The 2012 Atherosclerosis egg study: More smoking is associated with more plaque, unless you eat more eggs

I blogged before about the study by David Spence and colleagues, published online in July 2012 in the journal Atherosclerosis (). This study attracted a lot of media attention (e.g., ). The article is titled: “Egg yolk consumption and carotid plaque”. The study argues that “regular consumption of egg yolk should be avoided by persons at risk of cardiovascular disease”. It hints at egg yolks being unhealthy in general, possibly even more so than cigarettes.

I used the numbers in Table 2 of the article (only 5 rows of data, one per quintile; i.e., N=5) to conduct a type of analysis that is rarely if ever conducted in health studies – a moderating effects analysis. A previous blog post summarizes the results of one such analysis using WarpPLS (). It looked into the effect of the number of eggs consumed per week on the association between blood LDL cholesterol and plaque (carotid plaque). The conclusion, which is admittedly tentative due to the small sample (N=5), was that plaque decreased as LDL cholesterol increased with consumption of 2.3 eggs per week or more ().

Recently I ran an analysis on the moderating effect of number of eggs consumed per week on the association between cumulative smoking (measured in “pack years”) and plaque. As it turns out, if you fit a 3D surface to the five data points that you get for these three variables from Table 2 of the article, you end up with a relatively smooth surface. Below is a 3D plot of the 5 data points, followed by a best-fitting 3D surface (developed using an experimental algorithm).

Based on this best-fitting surface you could then generate a contour graph, shown below. The “lines” are called “isolines”. Each isoline refers to plaque values that are constant for a set of eggs per week and cumulative smoking combinations. Next to the isolines are the corresponding plaque values. The first impression is indeed that both egg consumption and smoking are causing plaque buildup, as plaque clearly increases as one moves toward the top-right corner of the graph.

But focus your attention on each individual isoline, one at a time. It is clear that plaque remains constant for increases in cumulative smoking, as long as egg consumption increases. Take for example the isoline that refers to 120 mm2 of plaque area. An increase in cumulative smoking from about 14.5 to 16 pack years leads to no increase in plaque if egg consumption goes up from about 2 to 2.3 eggs per week.

These within-isoline trends, which are fairly stable across isolines (they are all slanted to the right), clearly contradict the idea that eggs cause plaque buildup. So, why does plaque buildup seem to clearly increase with egg consumption? Here is a good reason: egg consumption is very strongly correlated with age, and plaque increases with age. The correlation is a whopping 0.916. And I am not talking about cumulative egg consumption, which the authors also measure, through a variable called “egg-yolk years”. No, I am talking about eggs per week. In this dataset, older folks were eating more eggs, period.

The correlation between plaque and age is even higher: 0.977. Given this, it makes sense to look at individual isolines. This would be analogous to what biostatisticians often call “adjusting for age”, or analyzing the effect of egg consumption on plaque buildup “keeping age constant”. A different technique is to “control for age”; this technique would be preferable had the correlations been lower (say, lower than 0.7), as collinearity levels might have been below acceptable thresholds.

The underlying logic of the “keeping age constant” technique is fairly sound in the face of such a high correlation, which would make “controlling for age” very difficult due to collinearity. When we “keep age constant”, the results point at egg consumption being protective among smokers.

But diehard fans of the idea that eggs are unhealthy could explain the results differently. Maybe egg consumption causes plaque to go up, but smoking has a protective effect. Again taking the isoline that refers to 120 mm2 of plaque area, these diehard fans could say that an increase in egg consumption from 2 to 2.3 eggs per week leads to no increase in plaque if cumulative smoking goes up from about 14.5 to 16 pack years.

Not too long ago I also blogged about a medical case study of a man who ate approximately 25 eggs (20 to 30) per day for over 15 years (probably well over), was almost 90 years old (88) when the case was published in the prestigious The New England Journal of Medicine, and was in surprisingly good health (). This man was not a smoker.

Perhaps if this man smoked 25 cigarettes per day, and ate no eggs, he would be in even better health eh!?

Does tallness cause heart disease? No, but sex does

Popular beliefs about medical issues are sometimes motivated by a statistical phenomenon known as “spurious relationship”, among other names. Two variables X and Y are influenced by a third variable C, which leads to X and Y being correlated and thus the impression that X and Y are causally associated.

Take a look at the table below, which I blogged about in a previous post (). This table shows that there is a strong unadjusted correlation between height and arterial stiffness, a marker of heart disease. The likelihood that the correlation is due to chance is lower than one tenth of a percentage point (P<.001).

Interestingly, the authors of the study even use height as a control variable to narrow down the “true” causes of arterial stiffness (column with adjusted results), assuming that height did indeed influence arterial stiffness and what they found to be a key predictor of arterial stiffness, 2-hour postprandial glucose.

But there is no convincing evidence that height causes heart disease, with exception of pathological extremes – e.g., acromegaly. Extremes tend to influence statistical results somewhat, leading to conflicting conclusions that end up being disseminated by the popular media (). This is one of the sources of popular beliefs about medical issues.

Another, more important, source are real confounders. And this takes us back to the issue of height being associated with heart disease. In fact, height will typically be significantly associated with heart disease in almost any study that includes men and women and does not control for biological sex.

One of the reasons is that women overall tend to have a significantly lower incident of heart disease than men. The other is that height is significantly lower among women than men, on average, even though there are several women who are taller than the average man.

The table above was from a study including both sexes. Therefore, the strong association between height and arterial stiffness is a “reflection” of the strong association between being male and increased arterial stiffness. If one were to add a variable coded as 0 for male and 1 for female, and use it in a multivariate analysis of predictor of arterial stiffness, together with height, the effect of height would probably “disappear”.

Biological sex is the control variable, the “confounder”, that the authors should have used to narrow down the “true” causes of arterial stiffness (second column in the table). In the absence of biological sex, controlling for height accomplished something similar, but in a “wobbly” way, leaving many readers scratching their heads in confusion.