Lifeworld

The “great blogosphere debate” rages on regarding the effects of carbohydrates and insulin on health. A lot of action has been happening recently on Peter’s blog, with knowledgeable folks chiming in, such as Peter himself, Dr. Harris, Dr. B.G. (my sista from anotha mista), John, Nigel, CarbSane, Gunther G., Ed, and many others.

I like to see open debate among people who hold different views consistently, are willing to back them up with at least some evidence, and keep on challenging each other’s views. It is very unlikely that any one person holds the whole truth regarding health matters. Unfortunately this type of debate also confuses a lot of people, particularly those blog lurkers who want to get all of their health information from one single source.

Part of that “great blogosphere debate” debate hinges on the effect of low or high carbohydrate dieting on total calorie consumption. Well, let us see what the China Study II data can tell us about that, and about a few other things.

WarpPLS was 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 here, visit the HealthCorrelator for Excel site and check under the sample datasets area.

The two graphs below show the relationships between various foods, carbohydrates as a percentage of total calories, and total calorie consumption. A basic linear analysis was employed here. As carbohydrates as a percentage of total calories go up, the diet generally becomes a high carbohydrate diet. As it goes down, we see a move to the low carbohydrate end of the scale.


The left parts of the two graphs above are very similar. They tell us that wheat flour consumption is very strongly and negatively associated with rice consumption; i.e., wheat flour displaces rice. They tell us that fruit consumption is positively associated with rice consumption. They also tell us that high wheat flour consumption is strongly and positively associated with being on a high carbohydrate diet.

Neither rice nor fruit consumption has a statistically significant influence on whether the diet is high or low in carbohydrates, with rice having some effect and fruit practically none. But wheat flour consumption does. Increases in wheat flour consumption lead to a clear move toward the high carbohydrate diet end of the scale.

People may find the above results odd, but they should realize that white glutinous rice is only 20 percent carbohydrate, whereas wheat flour products are usually 50 percent carbohydrate or more. Someone consuming 400 g of white rice per day, and no other carbohydrates, will be consuming only 80 g of carbohydrates per day. Someone consuming 400 g of wheat flour products will be consuming 200 g of carbohydrates per day or more.

Fruits generally have much less carbohydrate than white rice, even very sweet fruits. For example, an apple is about 12 percent carbohydrate.

There is a measure that reflects the above differences somewhat. That measure is the glycemic load of a food; not to be confused with the glycemic index.

The right parts of the graphs above tell us something else. They tell us that the percentage of carbohydrates in one’s diet is strongly associated with total calorie consumption, and that this is not the case with percentage of fat in one’s diet.

Given the above, one may be interested in looking at the contribution of individual foods to total calorie consumption. The graph below focuses on that. The results take nonlinearity into consideration; they were generated using the Warp3 algorithm option of WarpPLS.


As you can see, wheat flour consumption is more strongly associated with total calories than rice; both associations being positive. Animal food consumption is negatively associated, somewhat weakly but statistically significantly, with total calories. Let me repeat for emphasis: negatively associated. This means that, as animal food consumption goes up, total calories consumed go down.

These results may seem paradoxical, but keep in mind that animal foods displace wheat flour in this dataset. Note that I am not saying that wheat flour consumption is a confounder; it is controlled for in the model above.

What does this all mean?

Increases in both wheat flour and rice consumption lead to increases in total caloric intake in this dataset. Wheat has a stronger effect. One plausible mechanism for this is abnormally high blood glucose elevations promoting abnormally high insulin responses. Refined carbohydrate-rich foods are particularly good at raising blood glucose fast and keeping it elevated, because they usually contain a lot of easily digestible carbohydrates. The amounts here are significantly higher than anything our body is “designed” to handle.

In normoglycemic folks, that could lead to a “lite” version of reactive hypoglycemia, leading to hunger again after a few hours following food consumption. Insulin drives calories, as fat, into adipocytes. It also keeps those calories there. If insulin is abnormally elevated for longer than it should be, one becomes hungry while storing fat; the fat that should have been released to meet the energy needs of the body. Over time, more calories are consumed; and they add up.

The above interpretation is consistent with the result that the percentage of fat in one’s diet has a statistically non-significant effect on total calorie consumption. That association, although non-significant, is negative. Again, this looks paradoxical, but in this sample animal fat displaces wheat flour.

Moreover, fat leads to no insulin response. If it comes from animals foods, fat is satiating not only because so much in our body is made of fat and/or requires fat to run properly; but also because animal fat contains micronutrients, and helps with the absorption of those micronutrients.

Fats from oils, even the healthy ones like coconut oil, just do not have the latter properties to the same extent as unprocessed fats from animal foods. Think slow-cooking meat with some water, making it release its fat, and then consuming all that fat as a sauce together with the meat.

In the absence of industrialized foods, typically we feel hungry for those foods that contain nutrients that our body needs at a particular point in time. This is a subconscious mechanism, which I believe relies in part on past experience; the reason why we have “acquired tastes”.

Incidentally, fructose leads to no insulin response either. Fructose is naturally found mostly in fruits, in relatively small amounts when compared with industrial foods rich in refined sugars.

And no, the pancreas does not get “tired” from secreting insulin.

The more refined a carbohydrate-rich food is, the more carbohydrates it tends to pack per unit of weight. Carbohydrates also contribute calories; about 4 calories per g. Thus more carbohydrates should translate into more calories.

If someone consumes 50 g of carbohydrates per day in excess of caloric needs, that will translate into about 22.2 g of body fat being stored. Over a month, that will be approximately 666.7 g. Over a year, that will be 8 kg, or 17.6 lbs. Over 5 years, that will be 40 kg, or 88 lbs. This is only from carbohydrates; it does not consider other macronutrients.

There is no need to resort to the “tired pancreas” theory of late-onset insulin resistance to explain obesity in this context. Insulin resistance is, more often than not, a direct result of obesity. Type 2 diabetes is by far the most common type of diabetes; and most type 2 diabetics become obese or overweight before they become diabetic. There is clearly a genetic effect here as well, which seems to moderate the relationship between body fat gain and liver as well as pancreas dysfunction.

It is not that hard to become obese consuming refined carbohydrate-rich foods. It seems to be much harder to become obese consuming animal foods, or fruits.

John was overweight, out of shape, and experiencing fatigue. What did he do? He removed foods rich in refined carbohydrates and sugars from his diet. He also ditched industrial seed oils and started exercising. He used HealthCorrelator for Excel (HCE) to keep track of several health-related numbers over time (see figure below).


Over the period of time covered in the dataset, health markers steadily improved. For example, John’s HDL cholesterol went from a little under 40 mg/dl to just under 70; see chart below, one of many generated by HCE.


However, John’s blood pressure varied strangely during that time, as you can see on the chart below showing the variation of systolic blood pressure (SBP) against time. What could have been the reason for that? Salt intake is an unlikely culprit, as we’ve seen before.


As it turns out, John knew that heart rate could influence blood pressure somewhat, and he also knew that his doctor’s office measured his heart rate regularly. So he got the data from his doctor's office. When he entered heart rate as a column into HCE, the reason for his blood pressure swings became clear, as you can see on the figure below.


On the left part of the figure above are the correlations between SBP and each of the other health-related variables John measured, which HCE lists in order of strength. Heart rate shows up at the top, with a high 0.946 correlation with SBP. On the right part of the figure is the chart of SBP against heart rate.

As you can see, John's heart rate, measured at the doctor's office, varied from 61 to 90 bpm. Given that, John decided to measure his resting heart rate. John’s resting heart rate, measured after waking up using a simple wrist watch, was 61 bpm.

Mystery solved! John’s blood pressure fluctuations were benign, and caused by fluctuations in heart rate.

If John's SBP had been greater than 140, which did not happen, this could be seen as an unusual example of irregular white coat hypertension.

If you are interested, this YouTube video clip discusses in more detail the case above, from HCE’s use perspective. It shows how the heart rate column was added to the dataset in HCE, how the software generated correlations and graphs, and how they were interpreted.

Reference

Kock, N. (2010). HealthCorrelator for Excel 1.0 User Manual. Laredo, Texas: ScriptWarp Systems.

This post has been revised and re-published. The original comments are preserved below. 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.

I ran several analyses on the effects of fruit consumption on mortality on the China Study II dataset using WarpPLS. For other China Study analyses, many using WarpPLS as well as HCE, click here.

The results are pretty clear – fruit consumption has no significant effect on mortality.

The bar charts figure below shows what seems to be a slight downward trend in mortality, in the 35-69 and 70-79 age ranges, apparently due to fruit consumption.


As it turns out, that slight trend may be due to something else: in the China Study II dataset, fruit consumption is positively associated with both animal protein and fat consumption. And, as we have seen from previous analyses (e.g., this one), the latter two seem to be protective.

So, if you like to eat fruit, maybe you should also make sure that you eat animal protein and fat as well.

In this post on the China Study II data we have seen that wheat apparently displaces dietary fat a lot, primarily fat from animal sources. We have also seen in that post that wheat is strongly and positively associated with mortality in both the 35-69 and 70-79 age ranges, whereas dietary fat is strongly and negatively associated with mortality in those ranges.

This opens the door for the hypothesis that wheat increased mortality in the China Study II sample mainly by displacing dietary fat, and not necessarily by being a primary cause of health problems. In fact, given the strong displacement effect discussed in the previous post, I thought that this hypothesis was quite compelling. I was partly wrong, as you’ll see below.

A counterintuitive hypothesis no doubt, given that wheat is unlikely to have been part of the diet of our Paleolithic ancestors, and thus the modern human digestive tract may be maladapted to it. Moreover, wheat’s main protein (gluten) is implicated in celiac disease, and wheat contains plant toxins such as wheat germ agglutinin.

Still, we cannot completely ignore this hypothesis because: (a) the data points in its general direction; and (b) wheat-based foods are found in way more than trivial amounts in the diets of populations that have relatively high longevity, such as the French.

Testing the hypothesis essentially amounts to testing the significance of two mediating effects; of fat as a mediator of the effects of wheat on mortality, in both the 35-69 and 70-79 age ranges. There are two main approaches for doing this. One is the classic test discussed by Baron & Kenny (1986). The other is the modern test discussed by Preacher & Hayes (2004), and extended by Hayes & Preacher (2010) for nonlinear relationships.

I tested the meditating effects using both approaches, including the nonlinear variation. I used the software WarpPLS for this; the results below are from WarpPLS outputs. Other analyses of the China Study data using WarpPLS can be found here (calorie restriction and longevity), and here (wheat, rice, and cardiovascular disease). For yet other studies, click here.

The graphs below show the path coefficients and chance probabilities of two models. The one at the top-left suggests that wheat flour consumption seems to be associated with a statistically significant increase in mortality in the 70-79 age range (beta=0.23; P=0.04). The effect in the 35-69 age range is almost statistically significant (beta=0.22; P=0.09); the likelihood that it is due to chance is 9 percent (this is the meaning of the P=0.09=9/100=9%).


The graph at the bottom-right suggests that the variable “FatCal”, which is the percentage of calories coming from dietary fat, is indeed a significant mediator of the relationships above between wheat and mortality, in both ranges. But “FatCal” is only a partial mediator.

The reason why “FatCal” is not a “perfect” mediator is that the direct effects of wheat on mortality in both ranges are still relatively strong after “FatCal” is added to the model (i.e., controlled for). In fact, the effects of wheat on mortality don’t change that much with the introduction of the variable “FatCal”.

This analysis suggests that, in the China Study II sample, one of wheat’s main sins might indeed have been to displace dietary fat from animal sources. Wheat consumption is strongly and negatively associated with dietary fat (beta=-0.37; P<0.01), and dietary fat is relatively strongly and negatively associated with mortality in both ranges (more in the 70-79 age range).

Why is dietary fat more protective in the 70-79 than in the 35-69 age range, with the latter effect only being significant at the P=0.10 level (a 10 percent chance probability)? My interpretation is that, as with almost any dietary habit, it takes years for a chronically low fat diet to lead to problems. See graph below; fat was not a huge contributor to the total calorie intake in this sample.


The analysis suggests that wheat also caused problems via other paths. What are them? We can’t say for sure based on this dataset. Perhaps the paths involve lectins and/or gluten. One way or another, the relationship is complex. As you can see from the graph below, the relationship between wheat consumption and mortality is nonlinear for the 70-79 age range, most likely due to confounding factors. The effect size is small for the 35-69 age range, even though it looks linear or quasi-linear in that range.


As you might recall from this post, rice does NOT displace dietary fat, and it seems to be associated with increased longevity. Carbohydrate content per se does not appear to be the problem here. Both rice and wheat foods are rich in them, and have a high glycemic index. Wheat products tend to have a higher glycemic load though.

And why is dietary fat so important as to be significantly associated with increased longevity? This is not a trivial question, because if too much of that fat is stored as body fat it will actually decrease longevity. Dietary fat is very calorie-dense, and can be easily stored as body fat.

Dietary fat is important for various reasons, and probably some that we don’t know about yet. It leads to the formation of body fat, which is not only found in adipocytes or used only as a store of energy. Fat is a key component of a number of important tissues, including 60 percent of our brain. Since fat in the human body undergoes constant turnover, more in some areas than others, lack of dietary fat may compromise the proper functioning of various organs.

Without dietary fat, the very important fat-soluble vitamins (A, D, E and K) cannot be properly absorbed. Taking these vitamins in supplemental form will not work if you don’t consume fat as well. A very low fat diet is almost by definition a diet deficient in fat-soluble vitamins, even if those vitamins are consumed in large amounts via supplements.

Moreover, animals store fat-soluble vitamins in their body fat (as well as in organs), so we get these vitamins in one of their most natural and potent forms when we consume animal fat. Consuming copious amounts of olive and/or coconut oil will not have just the same effect.

References

Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality & Social Psychology, 51(6), 1173-1182.

Preacher, K.J., & Hayes, A.F. (2004). SPSS and SAS procedures for estimating indirect effects in simple mediation models. Behavior Research Methods, Instruments, & Computers, 36 (4), 717-731.

Hayes, A. F., & Preacher, K. J. (2010). Quantifying and testing indirect effects in simple mediation models when the constituent paths are nonlinear. Multivariate Behavioral Research, 45(4), 627-660.

This post is based on an analysis of a subset of the China Study II data, using HealthCorrelator for Excel (HCE), which is publicly available for download and use on a free trial basis. You can access the original data on the HCE web site, under “Sample datasets”.

HCE was designed to be used with small and individual personal datasets, but it can also be used with larger datasets for multiple individuals.

This analysis focuses on two main variables from the China Study II data: mortality in the 35-69 age range, and mortality in the 70-79 range. The table below shows the coefficients of association calculated by HCE for those two variables. The original variable labels are shown.


One advantage of looking at mortality in these ranges is that they are more likely to reflect the impact of degenerative diseases. Infectious diseases likely killed a lot of children in China at the time the data was being collected. Heart disease, on the other hand, is likely to have killed more people in the 35-69 and 70-79 ranges.

It is also good to have data for both ranges, because factors that likely increased longevity were those that were associated with decreased mortality in both ranges. For example, a factor that was strongly associated with mortality in the 35-69 range, but not the 70-79 range, might simply be very deadly in the former range.

The mortalities in both ranges are strongly correlated with each other, which is to be expected. Next, at the very top for both ranges, is sex. Being female is by far the variable with the strongest, and negative, association with mortality.

While I would expect females to live longer, the strengths of the associations make me think that there is something else going on here. Possibly different dietary or behavioral patterns displayed by females. Maybe smoking cigarettes or alcohol abuse was a lot less prevalent among them.

Markedly different lifestyle patterns between males and females may be a major confounding variable in the China Study sample.

Some of the variables are redundant; meaning that they are highly correlated and seem to measure the same thing. This is clear when one looks at the other coefficients of association generated by HCE.

For example, plant food consumption is strongly and negatively correlated with animal food consumption; so strongly that you could use either one of these two variables to measure the other, after inverting the scale. The same is true for consumption of rice and white flour.

Plant food consumption is not strongly correlated with plant protein consumption; many plant foods have little protein in them. The ones that have high protein content are typically industrialized and seed-based. The type of food most strongly associated with plant protein consumption is white flour, by far. The correlation is .645.

The figure below is based on the table above. I opened a separate instance of Excel, and copied the coefficients generated by HCE into it. Then I built two bar charts with them. The variable labels were replaced with more suggestive names, and some redundant variables were removed. Only the top 7 variables are shown, ordered from left to right on the bar charts in order of strength of association. The ones above the horizontal axis possibly increase mortality in each age range, whereas the ones at the bottom possibly decrease it.


When you look at these results as a whole, a few things come to mind.

White flour consumption doesn’t seem to be making people live longer; nor does plant food consumption in general. For white flour, it is quite the opposite. Plant food consumption reflects white flour consumption to a certain extent, especially in counties where rice consumption is low. These conclusions are consistent with previous analyses using more complex statistics.

Total food is positively associated with mortality in the 35-69 range, but not the 70-79 range. This may reflect the fact that folks who reach the age of 70 tend to naturally eat in moderation, so you don’t see wide variations in food consumption among those folks.

Eating in moderation does not mean practicing severe calorie restriction. This post suggests that calorie restriction doesn't seem to be associated with increased longevity in this sample. Eating well, but not too much, is.

The bar for rice (consumption) on the left chart is likely a mirror reflection of the white flour consumption, so it may appear to be good in the 35-69 range simply because it reflects reduced white flour consumption in that range.

Green vegetables seem to be good when you consider the 35-69 range, but not the 70-79 range.

Neither rice nor green vegetables seem to be bad either. For overall longevity they may well be neutral, with the benefits likely coming from their replacement of white flour in the diet.

Dietary fat seems protective overall, particularly together with animal foods in the 70-79 range. This may simply reflect a delayed protective effect of animal fat and protein consumption.

The protective effect of dietary fat becomes clear when we look at the relationship between carbohydrate calories and fat calories. Their correlation is -.957, which essentially means that carbohydrate intake seriously displaces fat intake.

Carbohydrates themselves may not be the problem, even if coming from high glycemic foods (except wheat flour, apparently). This post shows that they are relatively benign if coming from high glycemic rice, even at high intakes of 206 to 412 g/day. The problem seems to be caused by carbohydrates displacing nutrient-dense animal foods.

Interestingly, rice does not displace animal foods or fat in the diet. It is positively correlated with them. Wheat flour, on the other hand, displaces those foods. Wheat flour is negatively and somewhat strongly correlated with consumption of animal foods, as well as with animal fat and protein.

There are certainly several delayed effects here, which may be distorting the results somewhat.  Degenerative diseases don’t develop fast and kill folks right away. They often require many years of eating and doing the wrong things to be fatal.

HealthCorrelator for Excel (HCE) is now publicly available for download and use on a free trial basis. For those users who decide to buy it after trying, licenses are available for individuals and organizations. If you are a gym member, consider asking your gym to buy an organizational site license; this would allow the gym to distribute individual licenses at no cost to you and your colleagues.

HCE is a user-friendly Excel-based software that unveils important associations among health variables at the click of a button. Here are some of its main features:

- Easy to use yet powerful health management software.

- Estimates associations among any number of health variables.

- Automatically orders associations by decreasing absolute strength.

- Graphs relationships between pairs of health variables, for all possible combinations.

The beta testing was successfully completed, with fairly positive results. (Thank you beta testers!) Among beta testers were Mac users. The main request from beta testers was for more illustrative material on how to use HCE for specific purposes, such as losing body fat or managing blood glucose levels. This will be coming in the future in the form of posts and linked material.

To download a free trial version, good for 30 use sessions (which is quite a lot!), please visit the HealthCorrelator.com web site. There you will also find the software’s User Manual and various links to demo YouTube videos. You can also download sample datasets to try the software’s main features.

This call is closed. Beta testing has been successfully completed. HealthCorrelator for Excel (HCE) is now publicly available for download and use on a free trial basis. For those users who decide to buy it after trying, licenses are available for individuals and organizations.

To download a free trial version – as well as get the User Manual, view demo YouTube videos, and download and try sample datasets – visit the HealthCorrelator.com web site.

Most human traits (e.g., body fat percentage, blood pressure, propensity toward depression) are influenced by our genes; some more than others. The vast majority of traits are also influenced by environmental factors, the “nurture” part of the “nature-nurture” equation. Very few traits are “innate”, such as blood type.

This means that manipulating environmental factors, such as diet and lifestyle, can strongly influence how the traits are finally expressed in humans. But each individual tends to respond differently to diet and lifestyle changes, because each individual is unique in terms of his or her combination of “nature” and “nurture”. Even identical twins are different in that respect.

When plotted, traits that are influenced by our genes are distributed along a bell-shaped curve. For example, a trait like body fat percentage, when measured in a population of 1000 individuals, will yield a distribution of values that will look like a bell-shaped distribution. This type of distribution is also known in statistics as a “normal” distribution.

Why is that?

The additive effect of genes and the bell curve

The reason is purely mathematical. A measurable trait, like body fat percentage, is usually influenced by several genes. (Sometimes individual genes have a very marked effect, as in genes that “switch on or off” other genes.) Those genes appear at random in a population, and their various combinations spread in response to selection pressures. Selection pressures usually cause a narrowing of the bell-shaped curve distributions of traits in populations.

The genes interact with environmental influences, which also have a certain degree of randomness. The result is a massive combined randomness. It is this massive randomness that leads to the bell-curve distribution. The bell curve itself is not random at all, which is a fascinating aspect of this phenomenon. From “chaos” comes “order”. A bell curve is a well-defined curve that is associated with a function, the probability density function.

The underlying mathematical reason for the bell shape is the central limit theorem. The genes are combined in different individuals as combinations of alleles, where each allele is a variation (or mutation) of a gene. An allele set, for genes in different locations of the human DNA, forms a particular allele combination, called a genotype. The alleles combine their effects, usually in an additive fashion, to influence a trait.

Here is a simple illustration. Let us say one generates 1000 random variables, each storing 10 random values going from 0 to 1. Then the values stored in each of the 1000 random variables are added. This mimics the additive effect of 10 genes with random allele combinations. The result are numbers ranging from 1 to 10, in a population of 1000 individuals; each number is analogous to an allele combination. The resulting histogram, which plots the frequency of each allele combination (or genotype) in the population, is shown on the figure bellow. Each allele configuration will “push for” a particular trait range, making the trait distribution also have the same bell-shaped form.


The bell curve, research studies, and what they mean for you

Studies of the effects of diet and exercise on health variables usually report their results in terms of average responses in a group of participants. Frequently two groups are used, one control and one treatment. For example, in a diet-related study the control group may follow the Standard American Diet, and the treatment group may follow a low carbohydrate diet.

However, you are not the average person; the average person is an abstraction. Research on bell curve distributions tells us that there is about a 68 percentage chance that you will fall within a 1 standard deviation from the average, to the left or the right of the “middle” of the bell curve. Still, even a 0.5 standard deviation above the average is not the average. And, there is approximately a 32 percent chance that you will not be within the larger -1 to 1 standard deviation range. If this is the case, the average results reported may be close to irrelevant for you.

Average results reported in studies are a good starting point for people who are similar to the studies’ participants. But you need to generate your own data, with the goal of “knowing yourself through numbers” by progressively analyzing it. This is akin to building a “numeric diary”. It is not exactly an “N=1” experiment, as some like to say, because you can generate multiple data points (e.g., N=200) on how your body alone responds to diet and lifestyle changes over time.

HealthCorrelator for Excel (HCE)

I think I have finally been able to develop a software tool that can help people do that. I have been using it myself for years, initially as a prototype. You can see the results of my transformation on this post. The challenge for me was to generate a tool that was simple enough to use, and yet powerful enough to give people good insights on what is going on with their body.

The software tool is called HealthCorrelator for Excel (HCE). It runs on Excel, and generates coefficients of association (correlations, which range from -1 to 1) among variables and graphs at the click of a button.

This 5-minute YouTube video shows how the software works in general, and this 10-minute video goes into more detail on how the software can be used to manage a specific health variable. These two videos build on a very small sample dataset, and their focus is on HDL cholesterol management. Nevertheless, the software can be used in the management of just about any health-related variable – e.g., blood glucose, triglycerides, muscle strength, muscle mass, depression episodes etc.

You have to enter data about yourself, and then the software will generate coefficients of association and graphs at the click of a button. As you can see from the videos above, it is very simple. The interpretation of the results is straightforward in most cases, and a bit more complicated in a smaller number of cases. Some results will probably surprise users, and their doctors.

For example, a user who is a patient may be able to show to a doctor that, in the user’s specific case, a diet change influences a particular variable (e.g., triglycerides) much more strongly than a prescription drug or a supplement. More posts will be coming in the future on this blog about these and other related issues.

The idea that calorie restriction extends human life comes largely from studies of other species. The most relevant of those studies have been conducted with primates, where it has been shown that primates that eat a restricted calorie diet live longer and healthier lives than those that are allowed to eat as much as they want.

There are two main problems with many of the animal studies of calorie restriction. One is that, as natural lifespan decreases, it becomes progressively easier to experimentally obtain major relative lifespan extensions. (That is, it seems much easier to double the lifespan of an organism whose natural lifespan is one day than an organism whose natural lifespan is 80 years.) The second, and main problem in my mind, is that the studies often compare obese with lean animals.

Obesity clearly reduces lifespan in humans, but that is a different claim than the one that calorie restriction increases lifespan. It has often been claimed that Asian countries and regions where calorie intake is reduced display increased lifespan. And this may well be true, but the question remains as to whether this is due to calorie restriction increasing lifespan, or because the rates of obesity are much lower in countries and regions where calorie intake is reduced.

So, what can the China Study II data tell us about the hypothesis that calorie restriction increases longevity?

As it turns out, we can conduct a preliminary test of this hypothesis based on a key assumption. Let us say we compared two populations (e.g., counties in China), based on the following ratio: number of deaths at or after age 70 divided by number deaths before age 70. Let us call this the “ratio of longevity” of a population, or RLONGEV. The assumption is that the population with the highest RLONGEV would be the population with the highest longevity of the two. The reason is that, as longevity goes up, one would expect to see a shift in death patterns, with progressively more people dying old and fewer people dying young.

The 1989 China Study II dataset has two variables that we can use to estimate RLONGEV. They are coded as M005 and M006, and refer to the mortality rates from 35 to 69 and 70 to 79 years of age, respectively. Unfortunately there is no variable for mortality after 79 years of age, which limits the scope of our results somewhat. (This does not totally invalidate the results because we are using a ratio as our measure of longevity, not the absolute number of deaths from 70 to 79 years of age.) Take a look at these two previous China Study II posts (here, and here) for other notes, most of which apply here as well. The notes are at the end of the posts.

All of the results reported here are from analyses conducted using WarpPLS. Below is a model with coefficients of association; it is a simple model, since the hypothesis that we are testing is also simple. (Click on it to enlarge. Use the "CRTL" and "+" keys to zoom in, and CRTL" and "-" to zoom out.) The arrows explore associations between variables, which are shown within ovals. The meaning of each variable is the following: TKCAL = total calorie intake per day; RLONGEV = ratio of longevity; SexM1F2 = sex, with 1 assigned to males and 2 to females.



As one would expect, being female is associated with increased longevity, but the association is just shy of being statistically significant in this dataset (beta=0.14; P=0.07). The association between total calorie intake and longevity is trivial, and statistically indistinguishable from zero (beta=-0.04; P=0.39). Moreover, even though this very weak association is overall negative (or inverse), the sign of the association here does not fully reflect the shape of the association. The shape is that of an inverted J-curve; a.k.a. U-curve. When we split the data into total calorie intake terciles we get a better picture:


The second tercile, which refers to a total daily calorie intake of 2193 to 2844 calories, is the one associated with the highest longevity. The first tercile (with the lowest range of calories) is associated with a higher longevity than the third tercile (with the highest range of calories). These results need to be viewed in context. The average weight in this dataset was about 116 lbs. A conservative estimate of the number of calories needed to maintain this weight without any physical activity would be about 1740. Add about 700 calories to that, for a reasonable and healthy level of physical activity, and you get 2440 calories needed daily for weight maintenance. That is right in the middle of the second tercile.

In simple terms, the China Study II data seems to suggest that those who eat well, but not too much, live the longest. Those who eat little have slightly lower longevity. Those who eat too much seem to have the lowest longevity, perhaps because of the negative effects of excessive body fat.

Because these trends are all very weak from a statistical standpoint, we have to take them with caution. What we can say with more confidence is that the China Study II data does not seem to support the hypothesis that calorie restriction increases longevity.

Reference

Kock, N. (2010). WarpPLS 1.0 User Manual. Laredo, Texas: ScriptWarp Systems.

Notes

- The path coefficients (indicated as beta coefficients) reflect the strength of the relationships; they are a bit like standard univariate (or Pearson) correlation coefficients, except that they take into consideration multivariate relationships (they control for competing effects on each variable). Whenever nonlinear relationships were modeled, the path coefficients were automatically corrected by the software to account for nonlinearity.

- Only two data points per county were used (for males and females). This increased the sample size of the dataset without artificially reducing variance, which is desirable since the dataset is relatively small (each county, not individual, is a separate data point is this dataset). This also allowed for the test of commonsense assumptions (e.g., the protective effects of being female), which is always a good idea in a multivariate analyses because violation of commonsense assumptions may suggest data collection or analysis error. On the other hand, it required the inclusion of a sex variable as a control variable in the analysis, which is no big deal.

- Mortality from schistosomiasis infection (MSCHIST) does not confound the results presented here. Only counties where no deaths from schistosomiasis infection were reported have been included in this analysis. The reason for this is that mortality from schistosomiasis infection can severely distort the results in the age ranges considered here. On the other hand, removal of counties with deaths from schistosomiasis infection reduced the sample size, and thus decreased the statistical power of the analysis.

Researchers like to study samples of data and look for associations between variables. Often those associations are represented in the form of correlation coefficients, which go from -1 to 1. Another popular measure of association is the path coefficient, which usually has a narrower range of variation. What many researchers seem to forget is that the associations they find depend heavily on the sample they are looking at, and on the ranges of variation of the variables being analyzed.

A forgotten warning: Causation without correlation

Often those who conduct multivariate statistical analyses on data are unaware of certain limitations. Many times this is due to lack of familiarity with statistical tests. One warning we do see a lot though is: Correlation does not imply causation. This is, of course, absolutely true. If you take my weight from 1 to 20 years of age, and the price of gasoline in the US during that period, you will find that they are highly correlated. But common sense tells me that there is no causation whatsoever between these two variables.

So correlation does not imply causation alright, but there is another warning that is rarely seen: There can be strong causation without any correlation. Of course this can lead to even more bizarre conclusions than the “correlation does not imply causation” problem. If there is strong causation between variables B and Y, and it is not showing as a correlation, another variable A may “jump in” and “steal” that “unused correlation”; so to speak.

The chain smokers “study”

To illustrate this point, let us consider the following fictitious case, a study of “100 cities”. The study focuses on the effect of smoking and genes on lung cancer mortality. Smoking significantly increases the chances of dying from lung cancer; it is a very strong causative factor. Here are a few more details. Between 35 and 40 percent of the population are chain smokers. And there is a genotype (a set of genes), found in a small percentage of the population (around 7 percent), which is protective against lung cancer. All of those who are chain smokers die from lung cancer unless they die from other causes (e.g., accidents). Dying from other causes is a lot more common among those who have the protective genotype.

(I created this fictitious data with these associations in mind, using equations. I also added uncorrelated error into the equations, to make the data look a bit more realistic. For example, random deaths occurring early in life would reduce slightly any numeric association between chain smoking and cancer deaths in the sample of 100 cities.)

The table below shows part of the data, and gives an idea of the distribution of percentage of smokers (Smokers), percentage with the protective genotype (Pgenotype), and percentage of lung cancer deaths (MLCancer). (Click on it to enlarge. Use the "CRTL" and "+" keys to zoom in, and CRTL" and "-" to zoom out.) Each row corresponds to a city. The rest of the data, up to row 100, has a similar distribution.


The graphs below show the distribution of lung cancer deaths against: (a) the percentage of smokers, at the top; and (b) the percentage with the protective genotype, at the bottom. Correlations are shown at the top of each graph. (They can vary from -1 to 1. The closer they are to -1 or 1, the stronger is the association, negative or positive, between the variables.) The correlation between lung cancer deaths and percentage of smokers is slightly negative and statistically insignificant (-0.087). The correlation between lung cancer deaths and percentage with the protective genotype is negative, strong, and statistically significant (-0.613).


Even though smoking significantly increases the chances of dying from lung cancer, the correlations tell us otherwise. The correlations tell us that lung cancer does not seem to cause lung cancer deaths, and that having the protective genotype seems to significantly decrease cancer deaths. Why?

If there is no variation, there is no correlation

The reason is that the “researchers” collected data only about chain smokers. That is, the variable “Smokers” includes only chain smokers. If this was not a fictitious case, focusing the study on chain smokers could be seen as a clever strategy employed by researchers funded by tobacco companies. The researchers could say something like this: “We focused our analysis on those most likely to develop lung cancer.” Or, this could have been the result of plain stupidity when designing the research project.

By restricting their study to chain smokers the researchers dramatically reduced the variability in one particular variable: the extent to which the study participants smoked. Without variation, there can be no correlation. No matter what statistical test or software is used, no significant association will be found between lung cancer deaths and percentage of smokers based on this dataset. No matter what statistical test or software is used, a significant and strong association will be found between lung cancer deaths and percentage with the protective genotype.

Of course, this could lead to a very misleading conclusion. Smoking does not cause lung cancer; the real cause is genetic.

A note about diet

Consider the analogy between smoking and consumption of a particular food, and you will probably see what this means for the analysis of observational data regarding dietary choices and disease. This applies to almost any observational study, including the China Study. (Studies employing experimental control manipulations would presumably ensure enough variation in the variables studied.) In the China Study, data from dozens of counties were collected. One may find a significant association between consumption of food A and disease Y.

There may be a much stronger association between food B and disease Y, but that association may not show up in statistical analyses at all, simply because there is little variation in the data regarding consumption of food B. For example, all those sampled may have eaten food B; about the same amount. Or none. Or somewhere in between, within a rather small range of variation.

Statistical illiteracy, bad choices, and taxation

Statistics is a “necessary evil”. It is useful to go from small samples to large ones when we study any possible causal association. By doing so, one can find out whether an observed effect really applies to a larger percentage of the population, or is actually restricted to a small group of individuals. The problem is that we humans are very bad at inferring actual associations from simply looking at large tables with numbers. We need statistical tests for that.

However, ignorance about basic statistical phenomena, such as the one described here, can be costly. A group of people may eliminate food A from their diet based on coefficients of association resulting from what seem to be very clever analyses, replacing it with food B. The problem is that food B may be equally harmful, or even more harmful. And, that effect may not show up on statistical analyses unless they have enough variation in the consumption of food B.

Readers of this blog may wonder why we explicitly use terms like “suggests” when we refer to a relationship that is suggested by a significant coefficient of association (e.g., a linear correlation). This is why, among other reasons.

One does not have to be a mathematician to understand basic statistical concepts. And doing so can be very helpful in one’s life in general, not only in diet and lifestyle decisions. Even in simple choices, such as what to be on. We are always betting on something. For example, any investment is essentially a bet. Some outcomes are much more probable than others.

Once I had an interesting conversation with a high-level officer of a state government. I was part of a consulting team working on an information technology project. We were talking about the state lottery, which was a big source of revenue for the state, comparing it with state taxes. He told me something to this effect:

Our lottery is essentially a tax on the statistically illiterate.

In my last post on the China Study II, I analyzed the effect of total and HDL cholesterol on mortality from all cardiovascular diseases. The main conclusion was that total and HDL cholesterol were protective. Total and HDL cholesterol usually increase with intake of animal foods, and particularly of animal fat. The lowest mortality from all cardiovascular diseases was in the highest total cholesterol range, 172.5 to 180; and the highest mortality in the lowest total cholesterol range, 120 to 127.5. The difference was quite large; the mortality in the lowest range was approximately 3.3 times higher than in the highest.

This post focuses on the intake of two main plant foods, namely wheat flour and rice intake, and their relationships with mortality from all cardiovascular diseases. After many exploratory multivariate analyses, wheat flour and rice emerged as the plant foods with the strongest associations with mortality from all cardiovascular diseases. Moreover, wheat flour and rice have a strong and inverse relationship with each other, which suggests a “consumption divide”. Since the data is from China in the late 1980s, it is likely that consumption of wheat flour is even higher now. As you’ll see, this picture is alarming.

The main model and results

All of the results reported here are from analyses conducted using WarpPLS. Below is the model with the main results of the analyses. (Click on it to enlarge. Use the "CRTL" and "+" keys to zoom in, and CRTL" and "-" to zoom out.) The arrows explore associations between variables, which are shown within ovals. The meaning of each variable is the following: SexM1F2 = sex, with 1 assigned to males and 2 to females; MVASC = mortality from all cardiovascular diseases (ages 35-69); TKCAL = total calorie intake per day; WHTFLOUR = wheat flour intake (g/day); and RICE = and rice intake (g/day).


The variables to the left of MVASC are the main predictors of interest in the model. The one to the right is a control variable – SexM1F2. The path coefficients (indicated as beta coefficients) reflect the strength of the relationships. A negative beta means that the relationship is negative; i.e., an increase in a variable is associated with a decrease in the variable that it points to. The P values indicate the statistical significance of the relationship; a P lower than 0.05 generally means a significant relationship (95 percent or higher likelihood that the relationship is “real”).

In summary, the model above seems to be telling us that:

- As rice intake increases, wheat flour intake decreases significantly (beta=-0.84; P<0.01). This relationship would be the same if the arrow pointed in the opposite direction. It suggests that there is a sharp divide between rice-consuming and wheat flour-consuming regions.

- As wheat flour intake increases, mortality from all cardiovascular diseases increases significantly (beta=0.32; P<0.01). This is after controlling for the effects of rice and total calorie intake. That is, wheat flour seems to have some inherent properties that make it bad for one’s health, even if one doesn’t consume that many calories.

- As rice intake increases, mortality from all cardiovascular diseases decreases significantly (beta=-0.24; P<0.01). This is after controlling for the effects of wheat flour and total calorie intake. That is, this effect is not entirely due to rice being consumed in place of wheat flour. Still, as you’ll see later in this post, this relationship is nonlinear. Excessive rice intake does not seem to be very good for one’s health either.

- Increases in wheat flour and rice intake are significantly associated with increases in total calorie intake (betas=0.25, 0.33; P<0.01). This may be due to wheat flour and rice intake: (a) being themselves, in terms of their own caloric content, main contributors to the total calorie intake; or (b) causing an increase in calorie intake from other sources. The former is more likely, given the effect below.

- The effect of total calorie intake on mortality from all cardiovascular diseases is insignificant when we control for the effects of rice and wheat flour intakes (beta=0.08; P=0.35). This suggests that neither wheat flour nor rice exerts an effect on mortality from all cardiovascular diseases by increasing total calorie intake from other food sources.

- Being female is significantly associated with a reduction in mortality from all cardiovascular diseases (beta=-0.24; P=0.01). This is to be expected. In other words, men are women with a few design flaws, so to speak. (This situation reverses itself a bit after menopause.)

Wheat flour displaces rice

The graph below shows the shape of the association between wheat flour intake (WHTFLOUR) and rice intake (RICE). The values are provided in standardized format; e.g., 0 is the mean (a.k.a. average), 1 is one standard deviation above the mean, and so on. The curve is the best-fitting U curve obtained by the software. It actually has the shape of an exponential decay curve, which can be seen as a section of a U curve. This suggests that wheat flour consumption has strongly displaced rice consumption in several regions in China, and also that wherever rice consumption is high wheat flour consumption tends to be low.


As wheat flour intake goes up, so does cardiovascular disease mortality

The graphs below show the shapes of the association between wheat flour intake (WHTFLOUR) and mortality from all cardiovascular diseases (MVASC). In the first graph, the values are provided in standardized format; e.g., 0 is the mean (or average), 1 is one standard deviation above the mean, and so on. In the second graph, the values are provided in unstandardized format and organized in terciles (each of three equal intervals).



The curve in the first graph is the best-fitting U curve obtained by the software. It is a quasi-linear relationship. The higher the consumption of wheat flour in a county, the higher seems to be the mortality from all cardiovascular diseases. The second graph suggests that mortality in the third tercile, which represents a consumption of wheat flour of 501 to 751 g/day (a lot!), is 69 percent higher than mortality in the first tercile (0 to 251 g/day).

Rice seems to be protective, as long as intake is not too high

The graphs below show the shapes of the association between rice intake (RICE) and mortality from all cardiovascular diseases (MVASC). In the first graph, the values are provided in standardized format. In the second graph, the values are provided in unstandardized format and organized in terciles.



Here the relationship is more complex. The lowest mortality is clearly in the second tercile (206 to 412 g/day). There is a lot of variation in the first tercile, as suggested by the first graph with the U curve. (Remember, as rice intake goes down, wheat flour intake tends to go up.) The U curve here looks similar to the exponential decay curve shown earlier in the post, for the relationship between rice and wheat flour intake.

In fact, the shape of the association between rice intake and mortality from all cardiovascular diseases looks a bit like an “echo” of the shape of the relationship between rice and wheat flour intake. Here is what is creepy. This echo looks somewhat like the first curve (between rice and wheat flour intake), but with wheat flour intake replaced by “death” (i.e., mortality from all cardiovascular diseases).

What does this all mean?

- Wheat flour displacing rice does not look like a good thing. Wheat flour intake seems to have strongly displaced rice intake in the counties where it is heavily consumed. Generally speaking, that does not seem to have been a good thing. It looks like this is generally associated with increased mortality from all cardiovascular diseases.

- High glycemic index food consumption does not seem to be the problem here. Wheat flour and rice have very similar glycemic indices (but generally not glycemic loads; see below). Both lead to blood glucose and insulin spikes. Yet, rice consumption seems protective when it is not excessive. This is true in part (but not entirely) because it largely displaces wheat flour. Moreover, neither rice nor wheat flour consumption seems to be significantly associated with cardiovascular disease via an increase in total calorie consumption. This is a bit of a blow to the theory that high glycemic carbohydrates necessarily cause obesity, diabetes, and eventually cardiovascular disease.

- The problem with wheat flour is … hard to pinpoint, based on the results summarized here. Maybe it is the fact that it is an ultra-refined carbohydrate-rich food; less refined forms of wheat could be healthier. In fact, the glycemic loads of less refined carbohydrate-rich foods tend to be much lower than those of more refined ones. (Also, boiled brown rice has a glycemic load that is about three times lower than that of whole wheat bread; whereas the glycemic indices are about the same.) Maybe the problem is wheat flour's  gluten content. Maybe it is a combination of various factors, including these.

Reference

Kock, N. (2010). WarpPLS 1.0 User Manual. Laredo, Texas: ScriptWarp Systems.

Acknowledgment and notes

- Many thanks are due to Dr. Campbell and his collaborators for collecting and compiling the data used in this analysis. The data is from this site, created by those researchers to disseminate their work in connection with a study often referred to as the “China Study II”. It has already been analyzed by other bloggers. Notable analyses have been conducted by Ricardo at Canibais e Reis, Stan at Heretic, and Denise at Raw Food SOS.

- The path coefficients (indicated as beta coefficients) reflect the strength of the relationships; they are a bit like standard univariate (or Pearson) correlation coefficients, except that they take into consideration multivariate relationships (they control for competing effects on each variable). Whenever nonlinear relationships were modeled, the path coefficients were automatically corrected by the software to account for nonlinearity.

- The software used here identifies non-cyclical and mono-cyclical relationships such as logarithmic, exponential, and hyperbolic decay relationships. Once a relationship is identified, data values are corrected and coefficients calculated. This is not the same as log-transforming data prior to analysis, which is widely used but only works if the underlying relationship is logarithmic. Otherwise, log-transforming data may distort the relationship even more than assuming that it is linear, which is what is done by most statistical software tools.

- The R-squared values reflect the percentage of explained variance for certain variables; the higher they are, the better the model fit with the data. In complex and multi-factorial phenomena such as health-related phenomena, many would consider an R-squared of 0.20 as acceptable. Still, such an R-squared would mean that 80 percent of the variance for a particularly variable is unexplained by the data.

- The P values have been calculated using a nonparametric technique, a form of resampling called jackknifing, which does not require the assumption that the data is normally distributed to be met. This and other related techniques also tend to yield more reliable results for small samples, and samples with outliers (as long as the outliers are “good” data, and are not the result of measurement error).

- Only two data points per county were used (for males and females). This increased the sample size of the dataset without artificially reducing variance, which is desirable since the dataset is relatively small. This also allowed for the test of commonsense assumptions (e.g., the protective effects of being female), which is always a good idea in a complex analysis because violation of commonsense assumptions may suggest data collection or analysis error. On the other hand, it required the inclusion of a sex variable as a control variable in the analysis, which is no big deal.

- Since all the data was collected around the same time (late 1980s), this analysis assumes a somewhat static pattern of consumption of rice and wheat flour. In other words, let us assume that variations in consumption of a particular food do lead to variations in mortality. Still, that effect will typically take years to manifest itself. This is a major limitation of this dataset and any related analyses.

- Mortality from schistosomiasis infection (MSCHIST) does not confound the results presented here. Only counties where no deaths from schistosomiasis infection were reported have been included in this analysis. Mortality from all cardiovascular diseases (MVASC) was measured using the variable M059 ALLVASCc (ages 35-69). See this post for other notes that apply here as well.

First of all, many thanks are due to Dr. Campbell and his collaborators for collecting and compiling the data used in this analysis. This data is from this site, created by those researchers to disseminate the data from a study often referred to as the “China Study II”. It has already been analyzed by other bloggers. Notable analyses have been conducted by Ricardo at Canibais e Reis, Stan at Heretic, and Denise at Raw Food SOS.

The analyses in this post differ from those other analyses in various aspects. One of them is that data for males and females were used separately for each county, instead of the totals per county. Only two data points per county were used (for males and females). This increased the sample size of the dataset without artificially reducing variance (for more details, see “Notes” at the end of the post), which is desirable since the dataset is relatively small. This also allowed for the test of commonsense assumptions (e.g., the protective effects of being female), which is always a good idea in a complex analysis because violation of commonsense assumption may suggest data collection or analysis error. On the other hand, it required the inclusion of a sex variable as a control variable in the analysis, which is no big deal.

The analysis was conducted using WarpPLS. Below is the model with the main results of the analysis. (Click on it to enlarge. Use the "CRTL" and "+" keys to zoom in, and CRTL" and "-" to zoom out.) The arrows explore associations between variables, which are shown within ovals. The meaning of each variable is the following: SexM1F2 = sex, with 1 assigned to males and 2 to females; HDLCHOL = HDL cholesterol; TOTCHOL = total cholesterol; MSCHIST = mortality from schistosomiasis infection; and MVASC = mortality from all cardiovascular diseases.


The variables to the left of MVASC are the main predictors of interest in the model – HDLCHOL and TOTCHOL. The ones to the right are control variables – SexM1F2 and MSCHIST. The path coefficients (indicated as beta coefficients) reflect the strength of the relationships. A negative beta means that the relationship is negative; i.e., an increase in a variable is associated with a decrease in the variable that it points to. The P values indicate the statistical significance of the relationship; a P lower than 0.05 generally means a significant relationship (95 percent or higher likelihood that the relationship is “real”).

In summary, this is what the model above is telling us:

- As HDL cholesterol increases, total cholesterol increases significantly (beta=0.48; P<0.01). This is to be expected, as HDL is a main component of total cholesterol, together with VLDL and LDL cholesterol.

- As total cholesterol increases, mortality from all cardiovascular diseases decreases significantly (beta=-0.25; P<0.01). This is to be expected if we assume that total cholesterol is in part an intervening variable between HDL cholesterol and mortality from all cardiovascular diseases. This assumption can be tested through a separate model (more below). Also, there is more to this story, as noted below.

- The effect of HDL cholesterol on mortality from all cardiovascular diseases is insignificant when we control for the effect of total cholesterol (beta=-0.08; P=0.26). This suggests that HDL’s protective role is subsumed by the variable total cholesterol, and also that it is possible that there is something else associated with total cholesterol that makes it protective. Otherwise the effect of total cholesterol might have been insignificant, and the effect of HDL cholesterol significant (the reverse of what we see here).

- Being female is significantly associated with a reduction in mortality from all cardiovascular diseases (beta=-0.16; P=0.01). This is to be expected. In other words, men are women with a few design flaws. (This situation reverses itself a bit after menopause.)

- Mortality from schistosomiasis infection is significantly and inversely associated with mortality from all cardiovascular diseases (beta=-0.28; P<0.01). This is probably due to those dying from schistosomiasis infection not being entered in the dataset as dying from cardiovascular diseases, and vice-versa.

Two other main components of total cholesterol, in addition to HDL cholesterol, are VLDL and LDL cholesterol. These are carried in particles, known as lipoproteins. VLDL cholesterol is usually represented as a fraction of triglycerides in cholesterol equations (e.g., the Friedewald and Iranian equations). It usually correlates inversely with HDL; that is, as HDL cholesterol increases, usually VLDL cholesterol decreases. Given this and the associations discussed above, it seems that LDL cholesterol is a good candidate for the possible “something else associated with total cholesterol that makes it protective”. But waidaminet! Is it possible that the demon particle, the LDL, serves any purpose other than giving us heart attacks?

The graph below shows the shape of the association between total cholesterol (TOTCHOL) and mortality from all cardiovascular diseases (MVASC). The values are provided in standardized format; e.g., 0 is the average, 1 is one standard deviation above the mean, and so on. The curve is the best-fitting S curve obtained by the software (an S curve is a slightly more complex curve than a U curve).


The graph below shows some of the data in unstandardized format, and organized differently. The data is grouped here in ranges of total cholesterol, which are shown on the horizontal axis. The lowest and highest ranges in the dataset are shown, to highlight the magnitude of the apparently protective effect. Here the two variables used to calculate mortality from all cardiovascular diseases (MVASC; see “Notes” at the end of this post) were added. Clearly the lowest mortality from all cardiovascular diseases is in the highest total cholesterol range, 172.5 to 180; and the highest mortality in the lowest total cholesterol range, 120 to 127.5. The difference is quite large; the mortality in the lowest range is approximately 3.3 times higher than in the highest.


The shape of the S-curve graph above suggests that there are other variables that are confounding the results a bit. Mortality from all cardiovascular diseases does seem to generally go down with increases in total cholesterol, but the smooth inflection point at the middle of the S-curve graph suggests a more complex variation pattern that may be influenced by other variables (e.g., smoking, dietary patterns, or even schistosomiasis infection; see “Notes” at the end of this post).

As mentioned before, total cholesterol is strongly influenced by HDL cholesterol, so below is the model with only HDL cholesterol (HDLCHOL) pointing at mortality from all cardiovascular diseases (MVASC), and the control variable sex (SexM1F2).


The graph above confirms the assumption that HDL’s protective role is subsumed by the variable total cholesterol. When the variable total cholesterol is removed from the model, as it was done above, the protective effect of HDL cholesterol becomes significant (beta=-0.27; P<0.01). The control variable sex (SexM1F2) was retained even in this targeted HDL effect model because of the expected confounding effect of sex; females generally tend to have higher HDL cholesterol and less cardiovascular disease than males.

Below, in the “Notes” section (after the “Reference”) are several notes, some of which are quite technical. Providing them separately hopefully has made the discussion above a bit easier to follow. The notes also point at some limitations of the analysis. This data needs to be analyzed from different angles, using multiple models, so that firmer conclusions can be reached. Still, the overall picture that seems to be emerging is at odds with previous beliefs based on the same dataset.

What could be increasing the apparently protective HDL and total cholesterol in this dataset? High consumption of animal foods, particularly foods rich in saturated fat and cholesterol, are strong candidates. Low consumption of vegetable oils rich in linoleic acid, and of foods rich in refined carbohydrates, are also good candidates. Maybe it is a combination of these.

We need more analyses!

Reference:

Kock, N. (2010). WarpPLS 1.0 User Manual. Laredo, Texas: ScriptWarp Systems.


Notes:

- The path coefficients (indicated as beta coefficients) reflect the strength of the relationships; they are a bit like standard univariate (or Pearson) correlation coefficients, except that they take into consideration multivariate relationships (they control for competing effects on each variable).

- The R-squared values reflect the percentage of explained variance for certain variables; the higher they are, the better the model fit with the data. In complex and multi-factorial phenomena such as health-related phenomena, many would consider an R-squared of 0.20 as acceptable. Still, such an R-squared would mean that 80 percent of the variance for a particularly variable is unexplained by the data.

- The P values have been calculated using a nonparametric technique, a form of resampling called jackknifing, which does not require the assumption that the data is normally distributed to be met. This and other related techniques also tend to yield more reliable results for small samples, and samples with outliers (as long as the outliers are “good” data, and are not the result of measurement error).

- Colinearity is an important consideration in models that analyze the effect of multiple predictors on one single variable. This is particularly true for multiple regression models, where there is a temptation of adding many predictors to the model to see which ones come out as the “winners”. This often backfires, as colinearity can severely distort the results. Some multiple regression techniques, such as automated stepwise regression with backward elimination, are particularly vulnerable to this problem. Colinearity is not the same as correlation, and thus is defined and measured differently. Two predictor variables may be significantly correlated and still have low colinearity. A reasonably reliable measure of colinearity is the variance inflation factor. Colinearity was tested in this model, and was found to be low.

- An effort was made here to avoid multiple data points per county (even though this was available for some variables), because this could artificially reduce the variance for each variable, and potentially bias the results. The reason for this is that multiple answers from a single county would normally be somewhat correlated; a higher degree of intra-county correlation than inter-county correlation. The resulting bias would be difficult to control for, via one or more control variables. With only two data points per county, one for males and the other for females, one can control for intra-country correlation by adding a “dummy” sex variable to the analysis, as a control variable. This was done here.

- Mortality from schistosomiasis infection (MSCHIST) is a variable that tends to affect the results in a way that makes it more difficult to make sense of them. Generally this is true for any infectious diseases that significantly affect a population under study. The problem with infection is that people with otherwise good health or habits may get the infection, and people with bad health and habits may not. Since cholesterol is used by the human body to fight disease, it may go up, giving the impression that it is going up for some other reason. Perhaps instead of controlling for its effect, as done here, it would have been better to remove from the analysis those counties with deaths from schistosomiasis infection. (See also this post, and this one.)

- Different parts of the data were collected at different times. It seems that the mortality data is for the period 1986-88, and the rest of the data is for 1989. This may have biased the results somewhat, even though the time lag is not that long, especially if there were changes in certain health trends from one period to the other. For example, major migrations from one county to another could have significantly affected the results.

- The following measures were used, from this online dataset like the other measures. P002 HDLCHOL, for HDLCHOL; P001 TOTCHOL, for TOTCHOL; and M021 SCHISTOc, for MSCHIST.

- SexM1F2 is a “dummy” variable that was coded with 1 assigned to males and 2 to females. As such, it essentially measures the “degree of femaleness” of the respondents. Being female is generally protective against cardiovascular disease, a situation that reverts itself a bit after menopause.

- MVASC is a composite measure of the two following variables, provided as component measures of mortality from all cardiovascular diseases: M058 ALLVASCb (ages 0-34), and M059 ALLVASCc (ages 35-69). A couple of obvious problems: (a) they does not include data on people older than 69; and (b) they seem to capture a lot of diseases, including some that do not seem like typical cardiovascular diseases. A factor analysis was conducted, and the loadings and cross-loadings suggested good validity. Composite reliability was also good. So essentially MVASC is measured here as a “latent variable” with two “indicators”. Why do this? The reason is that it reduces the biasing effects of incomplete data and measurement error (e.g., exclusion of folks older than 69). By the way, there is always some measurement error in any dataset.

- This note is related to measurement error in connection with the indicators for MVASC. There is something odd about the variables M058 ALLVASCb (ages 0-34), and M059 ALLVASCc (ages 35-69). According to the dataset, mortality from cardiovascular diseases for ages 0-34 is typically higher than for 35-69, for many counties. Given the good validity and reliability for MVASC as a latent variable, it is possible that the values for these two indicator variables were simply swapped by mistake.