The 2012 Arch Intern Med red meat-mortality study: The “protective” effect of smoking

In a previous post () I used WarpPLS () to analyze the model below, using data reported in a recent study looking at the relationship between red meat consumption and mortality. The model below shows the different paths through which smoking influences mortality, highlighted in red. The study was not about smoking, but data was collected on that variable; hence this post.

When one builds a model like the one above, and tests it with empirical data, the person does something similar to what a physicist would do. The model is a graphical representation of a complex equation, which embodies the beliefs of the modeler. WarpPLS builds the complex equation automatically for the user, who would otherwise have to write it down using mathematical symbols.

The results yielded by the complex equation, partly in the form of coefficients of association for direct relationships (the betas next to the arrows), have a meaning. Some may look odd, and require novel interpretations, much in the same way that odd results from an equation describing planetary motions may have led to the development of the theory of black holes.

Nothing is actually "proven" by the results. They are part of the long and painstaking process we call "research". To advance new knowledge, one needs a lot more than a single study. Darwin's theory of evolution is still being tested. Based on various tests and partial refutations, it has itself evolved a great deal since its original formulation.

One set of results that are generated based on the model above by WarpPLS, in addition to coefficients for direct relationships, are coefficients of association called "total effects". They aggregate all of the effects, via multiple paths, between each pair of variables. Below is a table of total effects, with the total effects of smoking on diabetes incidence and overall mortality highlighted in red.

As you can see, the total effects of smoking on diabetes incidence and overall mortality are negative, but small enough to be considered insignificant. This is interesting, because smoking is definitely not health-promoting. Among hunter-gatherers, who often smoke tobacco, it increases the incidence of various types of cancer (). And it may be at the source of many of the health problems suggested by analyses on the China Study II data ().

So what are these results telling us? They tell us that smoking has an intermediate protective effect, very likely associated with its anorexic effect. Smoking is an appetite suppressor. Its total effect on food intake is negative, and strong. As we can see from the table of total effects, just below the two numbers highlighted in red, the total effect of smoking on food intake is -0.356.

Still, it looks like smoking is nearly as bad as overeating to the point of becoming obese (), in terms of its overall effect on health. Otherwise we would see a positive total effect on overall mortality of comparable strength to the negative total effect on food intake.

Smoking may make one eat less, but it ends up hastening one’s demise through different paths.

Cigarette Smoking-- Another Factor in the Obesity Epidemic

Obesity rates in the US have more than doubled in the last 30 years, and rates of childhood obesity and extreme adult obesity have tripled.  One third of US adults are considered obese, and another third overweight.  This is the "obesity epidemic".

The obesity epidemic has coincided with significant changes in the US diet, which are clearly involved.  However, there's another probable contributor that's often overlooked: declining smoking rates.  

Here's a graph of cigarette consumption over the last century in the US (1):
Read more »

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 ().

Strong causation can exist without any correlation: The strange case of the chain smokers, and a note about diet

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.