak effects revealed by this study.

Why are the effects so small?

The effects in this study are based on data aggregated by country. When data is aggregated by population, the level of variation in the data is reduced; sometimes dramatically, a problem that is proportional to the level of aggregation (e.g., the problem is greater for country aggregation than for city aggregation).

Because there can be no association without correlation, and no correlation without variation, coefficients of association tend to be reduced when data aggregation occurs. This is, in my view, the real problem behind what statisticians often refer to, in “statospeech”, as “ecological fallacy”. The effects in aggregated data are weaker than the effects one would get without aggregation.

So, I suspect that the effects in this study, which are fairly weak at the level of aggregation used (the country level), reflect much stronger effects at the individual level of analysis.

Bottom line

Should you avoid getting obese? Should you avoid consuming industrialized products with added sugar? I think so, and I would still have recommended these without this study. There seems to be no problem with natural foods containing sugar, such as fruits.

This study shows evidence that sugar in industrialized foods is associated with diabetes, independently from obesity, but it does not provide evidence that obesity doesn’t matter. It shows that both matter, independently of one another, which is an interesting finding that backs up Dr. Lustig’s calls for policies to specifically curb refined sugar consumption.

Again, what the study refers to as sugar, as availability but implying consumption, seems to refer mostly to industrialized foods where sugar was added to make them more enticing. Fruit consumption was also included in the study, and found to have no significant effect on diabetes prevalence.

Here is a more interesting question. If a group of people have a predisposition toward developing diabetes, due to any reason (genetic, epigenetic, environmental), what would be the probability that they would develop diabetes if they became obese and/or consumed unnatural sugar-added foods?

This type of question can be answered with a moderating effects analysis, but as I noted here before (), moderating effects analyses are not conducted in health research.

The steep obesity increase in the USA in the 1980s: In a sense, it reflects a major success story

Obesity rates have increased in the USA over the years, but the steep increase starting around the 1980s is unusual. Wang and Beydoun do a good job at discussing this puzzling phenomenon (), and a blog post by Discover Magazine provides a graph (see below) that clear illustrates it ().

What is the reason for this?

You may be tempted to point at increases in calorie intake and/or changes in macronutrient composition, but neither can explain this sharp increase in obesity in the 1980s. The differences in calorie intake and macronutrient composition are simply not large enough to fully account for such a steep increase. And the data is actually full of oddities.

For example, an article by Austin and colleagues (which ironically blames calorie consumption for the obesity epidemic) suggests that obese men in a NHANES (2005–2006) sample consumed only 2.2 percent more calories per day on average than normal weight men in a NHANES I (1971–1975) sample ().

So, what could be the main reason for the steep increase in obesity prevalence since the 1980s?

The first clue comes from an interesting observation. If you age-adjust obesity trends (by controlling for age), you end up with a much less steep increase. The steep increase in the graph above is based on raw, unadjusted numbers. There is a higher prevalence of obesity among older people (no surprise here). And older people are people that have survived longer than younger people. (Don’t be too quick to say “duh” just yet.)

This age-obesity connection also reflects an interesting difference between humans living “in the wild” and those who do not, which becomes more striking when we compare hunter-gatherers with modern urbanites. Adult hunter-gatherers, unlike modern urbanites, do not gain weight as they age; they actually lose weight (, ).

Modern urbanites gain a significant amount of weight, usually as body fat, particularly after age 40. The table below, from an article by Flegal and colleagues, illustrates this pattern quite clearly (). Obesity prevalence tends to be highest between ages 40-59 in men; and this has been happening since the 1960s, with the exception of the most recent period listed (1999-2000).

In the 1999-2000 period obesity prevalence in men peaked in the 60-74 age range. Why? With progress in medicine, it is likely that more obese people in that age range survived (however miserably) in the 1999-2000 period. Obesity prevalence overall tends to be highest between ages 40-74 in women, which is a wider range than in men. Keep in mind that women tend to also live longer than men.

Because age seems to be associated with obesity prevalence among urbanites, it would be reasonable to look for a factor that significantly increased survival rates as one of the main reasons for the steep increase in the prevalence of obesity in the USA in the 1980s. If significantly more people were surviving beyond age 40 in the 1980s and beyond, this would help explain the steep increase in obesity prevalence. People don’t die immediately after they become obese; obesity is a “disease” that first and foremost impairs quality of life for many years before it kills.

Now look at the graph below, from an article by Armstrong and colleagues (). It shows a significant decrease in mortality from infectious diseases in the USA since 1900, reaching a minimum point between 1950 and 1960 (possibly 1955), and remaining low afterwards. (The spike in 1918 is due to the influenza pandemic.) At the same time, mortality from non-infectious diseases remains relatively stable over the same period, leading to a similar decrease in overall mortality.

When proper treatment options are not available, infectious diseases kill disproportionately at ages 15 and under (). Someone who was 15 years old in the USA in 1955 would have been 40 years old in 1980, if he or she survived. Had this person been obese, this would have been just in time to contribute to the steep increase in obesity trends in the USA. This increase would be cumulative; if this person were to live to the age of 70, he or she would be contributing to the obesity statistics up to 2010.

Americans are clearly eating more, particularly highly palatable industrialized foods whose calorie-to-nutrient ratio is high. Americans are also less physically active. But one of the fundamental reasons for the sharp increase in obesity rates in the USA since the early 1980s is that Americans have been surviving beyond age 40 in significantly greater numbers.

This is due to the success of modern medicine and public health initiatives in dealing with infectious diseases.

PS: It is important to point out that this post is not about the increase in American obesity in general over the years, but rather about the sharp increase in obesity since the early 1980s. A few alternative hypotheses have been proposed in the comments section, of which one seems to have been favored by various readers: a significant increase in consumption of linoleic acid (not to be confused with linolenic acid) since the early 1980s.

The China Study II: Wheat’s total effect on mortality is significant, complex, and highlights the negative effects of low animal fat diets

The graph below shows the results of a multivariate nonlinear WarpPLS () analysis including the variables listed below. Each row in the dataset refers to a county in China, from the publicly available China Study II dataset (). As always, I thank Dr. Campbell and his collaborators for making the data publicly available. Other analyses based on the same dataset are also available ().
    - Wheat: wheat flour consumption in g/d.
    - Aprot: animal protein consumption in g/d.
    - PProt: plant protein consumption in g/d.
    - %FatCal: percentage of calories coming from fat.
    - Mor35_69: number of deaths per 1,000 people in the 35-69 age range.
    - Mor70_79: number of deaths per 1,000 people in the 70-79 age range.

Below are the total effects of wheat flour consumption, along with the number of paths used to calculate them, and the respective P values (i.e., probabilities that the effects are due to chance). Total effects are calculated by considering all of the paths connecting two variables. Identifying each path is a bit like solving a maze puzzle; you have to follow the arrows connecting the two variables. Version 3.0 of WarpPLS (soon to be released) does that automatically, and also calculates the corresponding P values.

To the best of my knowledge, this is the first time that total effects are calculated for this dataset. As you can see, the total effects of wheat flour consumption on mortality in the 35-69 and 70-79 age ranges are both significant, and fairly complex in this model, each relying on 7 paths. The P value for mortality in the 35-69 age range is 0.038; in other words, the probability that the effect is “real”, and thus not due to chance, is 96.2 percent (100-3.8=96.2). The P value for mortality in the 70-79 age range is 0.024; a 97.6 percent probability that the effect is “real”.

Note that in the model the effects of wheat flour consumption on mortality in both age ranges are hypothesized to be mediated by animal protein consumption, plant protein consumption, and fat consumption. These mediating effects have been suggested by previous analyses discussed on this blog (). The strongest individual paths are between wheat flour consumption and plant protein consumption, plant protein consumption and animal protein consumption, as well as animal protein consumption and fat consumption.

So wheat flour consumption contributes to plant protein consumption, probably by being a main source of plant protein (through gluten). Plant protein consumption in turn decreases animal protein consumption, which significantly decreases fat consumption. From this latter connection we can tell that most of the fat consumed likely came from animal sources.

How much fat and protein are we talking about? The graphs below tell us how much, and these graphs are quite interesting. They suggest that, in this dataset, daily protein consumption tended to be on average 60 g, whatever the source. If more protein came from plant foods, the proportion from animal foods went down, and vice-versa.

The more animal protein consumed, the more fat is also consumed in this dataset. And that is animal fat, which comes mostly in the form of saturated and monounsaturated fats, in roughly equal amounts. How do I know that it is animal fat? Because of the strong association with animal protein. By the way, with a few exceptions (e.g., some species of fatty fish) animal foods in general provide only small amounts of polyunsaturated fats – omega-3 and omega-6.

Individually, animal protein and wheat flour consumption have the strongest direct effects on mortality in both age ranges. Animal protein consumption is protective, and wheat flour consumption detrimental.

Does the connection between animal protein, animal fat, and longevity mean that a diet high in saturated and monounsaturated fats is healthy for most people? Not necessarily, at least without extrapolation, although the results do not suggest otherwise. Look at the amounts of fat consumed per day. They range from a little less than 20 g/d to a little over 90 g/d. By comparison, one steak of top sirloin (about 380 g of meat, cooked) trimmed to almost no visible fat gives you about 37 g of fat.

These results do suggest that consumption of animal fats, primarily saturated and monounsaturated fats, is likely to be particularly healthy in the context of a low fat diet. Or, said in a different way, these results suggest that longevity is decreased by diets that are low in animal fats.

How much fat should one eat? In this dataset, the more fat was consumed together with animal protein (i.e., the more animal fat was consumed), the better in terms of longevity. In other words, in this dataset the lowest levels of mortality were associated with the highest levels of animal fat consumption. The highest level of fat consumption in the dataset was a little over 90 g/d.

What about higher fat intake contexts? Well, we know that men on a high fat diet such as a variation of the Optimal Diet can consume on average a little over 170 g/d of animal fat (130 g/d for women), and their health markers remain generally good ().

One of the critical limiting factors, in terms of health, seems to be the amount of animal fat that one can eat and still remain relatively lean. Dietary saturated and monounsaturated fats are healthy. But when accumulated as excess body fat, beyond a certain level, they become pro-inflammatory.

HCE user experience: The anabolic range may be better measured in seconds than repetitions

It is not uncommon for those who do weight training to see no gains over long periods of time for certain weight training exercises (e.g., overhead press), even while they experience gains in other types of exercise (e.g., regular squats).

HealthCorrelator for Excel (HCE) and its main outputs, coefficients of association and graphs (), have been helping some creative users identify the reasons why they see no gains, and break out of the stagnation periods.

It may be a good idea to measure the number of seconds of effort per set; in addition to other variables such as numbers of sets and repetitions, and the amount of weight lifted. In some cases, an inverted J curve, full or partial (just the left side of it), shows up suggesting that the number of seconds of effort in a particular type of weight training exercise is a better predictor of muscle gain than the number of repetitions used.

The inverted J curve is similar to the one discussed in a previous post on HCE used for weight training improvement, where the supercompensation phenomenon is also discussed ().

Repetitions in the 6-12 range are generally believed to lead to peak anabolic response, and this is generally true for weight training exercises conducted in good form and to failure. It is also generally believed that muscular effort should be maintained for 20 to 120 seconds for peak anabolic response.

The problem is that in certain cases not even 12 repetitions lead to at least 20 seconds of effort. This is usually the case when the repetitions are performed very quickly. There are a couple of good reasons why this may happen: the person has above-average muscular power, or the range of motion used is limited.

What is muscular power, and why would someone want to limit the range of motion used in a weight training exercise?

Muscular power is different from muscular strength, and is normally distributed (bell curve) across the population, like most human traints (). Muscular power is related to the speed with which an individual can move a certain amount of weight. Muscular strength is related to the amount of weight moved. Frequently people who perform amazing feats of strength, like Dennis Rogers (), have above-average muscular power.

As for limiting the range of motion used in a weight training exercise, one of the advantages of doing so is that it reduces the risk of injury, as a wise commenter pointed out here some time ago (). It also has the advantage of increasing the number of variations of an exercise that can be used at different points in time; which is desirable, as variation is critical for sustained supercompensation ().

The picture below is from a YouTube video clip showing champion natural bodybuilder Doug Miller performing 27 repetitions of the deadlift with 405 lbs (). Doug is one of the co-authors of the book Biology for Bodybuilders, which has been reviewed here ().

The point of showing the video clip above is that the range of repetitions used would be perceived as quite high by many bodybuilders, but is nevertheless the one leading to a peak anabolic response for Doug. If you pay careful attention to the video, you will notice that Doug completes the 27 repetitions in 45 seconds, well within the anabolic range. If he had completed only 12 repetitions, at about the same pace, he would have done that a few seconds before hitting the 20-second mark.

Doug completes those 27 repetitions relatively quickly, because he has above-average muscular power, in addition to having above-average muscular strength.

Finding your sweet spot for muscle gain with HCE

In order to achieve muscle gain, one has to repeatedly hit the “supercompensation” window, which is a fleeting period of time occurring at some point in the muscle recovery phase after an intense anaerobic exercise session. The figure below, from Vladimir Zatsiorsky’s and William Kraemer’s outstanding book Science and Practice of Strength Training () provides an illustration of the supercompensation idea. Supercompensation is covered in more detail in a previous post ().

Trying to hit the supercompensation window is a common denominator among HealthCorrelator for Excel (HCE) users who employ the software () to maximize muscle gain. (That is, among those who know and subscribe to the theory of supercompensation.) This post outlines what I believe is a good way of doing that while avoiding some pitfalls. The data used in the example that follows has been created by me, and is based on a real case. I disguised the data, simplified it, added error etc. to make the underlying method relatively easy to understand, and so that the data cannot be traced back to its “real case” user (for privacy).

Let us assume that John Doe is an intermediate weight training practitioner. That is, he has already gone through the beginning stage where most gains come from neural adaptation. For him, new gains in strength are a reflection of gains in muscle mass. The table below summarizes the data John obtained when he decided to vary the following variables in order to see what effects they have on his ability to increase the weight with which he conducted the deadlift () in successive exercise sessions:
    - Number of rest days in between exercise sessions (“Days of rest”).
    - The amount of weight he used in each deadlift session (“Deadlift weight”).
    - The amount of weight he was able to add to the bar each session (“Delta weight”).
    - The number of deadlift sets and reps (“Deadlift sets” and “Deadlift reps”, respectively).
    - The total exercise volume in each session (“Deadlift volume”). This was calculated as follows: “Deadlift weight” x “Deadlift sets” x “Deadlift reps”.

John’s ability to increase the weight with which he conducted the deadlift in each session is measured as “Delta weight”. That was his main variable of interest. This may not look like an ideal choice at first glance, as arguably “Deadlift volume” is a better measure of total effort and thus actual muscle gain. The reality is that this does not matter much in his case, because: John had long rest periods within sets, of around 5 minutes; and he made sure to increase the weight in each successive session as soon as he felt he could, and by as much as he could, thus never doing more than 24 reps. If you think that the number of reps employed by John is too high, take a look at a post in which I talk about Doug Miller and his ideas on weight training ().

Below are three figures, with outputs from HCE: a table showing the coefficients of association between “Delta weight” and the other variables, and two graphs showing the variation of “Delta weight” against “Deadlift volume” and “Days of rest”. As you can see, nothing seems to be influencing “Delta weight” strongly enough to reach the 0.6 level that I recommend as the threshold for a “real effect” to be used in HCE analyses. There are two possibilities here: it is what it looks it is, that is, none of the variables influence “Delta weight”; or there are effects, but they do not show up in the associations table (as associations equal to or greater than 0.6) because of nonlinearity.

The graph of “Delta weight” against “Deadlift volume” is all over the place, suggesting a lack of association. This is true for the other variables as well, except “Days of rest”; the last graph above. That graph, of “Delta weight” against “Days of rest”, suggests the existence of a nonlinear association with the shape of an inverted J curve. This type of association is fairly common. In this case, it seems that “Delta weight” is maximized in the 6-7 range of “Days of rest”. Still, even varying things almost randomly, John achieved a solid gain over the time period. That was a 33 percent gain from the baseline “Deadlift weight”, a gain calculated as: (285-215)/215.

HCE, unlike WarpPLS (), does not take nonlinear relationships into consideration in the estimation of coefficients of association. In order to discover nonlinear associations, users have to inspect the graphs generated by HCE, as John did. Based on his inspection, John decided to changes things a bit, now working out on the right side of the J curve, with 6 or more “Days of rest”. That was difficult for John at first, as he was addicted to exercising at a much higher frequency; but after a while he became a “minimalist”, even trying very long rest periods.

Below are four figures. The first is a table summarizing the data John obtained for his second trial. The other three are outputs from HCE, analogous to those obtained in the first trial: a table showing the coefficients of association between “Delta weight” and the other variables, two graphs (side-by-side) showing “Delta weight” against “Deadlift sets” and “Deadlift reps”, and one graph of “Delta weight” against “Days of rest”. As you can see, “Days of rest” now influences “Delta weight” very strongly. The corresponding association is a very high -0.981! The negative sign means that “Delta weight” decreases as “Days of rest” increase. This does NOT mean that rest is not important; remember, John is now operating on the right side of the J curve, with 6 or more “Days of rest”.

The last graph above suggests that taking 12 or more “Days of rest” shifted things toward the end of the supercompensation window, in fact placing John almost outside of that window at 13 “Days of rest”. Even so, there was no loss of strength, and thus probably no muscle loss. Loss of strength would be suggested by a negative “Delta weight”, which did not occur (the “Delta weight” went down to zero, at 13 “Days of rest”). The two graphs shown side-by-side suggest that 2 “Deadlift sets” seem to work just as well for John as 3 or 4, and that “Deadlift reps” in the 18-24 range also work well for John.

In this second trial, John achieved a better gain over a similar time period than in the first trial. That was a 36 percent gain from the baseline “Deadlift weight”, a gain calculated as: (355-260)/260. John started with a lower baseline than in the end of the first trial period, probably due to detraining, but achieved a final “Deadlift weight” that was likely very close to his maximum potential (at the reps used). Because of this, the 36 percent gain in the period is a lot more impressive than it looks, as it happened toward the end of a saturation curve (e.g., the far right end of a logarithmic curve).

One important thing to keep in mind is that if an HCE user identifies a nonlinear relationship of the J-curve type by inspecting the graphs like John did, in further analyses the focus should be on the right or left side of the curve by either: splitting the dataset into two, and running a separate analysis for each new dataset; or running a new trial, now sticking with a range of variation on the right or left side of the curve, as John did. The reason is that nonlinear relationships tend to distort the linear coefficients calculated by HCE, hiding a real relationship between two variables.

This is a very simplified example. Most serious bodybuilders will measure variations in a number of variables at the same time, for a number of different exercise types and formats, and for longer periods. That is, their “HealthData” sheet in HCE will be a lot more complex. They will also have multiple instances of HCE running on their computer. HCE is a collection of sheets and code that can be copied, and saved with different names. The default is “HCE_1_0.xls” or “HCE_1_0.xlsm”, depending on which version you are using. Each new instance of HCE may contain a different dataset for analysis, stored in the “HealthData” sheet.

It is strongly recommended that you keep your data in a separate set of sheets, as a backup. That is, do not store all your data in the “HealthData” sheets in different HCE instances. Also, when you copy your data into the “HealthData” sheet in HCE, copy only the values and formats, and NOT the formulas. If you copy the formulas, you may end up having some problems, as some of the cells in the “HealthData” sheet will not be storing values. I also recommend storing values for other types variables, particularly perception-based variables.

Examples of perception-based variables are: “Perceived stress”, “Perceived delayed onset muscle soreness (DOMS)”, and “Perceived non-DOMS pain”. These can be answered on Likert-type scales, such as scales going from 1 (very strongly disagree) to 7 (very strongly agree) in response to self-prepared question-statements like “I feel stressed out” (for “Perceived stress”). If you find that a variable like “Perceived non-DOMS pain” is associated with working out at a particular volume range, that may help you avoid serious injury in the future, as non-DOMS pain is not a very good sign (). You also may find that working out in the volume range that is associated with non-DOMS pain adds nothing in terms of muscle gain.

Generally speaking, I think that many people will find out that their sweet spot for muscle gain involves less frequent exercise at lower volumes than they think. Still, each individual is unique; there is no one quite like John. The relationship between “Delta weight” and “Days of rest” varies from person to person based on age; older folks generally require more rest. It also varies based on whether the person is dieting or not; less food intake leads to longer recovery periods. Women will probably see visible lower-body muscle gain, but very little visible upper-body muscle gain (in the absence of steroid use), even as they experience upper-body strength gains. Other variables of interest for both men and women may be body weight, body fat percentage, and perceived muscle tone.

Triglycerides, VLDL, and industrial carbohydrate-rich foods

Below are the coefficients of association calculated by HealthCorrelator for Excel (HCE) for user John Doe. The coefficients of association are calculated as linear correlations in HCE (). The focus here is on the associations between fasting triglycerides and various other variables. Take a look at the coefficient of association at the top, with VLDL cholesterol, indicated with a red arrow. It is a very high 0.999.

Whoa! What is this – 0.999! Is John Doe a unique case? No, this strong association between fasting triglycerides and VLDL cholesterol is a very common pattern among HCE users. The reason is simple. VLDL cholesterol is not normally measured directly, but typically calculated based on fasting triglycerides, by dividing the fasting triglycerides measurement by 5. And there is an underlying reason for that - fasting triglycerides and VLDL cholesterol are actually very highly correlated, based on direct measurements of these two variables.

But if VLDL cholesterol is calculated based on fasting triglycerides (VLDL cholesterol  = fasting triglycerides / 5), how come the correlation is 0.999, and not a perfect 1? The reason is the rounding error in the measurements. Whenever you see a correlation this high (i.e., 0.999), it is reasonable to suspect that the source is an underlying linear relationship disturbed by rounding error.

Fasting triglycerides are probably the most useful measures on standard lipid panels. For example, fasting triglycerides below 70 mg/dl suggest a pattern of LDL particles that is predominantly of large and buoyant particles. This pattern is associated with a low incidence of cardiovascular disease (). Also, chronically high fasting triglycerides are a well known marker of the metabolic syndrome, and a harbinger of type 2 diabetes.

Where do large and buoyant LDL particles come from? They frequently start as "big" (relatively speaking) blobs of fat, which are actually VLDL particles. The photo is from the excellent book by Elliott & Elliott (); it shows, on the same scale: (a) VLDL particles, (b) chylomicrons, (c) LDL particles, and (d) HDL particles. The dark bar at the bottom of each shot is 1000 A in length, or 100 nm (A = angstrom; nm = nanometer; 1 nm = 10 A).

If you consume an excessive amount of carbohydrates, my theory is that your liver will produce an abnormally large number of small VLDL particles (also shown on the photo above), a proportion of which will end up as small and dense LDL particles. The liver will do that relatively quickly, probably as a short-term compensatory mechanism to avoid glucose toxicity. It will essentially turn excess glucose, from excess carbohydrates, into fat. The VLDL particles carrying that fat in the form of triglycerides will be small because the liver will be in a hurry to clear the excess glucose in circulation, and will have no time to produce large particles, which take longer to produce individually.

This will end up leading to excess triglycerides hanging around in circulation, long after they should have been used as sources of energy. High fasting triglycerides will be a reflection of that. The graphs below, also generated by HCE for John Doe, show how fasting triglycerides and VLDL cholesterol vary in relation to refined carbohydrate consumption. Again, the graphs are not identical in shape because of rounding error; the shapes are almost identical.

Small and dense LDL particles, in the presence of other factors such as systemic inflammation, will contribute to the formation of atherosclerotic plaques. Again, the main source of these particles would be an excessive amount of carbohydrates. What is an excessive amount of carbohydrates? Generally speaking, it is an amount beyond your liver’s capacity to convert the resulting digestion byproducts, fructose and glucose, into liver glycogen. This may come from spaced consumption throughout the day, or acute consumption in an unnatural form (a can of regular coke), or both.

Liver glycogen is sugar stored in the liver. This is the main source of sugar for your brain. If your blood sugar levels become too low, your brain will get angry. Eventually it will go from angry to dead, and you will finally find out what awaits you in the afterlife.

Should you be a healthy athlete who severely depletes liver glycogen stores on a regular basis, you will probably have an above average liver glycogen storage and production capacity. That will be a result of long-term compensatory adaptation to glycogen depleting exercise (). As such, you may be able to consume large amounts of carbohydrates, and you will still not have high fasting triglycerides. You will not carry a lot of body fat either, because the carbohydrates will not be converted to fat and sent into circulation in VLDL particles. They will be used to make liver glycogen.

In fact, if you are a healthy athlete who severely depletes liver glycogen stores on a regular basis, excess calories will be just about the only thing that will contribute to body fat gain. Your threshold for “excess” carbohydrates will be so high that you will feel like the whole low carbohydrate community is not only misguided but also part of a conspiracy against people like you. If you are also an aggressive blog writer, you may feel compelled to tell the world something like this: “Here, I can eat 300 g of carbohydrates per day and maintain single-digit body fat levels! Take that you low carbohydrate idiots!”

Let us say you do not consume an excessive amount of carbohydrates; again, what is excessive or not varies, probably dramatically, from individual to individual. In this case your liver will produce a relatively small number of fat VLDL particles, which will end up as large and buoyant LDL particles. The fat in these large VLDL particles will likely not come primarily from conversion of glucose and/or fructose into fat (i.e., de novo lipogenesis), but from dietary sources of fat.

How do you avoid consuming excess carbohydrates? A good way of achieving that is to avoid man-made carbohydrate-rich foods. Another is adopting a low carbohydrate diet. Yet another is to become a healthy athlete who severely depletes liver glycogen stores on a regular basis; then you can eat a lot of bread, pasta, doughnuts and so on, and keep your fingers crossed for the future.

Either way, fasting triglycerides will be strongly correlated with VLDL cholesterol, because VLDL particles contain both triglycerides (“encapsulated” fat, not to be confused with “free” fatty acids) and cholesterol. If a large number of VLDL particles are produced by one’s liver, the person’s fasting triglycerides reading will be high. If a small number of VLDL particles are produced, even if they are fat particles, the fasting triglycerides reading will be relatively low. Neither VLDL cholesterol nor fasting triglycerides will be zero though.

Now, you may be wondering, how come a small number of fat VLDL particles will eventually lead to low fasting triglycerides? After all, they are fat particles, even though they occur in fewer numbers. My hypothesis is that having a large number of small-dense VLDL particles in circulation is an abnormal, unnatural state, and that our body is not well designed to deal with that state. Use of lipoprotein-bound fat as a source of energy in this state becomes somewhat less efficient, leading to high triglycerides in circulation; and also to hunger, as our mitochondria like fat.

This hypothesis, and the theory outlined above, fit well with the numbers I have been seeing for quite some time from HCE users. Note that it is a bit different from the more popular theory, particularly among low carbohydrate writers, that fat is force-stored in adipocytes (fat cells) by insulin and not released for use as energy, also leading to hunger. What I am saying here, which is compatible with this more popular theory, is that lipoproteins, like adipocytes, also end up holding more fat than they should if you consume excess carbohydrates, and for longer.

Want to improve your health? Consider replacing things like bread and cereal with butter and eggs in your diet (). And also go see you doctor (); if he disagrees with this recommendation, ask him to read this post and explain why he disagrees.

The China Study II: How gender takes us to the elusive and deadly factor X

The graph below shows the mortality in the 35-69 and 70-79 age ranges for men and women for the China Study II dataset. I discussed other results in my two previous posts () (), all taking us to this post. The full data for the China Study II study is publicly available (). The mortality numbers are actually averages of male and female deaths by 1,000 people in each of several counties, in each of the two age ranges.

Men do tend to die earlier than women, but the difference above is too large.

Generally speaking, when you look at a set time period that is long enough for a good number of deaths (not to be confused with “a number of good deaths”) to be observed, you tend to see around 5-10 percent more deaths among men than among women. This is when other variables are controlled for, or when men and women do not adopt dramatically different diets and lifestyles. One of many examples is a study in Finland (); you have to go beyond the abstract on this one.

As you can see from the graph above, in the China Study II dataset this difference in deaths is around 50 percent!

This huge difference could be caused by there being significantly more men than women per county included the dataset. But if you take a careful look at the description of the data collection methods employed (), this does not seem to be the case. In fact, the methodology descriptions suggest that the researchers tried to have approximately the same number of women and men studied in each county. The numbers reported also support this assumption.

As I said before, this is a well executed research project, for which Dr. Campbell and his collaborators should be commended. I may not agree with all of their conclusions, but this does not detract even a bit from the quality of the data they have compiled and made available to us all.

So there must be another factor X causing this enormous difference in mortality (and thus longevity) among men and women in the China Study II dataset.

What could be this factor X?

This situation helps me illustrate a point that I have made here before, mostly in the comments under other posts. Sometimes a variable, and its effects on other variables, are mostly a reflection of another unmeasured variable. Gender is a variable that is often involved in this type of situation. Frequently men and women do things very differently in a given population due to cultural reasons (as opposed to biological reasons), and those things can have a major effect on their health.

So, the search for our factor X is essentially a search for a health-relevant variable that is reflected by gender but that is not strictly due to the biological aspects that make men and women different (these can explain only a 5-10 percent difference in mortality). That is, we are looking for a variable that shows a lot of variation between men and women, that is behavioral, and that has a clear impact on health. Moreover, as it should be clear from my last post, we are looking for a variable that is unrelated to wheat flour and animal protein consumption.

As it turns out, the best candidate for the factor X is smoking, particularly cigarette smoking.

The second best candidate for factor X is alcohol abuse. Alcohol abuse can be just as bad for one’s health as smoking is, if not worse, but it may not be as good a candidate for factor X because the difference in prevalence between men and women does not appear to be just as large in China (). But it is still large enough for us to consider it a close second as a candidate for factor X, or a component of a more complex factor X – a composite of smoking, alcohol abuse and a few other coexisting factors that may be reflected by gender.

I have had some discussions about this with a few colleagues and doctoral students who are Chinese (thanks William and Wei), and they mentioned stress to me, based on anecdotal evidence. Moreover, they pointed out that stressful lifestyles, smoking, and alcohol abuse tend to happen together - with a much higher prevalence among men than women.

What an anti-climax for this series of posts eh?

With all the talk on the Internetz about safe and unsafe starches, animal protein, wheat bellies, and whatnot! C’mon Ned, give me a break! What about insulin!? What about leucine deficiency … or iron overload!? What about choline!? What about something truly mysterious, related to an obscure or emerging biochemistry topic; a hormone du jour like leptin perhaps? Whatever, something cool!

Smoking and alcohol abuse!? These are way too obvious. This is NOT cool at all!

Well, reality is often less mysterious than we want to believe it is.

Let me focus on smoking from here on, since it is the top candidate for factor X, although much of the following applies to alcohol abuse and a combination of the two as well.

One gets different statistics on cigarette smoking in China depending on the time period studied, but one thing seems to be a common denominator in these statistics. Men tend to smoke in much, much higher numbers than women in China. And this is not a recent phenomenon.

For example, a study conducted in 1996 () states that “smoking continues to be prevalent among more men (63%) than women (3.8%)”, and notes that these results are very similar to those in 1984, around the time when the China Study II data was collected.

A 1995 study () reports similar percentages: “A total of 2279 males (67%) but only 72 females (2%) smoke”. Another study () notes that in 1976 “56% of the men and 12% of the women were ever-smokers”, which together with other results suggest that the gap increased significantly in the 1980s, with many more men than women smoking. And, most importantly, smoking industrial cigarettes.

So we are possibly talking about a gigantic difference here; the prevalence of industrial cigarette smoking among men may have been over 30 times the prevalence among women in the China Study II dataset.

Given the above, it is reasonable to conclude that the variable “SexM1F2” reflects very strongly the variable “Smoking”, related to industrial cigarette smoking, and in an inverse way. I did something that, grossly speaking, made the mysterious factor X explicit in the WarpPLS model discussed in my previous post. I replaced the variable “SexM1F2” in the model with the variable “Smoking” by using a reverse scale (i.e., 1 and 2, but reversing the codes used for “SexM1F2”). The results of the new WarpPLS analysis are shown on the graph below. This is of course far from ideal, but gives a better picture to readers of what is going on than sticking with the variable “SexM1F2”.

With this revised model, the associations of smoking with mortality in the 35-69 and 70-79 age ranges are a lot stronger than those of animal protein and wheat flour consumption. The R-squared coefficients for mortality in both ranges are higher than 20 percent, which is a sign that this model has decent explanatory power. Animal protein and wheat flour consumption are still significantly associated with mortality, even after we control for smoking; animal protein seems protective and wheat flour detrimental. And smoking’s association with the amount of animal protein and wheat flour consumed is practically zero.

Replacing “SexM1F2” with “Smoking” would be particularly far from ideal if we were analyzing this data at the individual level. It could lead to some outlier-induced errors; for example, due to the possible existence of a minority of female chain smokers. But this variable replacement is not as harmful when we look at county-level data, as we are doing here.

In fact, this is as good and parsimonious model of mortality based on the China Study II data as I’ve ever seen based on county level data.

Now, here is an interesting thing. Does the original China Study II analysis of univariate correlations show smoking as a major problem in terms of mortality? Not really.

The table below, from the China Study II report (), shows ALL of the statistically significant (P<0.05) univariate correlations with mortality in 70-79 age range. I highlighted the only measure that is directly related to smoking; that is “dSMOKAGEm”, listed as “questionnaire AGE MALE SMOKERS STARTED SMOKING (years)”.

The high positive correlation with “dSMOKAGEm” does not even make a lot of sense, as one would expect a negative correlation here – i.e., the earlier in life folks start smoking, the higher should be the mortality. But this reverse-signed correlation may be due to smokers who get an early start dying in disproportionally high numbers before they reach age 70, and thus being captured by another age range mortality variable. The fact that other smoking-related variables are not showing up on the table above is likely due to distortions caused by inter-correlations, as well as measurement problems like the one just mentioned.

As one looks at these univariate correlations, most of them make sense, although several can be and probably are distorted by correlations with other variables, even unmeasured variables. And some unmeasured variables may turn out to be critical. Remember what I said in my previous post – the variable “SexM1F2” was introduced by me; it was not in the original dataset. “Smoking” is this variable, but reversed, to account for the fact that men are heavy smokers and women are not.

Univariate correlations are calculated without adjustments or control. To correct this problem one can adjust a variable based on other variables; as in “adjusting for age”. This is not such a good technique, in my opinion; it tends to be time-consuming to implement, and prone to errors. One can alternatively control for the effects of other variables; a better technique, employed in multivariate statistical analyses. This latter technique is the one employed in WarpPLS analyses ().

Why don’t more smoking-related variables show up on the univariate correlations table above? The reason is that the table summarizes associations calculated based on data for both sexes. Since the women in the dataset smoked very little, including them in the analysis together with men lowers the strength of smoking-related associations, which would probably be much stronger if only men were included. It lowers the strength of the associations to the point that their P values become higher than 0.05, leading to their exclusion from tables like the one above. This is where the aggregation process that may lead to ecological fallacy shows its ugly head.

No one can blame Dr. Campbell for not issuing warnings about smoking, even as they came mixed with warnings about animal food consumption (). The former warnings, about smoking, make a lot of sense based on the results of the analyses in this and the last two posts.

The latter warnings, about animal food consumption, seem increasingly ill-advised. Animal food consumption may actually be protective in regards to the factor X, as it seems to be protective in terms of wheat flour consumption ().

The China Study II: Gender, mortality, and the mysterious factor X

WarpPLS and HealthCorrelator for Excel were used to do the analyses below. For other China Study analyses, many using WarpPLS as well as HealthCorrelator for Excel, click here. For the dataset used, visit the HealthCorrelator for Excel site and check under the sample datasets area. As always, I thank Dr. T. Colin Campbell and his collaborators for making the data publicly available for independent analyses.

In my previous post I mentioned some odd results that led me to additional analyses. Below is a screen snapshot summarizing one such analysis, of the ordered associations between mortality in the 35-69 and 70-79 age ranges and all of the other variables in the dataset. As I said before, this is a subset of the China Study II dataset, which does not include all of the variables for which data was collected. The associations shown below were generated by HealthCorrelator for Excel.

The top associations are positive and with mortality in the other range (the “M006 …” and “M005 …” variables). This is to be expected if ecological fallacy is not a big problem in terms of conclusions drawn from this dataset. In other words, the same things cause mortality to go up in the two age ranges, uniformly across counties. This is reassuring from a quantitative analysis perspective.

The second highest association in both age ranges is with the variable “SexM1F2”. This variable is a “dummy” variable coded as 1 for male sex and 2 for female, which I added to the dataset myself – it did not exist in the original dataset. The association in both age ranges is negative, meaning that being female is protective. They reflect in part the role of gender on mortality, more specifically the biological aspects of being female, since we have seen before in previous analyses that being female is generally health-protective.

I was able to add a gender-related variable to the model because the data was originally provided for each county separately for males and females, as well as through “totals” that were calculated by aggregating data from both males and females. So I essentially de-aggregated the data by using data from males and females separately, in which case the totals were not used (otherwise I would have artificially reduced the variance in all variables, also possibly adding uniformity where it did not belong). Using data from males and females separately is the reverse of the aggregation process that can lead to ecological fallacy problems.

Anyway, the associations with the variable “SexM1F2” got me thinking about a possibility. What if females consumed significantly less wheat flour and more animal protein in this dataset? This could be one of the reasons behind these strong associations between being female and living longer. So I built a more complex WarpPLS model than the one in my previous post, and ran a linear multivariate analysis on it. The results are shown below.

What do these results suggest? They suggest no strong associations between gender and wheat flour or animal protein consumption. That is, when you look at county averages, men and women consumed about the same amounts of wheat flour and animal protein. Also, the results suggest that animal protein is protective and wheat flour is detrimental, in terms of longevity, regardless of gender. The associations between animal protein and wheat flour are essentially the same as the ones in my previous post. The beta coefficients are a bit lower, but some P values improved (i.e., decreased); the latter most likely due to better resample set stability after including the gender-related variable.

Most importantly, there is a very strong protective effect associated with being female, and this effect is independent of what the participants ate.

Now, if you are a man, don’t rush to take hormones to become a woman with the goal of living longer just yet. This advice is not only due to the likely health problems related to becoming a transgender person; it is also due to a little problem with these associations. The problem is that the protective effect suggested by the coefficients of association between gender and mortality seems too strong to be due to men "being women with a few design flaws".

There is a mysterious factor X somewhere in there, and it is not gender per se. We need to find a better candidate.

One interesting thing to point out here is that the above model has good explanatory power in regards to mortality. I'd say unusually good explanatory power given that people die for a variety of reasons, and here we have a model explaining a lot of that variation. The model  explains 45 percent of the variance in mortality in the 35-69 age range, and 28 percent of the variance in the 70-79 age range.

In other words, the model above explains nearly half of the variance in mortality in the 35-69 age range. It could form the basis of a doctoral dissertation in nutrition or epidemiology with important  implications for public health policy in China. But first the factor X must be identified, and it must be somehow related to gender.

Next post coming up soon ...

The China Study II: Animal protein, wheat, and mortality … there is something odd here!

WarpPLS and HealthCorrelator for Excel were used in the analyses below. For other China Study analyses, many using WarpPLS and HealthCorrelator for Excel, click here. For the dataset used, visit the HealthCorrelator for Excel site and check under the sample datasets area. I thank Dr. T. Colin Campbell and his collaborators at the University of Oxford for making the data publicly available for independent analyses.

The graph below shows the results of a multivariate linear WarpPLS analysis including the following variables: Wheat (wheat flour consumption in g/d), Aprot (animal protein consumption in g/d), Mor35_69 (number of deaths per 1,000 people in the 35-69 age range), and Mor70_79 (number of deaths per 1,000 people in the 70-79 age range).

Just a technical comment here, regarding the possibility of ecological fallacy. I am not going to get into this in any depth now, but let me say that the patterns in the data suggest that, with the possible exception of some variables (e.g., blood glucose, gender; the latter will get us going in the next few posts), ecological fallacy due to county aggregation is not a big problem. The threat of ecological fallacy exists, here and in many other datasets, but it is generally overstated (often by those whose previous findings are contradicted by aggregated results).

I have not included plant protein consumption in the analysis because plant protein consumption is very strongly and positively associated with wheat flour consumption. The reason is simple. Almost all of the plant protein consumed by the participants in this study was probably gluten, from wheat products. Fruits and vegetables have very small amounts of protein. Keeping that in mind, what the graph above tells us is that:

- Wheat flour consumption is significantly and negatively associated with animal protein consumption. This is probably due to those eating more wheat products tending to consume less animal protein.

- Wheat flour consumption is positively associated with mortality in the 35-69 age range. The P value (P=0.06) is just shy of the 5 percent (i.e., P=0.05) that most researchers would consider to be the threshold for statistical significance. More consumption of wheat in a county, more deaths in this age range.

- Wheat flour consumption is significantly and positively associated with mortality in the 70-79 age range. More consumption of wheat in a county, more deaths in this age range.

- Animal protein consumption is not significantly associated with mortality in the 35-69 age range.

- Animal protein consumption is significantly and negatively associated with mortality in the 70-79 age range. More consumption of animal protein in a county, fewer deaths in this age range.

Let me tell you, from my past experience analyzing health data (as well as other types of data, from different fields), that these coefficients of association do not suggest super-strong associations. Actually this is also indicated by the R-squared coefficients, which vary from 3 to 7 percent. These are the variances explained by the model on the variables above the R-squared coefficients. They are low, which means that the model has weak explanatory power.

R-squared coefficients of 20 percent and above would be more promising. I hate to disappoint hardcore carnivores and the fans of the “wheat is murder” theory, but these coefficients of association and variance explained are probably way less than what we would expect to see if animal protein was humanity's salvation and wheat its demise.

Moreover, the lack of association between animal protein consumption and mortality in the 35-69 age range is a bit strange, given that there is an association suggestive of a protective effect in the 70-79 age range.

Of course death happens for all kinds of reasons, not only what we eat. Still, let us take a look at some other graphs involving these foodstuffs to see if we can form a better picture of what is going on here. Below is a graph showing mortality at the two age ranges for different levels of animal protein consumption. The results are organized in quintiles.

As you can see, the participants in this study consumed relatively little animal protein. The lowest mortality in the 70-79 age range, arguably the range of higher vulnerability, was for the 28 to 35 g/d quintile of consumption. That was the highest consumption quintile. About a quarter to a third of 1 lb/d of beef, and less of seafood (in general), would give you that much animal protein.

Keep in mind that the unit of analysis here is the county, and that these results are based on county averages. I wish I had access to data on individual participants! Still I stand by my comment earlier on ecological fallacy. Don't worry too much about it just yet.

Clearly the above results and graphs contradict claims that animal protein consumption makes people die earlier, and go somewhat against the notion that animal protein consumption causes things that make people die earlier, such as cancer. But they do so in a messy way - that spike in mortality in the 70-79 age range for 21-28 g/d of animal protein is a bit strange.

Below is a graph showing mortality at the two age ranges (i.e., 35-69 and 70-79) for different levels of wheat flour consumption. Again, the results are shown in quintiles.

Without a doubt the participants in this study consumed a lot of wheat flour. The lowest mortality in the 70-79 age range, which is the range of higher vulnerability, was for the 300 to 450 g/d quintile of wheat flour consumption. The high end of this range is about 1 lb/d of wheat flour! How many slices of bread would this be equivalent to? I don’t know, but my guess is that it would be many.

Well, this is not exactly the smoking gun linking wheat with early death, a connection that has been reaching near mythical proportions on the Internetz lately. Overall, the linear trend seems to be one of decreased longevity associated with wheat flour consumption, as suggested by the WarpPLS results, but the relationship between these two variables is messy and somewhat weak. It is not even clearly nonlinear, at least in terms of the ubiquitous J-curve relationship.

Frankly, there is something odd about these results.

This oddity led to me to explore, using HealthCorrelator for Excel, all ordered associations between mortality in the 35-69 and 70-79 age ranges and all of the other variables in the dataset. That in turn led me to a more complex WarpPLS analysis, which I’ll talk about in my next post, which is still being written.

I can tell you right now that there will be more oddities there, which will eventually take us to what I refer to as the mysterious factor X. Ah, by the way, that factor X is not gender - but gender leads us to it.