The Friedewald and Iranian equations: Fasting triglycerides can seriously distort calculated LDL

Standard lipid profiles provide LDL cholesterol measures based on equations that usually have the following as their inputs (or independent variables): total cholesterol, HDL cholesterol, and triglycerides.

Yes, LDL cholesterol is not measured directly in standard lipid profile tests! This is indeed surprising, since cholesterol-lowering drugs with negative side effects are usually prescribed based on estimated (or "fictitious") LDL cholesterol levels.

The most common of these equations is the Friedewald equation. Through the Friedewald equation, LDL cholesterol is calculated as follows (where TC = total cholesterol, and TG = triglycerides). The inputs and result are in mg/dl.

    LDL = TC – HDL – TG / 5

Here is one of the problems with the Friedewald equation. Let us assume that an individual has the following lipid profile numbers: TC = 200, HDL = 50, and TG = 150. The calculated LDL will be 120. Let us assume that this same individual reduces triglycerides to 50, from the previous 150, keeping all of the other measures constant with except of HDL, which goes up a bit to compensate for the small loss in total cholesterol associated with the decrease in triglycerides (there is always some loss, because the main carrier of triglycerides, VLDL, also carries some cholesterol). This would normally be seen as an improvement. However, the calculated LDL will now be 140, and a doctor will tell this person to consider taking statins!

There is evidence that, for individuals with low fasting triglycerides, a more precise equation is one that has come to be known as the “Iranian equation”. The equation has been proposed by Iranian researchers in an article published in the Archives of Iranian Medicine (Ahmadi et al., 2008), hence its nickname. Through the Iranian equation, LDL is calculated as follows. Again, the inputs and result are in mg/dl.

    LDL = TC / 1.19 + TG / 1.9 – HDL / 1.1 – 38

The Iranian equation is based on linear regression modeling, which is a good sign, although I would have liked it even better if it was based on nonlinear regression modeling. The reason is that relationships between variables describing health-related phenomena are often nonlinear, leading to biased linear estimations. With a good nonlinear analysis algorithm, a linear relationship will also be captured; that is, the “curve” that describes the relationship will default to a line if the relationship is truly linear (see: warppls.com).

The Iranian equation yields high values of LDL cholesterol when triglycerides are high; much higher than those generated by the Friedewald equation. If those are not overestimations (and there is some evidence that, if they are, it is not by much), they describe an alarming metabolic pattern, because high triglycerides are associated with small-dense LDL particles. These particles are the most potentially atherogenic of the LDL particles, in the presence of other factors such as chronic inflammation.

In other words, the Iranian equation gives a clearer idea than the Friedewald equation about the negative health effects of high triglycerides. You need a large number of small-dense LDL particles to carry a high amount of LDL cholesterol.

An even more precise measure of LDL particle configuration is the VAP test; this post has a discussion of a sample VAP test report.

Reference:

Ahmadi SA, Boroumand MA, Gohari-Moghaddam K, Tajik P, Dibaj SM. (2008). The impact of low serum triglyceride on LDL-cholesterol estimation. Archives of Iranian Medicine, 11(3), 318-21.

Do prominent health gurus live longer?

Many years ago, when I started blogging about health issues, I noticed a couple of interesting patterns. The first pattern is that prominent health “gurus” often talk about having had serious health problems in their past, which they describe as having motivated them to do research on health issues – and thus become health gurus. Frequently these problems pop up before 45 years of age; this is a threshold beyond which there is a clearly noticeable increase in severity of health problems.

In fact, I remember being somewhat surprised by one such “guru” (I will not name him), who would regularly write posts saying something to the effect that “… finally, my health is now on the right track …” In other words, every few months or so this person had to deal with serious health problems, always coming up with reasonable knowledge-based solutions. The knowledge seemed to be of good quality, but this guy’s health was poor to say the least.

The second pattern, related to the above, is that prominent health gurus seem to have a below average life expectancy. The life expectancy for the general population is around 79 years of age in the USA at the time of this writing, according to the World Health Organization (). Anthony Colpo has written an interesting post about this below average life expectancy pattern among health gurus ().

To better understand and illustrate this situation to our blog’s readers, I created a dataset with 100 records, corresponding to 100 health gurus, with various variables interacting in ways that reflect the above observations. The observations are summarized as assumptions, listed later. The following variables are on a scale from 1 to 7; in real life they would have been measured retrospectively, looking back at a guru’s entire life:

- The guru's health before age 45 (BEF45).

- The guru's knowledge about health issues (KNOWL).

- The guru's health after age 45 (AFT45).

- The guru's prominence (GPROM).

Finally, the variable below is on a continuous scale of years, with an average of 79 and a standard deviation of 10. As mentioned earlier, 79 is the life expectancy for someone living in the USA at the time of this writing. The standard deviation of 10, which approximates that figure in the USA, means that approximately 68 percent of the individuals in the simulated dataset will have a life expectancy between 69 and 89. That is 79-10 and 79+10, respectively.

- The guru's age at the time of death (GAGED).

This experimental exercise with simulated data can be seen as a simulation “game”, where various variables interact to generate results that are not obvious. A widely used process to create data is known as the Monte Carlo method (), which is what we used here. I also made the following assumptions in the data creation process:

- That the poorer is the guru's health before age 45 (BEF45), the greater is the guru's knowledge about health issues (KNOWL). The reason for this is that poor health compels the person to study about health issues.

- That the poorer is the guru's health before age 45 (BEF45), the poorer is the guru's health after age 45 (AFT45). This assumes that the person has an underlying condition that causes the poor health in the first place, and that can be exacerbated by a poor diet and lifestyle.

- That the greater is the guru's knowledge about health issues (KNOWL), the better is the guru's health after age 45 (AFT45). This counteracts the effect above, and assumes that the knowledge is put to good use and contributes to improving the person’s health.

- That the greater is the guru's knowledge about health issues (KNOWL), the greater is also the guru's prominence (GPROM). In other words, a guru’s status among followers is enhanced by the guru’s knowledge.

- That the better is the guru's health after age 45 (AFT45), the higher is the guru's age at the time of death (GAGED).

A final assumption made is that the causal relationships laid out above have a small effect size (more technically, that they are associated with f-squared coefficients slightly below 0.1), meaning that random influences are not only present but also play a big role in what happens in the simulation. The causality links are summarized in the graph below, created with WarpPLS (). We also used this software to analyze the data.

Note that in our simulated data the guru's prominence (GPROM) does not directly influence the guru's age at the time of death (GAGED). Stated differently, there is no causality link between GPROM and GAGED, one way or the other, even though these two variables are likely to be correlated due to the network of causality links in which they exist. Nevertheless, it is by looking at the relationship between these two variables, GPROM and GAGED, that we can answer the question in the title of this post: Do prominent health gurus live longer?

And the answer appears to be “no” in our simulation. The plot below shows the relationship between a guru's prominence (GPROM), on the horizontal axis, and the guru's age at the time of death (GAGED), on the vertical axis. Each data point refers to a guru. On average, the greater a guru's prominence, the lower seems to be the guru’s life expectancy. Each one-point increase in prominence is associated, on average, with approximately a one-year decrease in life expectancy.

Note that there is one very prominent guru whose age at the time of death was around 95; the data point at the top-right corner (GPROM=7, GAGED~95). This happened largely by chance in our data. Nevertheless, assuming that our data somewhat reflects what could happen in real life, the followers of the guru would probably point at that longevity as being caused by the guru’s knowledge about health issues. They would likely be wrong.

Our dataset also allows us to estimate the probability that a fairly prominent guru (GPROM greater than 4, on a 1-7 scale) would have a below average life expectancy (GAGED lower than 79). That conditional probability would be approximately 60 percent.

Is heavy physical activity a major trigger of death by sudden cardiac arrest? Not in Oregon

The idea that heavy physical activity is a main trigger of heart attacks is widespread. Often endurance running and cardio-type activities are singled out. Some people refer to this as “death by running”.

Good cardiology textbooks, such as the Mayo Clinic Cardiology, tend to give us a more complex and complete picture. So do medical research articles that report on studies of heart attacks based on comprehensive surveys.

Reddy and colleagues (2009) studied sudden cardiac arrest events followed by death from 2002 to 2005 in Multnomah County in Oregon. This study was part of the ongoing Oregon Sudden Unexpected Death Study. Multnomah County has an area of 435 square miles, and had a population of over 677 thousand at the time of the study. The full reference to the article and a link to a full-text version are at the end of this post.

The researchers grouped deaths by sudden cardiac arrests (SCAs) according to the main type of activity being performed before the event. Below is how the authors defined the activities, quoted verbatim from the article. MET is a measure of the amount of energy spent in the activity; one MET is the amount of energy spent by a person sitting quietly.

- Sleep (MET 0.9): subjects who were sleeping when they sustained SCA.
- Light activity (MET 1.0–3.4): included bathing, dressing, cooking, cleaning, feeding, household walking and driving.
- Moderate activity (MET 3.5–5.9): included walking for exercise, mowing lawn, gardening, working in the yard, dancing.
- Heavy activity (MET score ≥6): included sports such as tennis, running, jogging, treadmill, skiing, biking.
- Sexual activity (MET score 1.3): included acts of sexual intercourse.

What did they find? Not what many people would expect.

The vast majority of the people dying of sudden cardiac arrest were doing things that fit the “light activity” group above prior to their death. This applies to both genders. The figure below (click to enlarge) shows the percentages of men and women who died from sudden cardiac arrest, grouped by activity type.

Sudden cardiac arrests were also categorized as witnessed or un-witnessed. For witnessed, someone saw them happening. For un-witnessed, the person was seen alive, and within 24 hours had died. So the data for witnessed sudden cardiac arrests is a bit more reliable. The table below displays the distribution of mean age, gender and known coronary artery disease (CAD) in those with witnessed sudden cardiac arrest.

Look at the bottom row, showing those with known coronary artery disease. Again, light activity is the main trigger. Sleep comes second. The numbers within parentheses refer to percentages within each activity group. Those percentages are not very helpful in the identification of the most important triggers, although they do suggest that coronary artery disease is a major risk factor. For example, among those who died from sudden cardiac arrest while having sex, 57 percent had known coronary artery disease. For light activity, 36 percent had known coronary artery disease.

As a caveat, it is worth noting that heavy activity appears to be more of a trigger in younger individuals than in older ones. This may simply reflect the patterns of activities at different ages. However, this does not seem to properly account for the large differences observed in triggers; the standard deviation for age in the heavy activity group was large enough to include plenty of seniors. Still, it would have been nice to see a multivariate analysis controlling for various effects, including age.

So what is going on here?

The authors give us a hint. The real culprit may be bottled up emotional stress and sleep disorders; the latter may be caused by stress, as well as by obesity and other related problems. They have some data that points in those directions. That makes some sense.

We humans have evolved “fight-or-flight” mechanisms that involve large hormonal discharges in response to stressors. Our ancestors needed those. For example, they needed those to either fight or run for their lives in response to animal attacks.

Modern humans experience too many stressors while sitting down, as in stressful car commutes and nasty online interactions. The stresses cause “fight-or-flight” hormonal discharges, but are followed by neither “fight” nor “flight” in most cases. This cannot be very good for us.

Death by running!? More like death by not running!

Reference:

Reddy, P.R., Reinier, K., Singh, T., Mariani, R., Gunson, K., Jui, J., & Chugh, S.S. (2009). Physical activity as a trigger of sudden cardiac arrest: The Oregon Sudden Unexpected Death Study. International Journal of Cardiology, 131(3), 345–349.

What is a good low carbohydrate diet? It is a low calorie one

What is a good low carbohydrate diet?

For me, and many people I know, the answer is: a low calorie one. What this means, in simple terms, is that a good low carbohydrate diet is one with plenty of seafood and organ meats in it, and also plenty of veggies. These are low carbohydrate foods that are also naturally low in calories. Conversely, a low carbohydrate diet of mostly beef and eggs would be a high calorie one.

Seafood and organ meats provide essential fatty acids and are typically packed with nutrients. Because of that, they tend to be satiating. In fact, certain organ meats, such as beef liver, are so packed with nutrients that it is a good idea to limit their consumption. I suggest eating beef liver once or twice a week only. As for seafood, it seems like a good idea to me to get half of one’s protein from them.

Does this mean that the calories-in-calories-out idea is correct? No, and there is no need to resort to complicated and somewhat questionable feedback-loop arguments to prove that calories-in-calories-out is wrong. Just consider this hypothetical scenario; a thought experiment. Take two men, one 25 years of age and the other 65, both with the same weight. Put them on the same exact diet, on the same exact weight training regime, and keep everything else the same.

What will happen? Typically the 65-year-old will put on more body fat than the 25-year-old, and the latter will put on more lean body mass. This will happen in spite of the same exact calories-in-calories-out profile. Why? Because their hormonal mixes are different. The 65-year-old will typically have lower levels of circulating growth hormone and testosterone, both of which significantly affect body composition.

As you can see, it is not all about insulin, as has been argued many times before. In fact, average and/or fasting insulin may be the same for the 65- and 25-year-old men. And, still, the 65-year-old will have trouble keeping his body fat low and gaining muscle. There are other hormones involved, such as leptin and adiponectin, and probably several that we don’t know about yet.

A low carbohydrate diet appears to be ideal for many people, whether that is due to a particular health condition (e.g., diabetes) or simply due to a genetic makeup that favors this type of diet. By adopting a low carbohydrate diet with plenty of seafood, organ meats, and veggies, you will make it a low calorie diet. If that leads to a calorie deficit that is too large, you can always add a bit more of fat to it. For example, by cooking fish with butter and adding bacon to beef liver.

One scenario where I don’t see the above working well is if you are a competitive athlete who depletes a significant amount of muscle glycogen on a daily basis – e.g., 250 g or more. In this case, it will be very difficult to replenish glycogen only with protein, so the person will need more carbohydrates. He or she would need a protein intake in excess of 500 g per day for replenishing 250 g of glycogen only with protein.

Total cholesterol and cardiovascular disease: A U-curve relationship

The hypothesis that blood cholesterol levels are positively correlated with heart disease (the lipid hypothesis) dates back to Rudolph Virchow in the mid-1800s.

One famous study that supported this hypothesis was Ancel Keys's Seven Countries Study, conducted between the 1950s and 1970s. This study eventually served as the foundation on which much of the advice that we receive today from doctors is based, even though several other studies have been published since that provide little support for the lipid hypothesis.

The graph below (from O Primitivo) shows the results of one study, involving many more countries than Key's Seven Countries Study, that actually suggests a NEGATIVE linear correlation between total cholesterol and cardiovascular disease.

Now, most relationships in nature are nonlinear, with quite a few following a pattern that looks like a U-curve (plain or inverted); sometimes called a J-curve pattern. The graph below (also from O Primitivo) shows the U-curve relationship between total cholesterol and mortality, with cardiovascular disease mortality indicated through a dotted red line at the bottom.

This graph has been obtained through a nonlinear analysis, and I think it provides a better picture of the relationship between total cholesterol (TC) and mortality. Based on this graph, the best range of TC that one can be at is somewhere between 210, where cardiovascular disease mortality is minimized; and 220, where total mortality is minimized.

The total mortality curve is the one indicated through the full blue line at the top. In fact, it suggests that mortality increases sharply as TC decreases below 200.

Now, these graphs relate TC with disease and mortality, and say nothing about LDL cholesterol (LDL). In my own experience, and that of many people I know, a TC of about 200 will typically be associated with a slightly elevated LDL (e.g., 110 to 150), even if one has a high HDL cholesterol (i.e., greater than 60).

Yet, most people who have a LDL greater than 100 will be told by their doctors, usually with the best of the intentions, to take statins, so that they can "keep their LDL under control". (LDL levels are usually calculated, not measured directly, which itself creates a whole new set of problems.)

Alas, reducing LDL to 100 or less will typically reduce TC below 200. If we go by the graphs above, especially the one showing the U-curves, these folks' risk for cardiovascular disease and mortality will go up - exactly the opposite effect that they and their doctors expected. And that will cost them financially as well, as statin drugs are expensive, in part to pay for all those TV ads.

What is your optimal weight? Maybe it is the one that minimizes your waist-to-weight ratio

There is a significant amount of empirical evidence suggesting that, for a given individual and under normal circumstances, the optimal weight is the one that maximizes the ratio below, where: L = lean body mass, and T = total mass.

L / T

L is difficult and often costly to measure. T can be measured easily, as one’s total weight.

Through some simple algebraic manipulations, you can see below that the ratio above can be rewritten in terms of one’s body fat mass (F).

L / T = (T – F) / T = 1 – F / T

Therefore, in order to maximize L / T, one should maximize 1 – F / T. This essentially means that one should minimize the second term, or the ratio below, which is one’s body fat mass (F) divided by one’s weight (T).

F / T

So, you may say, all I have to do is to minimize my body fat percentage. The problem with this is that body fat percentage is very difficult to measure with precision, and, perhaps more importantly, body fat percentage is associated with lean body mass (and also weight) in a nonlinear way.

In English, it becomes increasingly difficult to retain lean body mass as one's body fat percentage goes down. Mathematically, body fat percentage (F / T) is a nonlinear function of T, where this function has the shape of a J curve.

This is what complicates matters, making the issue somewhat counterintuitive. Six-pack abs may look good, but many people would have to sacrifice too much lean body mass for their own good to get there. Genetics definitely plays a role here, as well as other factors such as age.

Keep in mind that this (i.e., F / T) is a ratio, not an absolute measure. Given this, and to facilitate measurement, we can replace F with a variable that is highly correlated with it, and that captures one or more important dimensions particularly well. This new variable would be a proxy for F. One the most widely used proxies in this type of context is waist circumference. We’ll refer to it as W.

W may well be a very good proxy, because it is a measure that is particularly sensitive to visceral body fat mass, an important dimension of body fat mass. W likely captures variations in visceral body fat mass at the levels where this type of body fat accumulation seems to cause health problems.

Therefore, the ratio that most of us would probably want to minimize is the following, where W is one’s waist circumference, and T is one’s weight.

W / T = waist / weight

Based on the experience of HCE () users, variations in this ratio are likely to be small and require 4-decimals or more to be captured. If you want to avoid having so many decimals, you can multiply the ratio by 1000. This will have no effect on the use of the ratio to find your optimal weight; it is analogous to multiplying a ratio by 100 to express it as a percentage.

Also based on the experience of HCE users, there are fluctuations that make the ratio look like it is changing direction when it is not actually doing that. Many of these fluctuations may be due to measurement error.

If you are obese, as you lose weight through dieting, the waist / weight ratio should go down, because you will be losing more body fat mass than lean body mass, in proportion to your total body mass.

It would arguably be wise to stop losing weight when the waist / weight ratio starts going up, because at that point you will be losing more lean body mass than body fat mass, in proportion to your total body mass.

One’s lowest waist / weight ratio at a given point in time should vary depending on a number of factors, including: diet, exercise, general lifestyle, and age. This lowest ratio will also be dependent on one’s height and genetic makeup.

Mathematically, this lowest ratio is the ratio at which d(W / T) / dT = 0 and d(d(W / T) / dT) / dT > 0. That is, the first derivative of W / T with respect to T equals zero, and the second derivative is greater than zero.

The lowest waist / weight ratio is unique to each individual, and can go up and down over time (e.g., resistance exercise will push it down). Here I am talking about one's lowest waist / weight ratio at a given point in time, not one's waist / weight ratio at a given point in time.

This optimal waist / weight ratio theory is one of the most compatible with evidence regarding the lowest mortality body mass index (, ). Nevertheless, it is another ratio that gets a lot of attention in the health-related literature. I am talking about the waist / hip ratio (). In this literature, waist circumference is often used alone, not as part of a ratio.

Vitamin D production from UV radiation: The effects of total cholesterol and skin pigmentation

Our body naturally produces as much as 10,000 IU of vitamin D based on a few minutes of sun exposure when the sun is high. Getting that much vitamin D from dietary sources is very difficult, even after “fortification”.

The above refers to pre-sunburn exposure. Sunburn is not associated with increased vitamin D production; it is associated with skin damage and cancer.

Solar ultraviolet (UV) radiation is generally divided into two main types: UVB (wavelength: 280–320 nm) and UVA (320–400 nm). Vitamin D is produced primarily based on UVB radiation. Nevertheless, UVA is much more abundant, amounting to about 90 percent of the sun’s UV radiation.

UVA seems to cause the most skin damage, although there is some debate on this. If this is correct, one would expect skin pigmentation to be our body’s defense primarily against UVA radiation, not UVB radiation. If so, one’s ability to produce vitamin D based on UVB should not go down significantly as one’s skin becomes darker.

Also, vitamin D and cholesterol seem to be closely linked. Some argue that one is produced based on the other; others that they have the same precursor substance(s). Whatever the case may be, if vitamin D and cholesterol are indeed closely linked, one would expect low cholesterol levels to be associated with low vitamin D production based on sunlight.

Bogh et al. (2010) published a very interesting study; one of those studies that remain relevant as time goes by. The link to the study was provided by Ted Hutchinson in the comments sections of a another post on vitamin D. The study was published in a refereed journal with a solid reputation, the Journal of Investigative Dermatology.

The study by Bogh et al. (2010) is particularly interesting because it investigates a few issues on which there is a lot of speculation. Among the issues investigated are the effects of total cholesterol and skin pigmentation on the production of vitamin D from UVB radiation.

The figure below depicts the relationship between total cholesterol and vitamin D production based on UVB radiation. Vitamin D production is referred to as “delta 25(OH)D”. The univariate correlation is a fairly high and significant 0.51.

25(OH)D is the abbreviation for calcidiol, a prehormone that is produced in the liver based on vitamin D3 (cholecalciferol), and then converted in the kidneys into calcitriol, which is usually abbreviated as 1,25-(OH)2D3. The latter is the active form of vitamin D.

The table below shows 9 columns; the most relevant ones are the last pair at the right. They are the delta 25(OH)D levels for individuals with dark and fair skin after exposure to the same amount of UVB radiation. The difference in vitamin D production between the two groups is statistically indistinguishable from zero.

So there you have it. According to this study, low total cholesterol seems to be associated with impaired ability to produce vitamin D from UVB radiation. And skin pigmentation appears to have little effect on the amount of vitamin D produced.

The study has a few weaknesses, as do almost all studies. For example, if you take a look at the second pair of columns from the right on the table above, you’ll notice that the baseline 25(OH)D is lower for individuals with dark skin. The difference was just short of being significant at the 0.05 level.

What is the problem with that? Well, one of the findings of the study was that lower baseline 25(OH)D levels were significantly associated with higher delta 25(OH)D levels. Still, the baseline difference does not seem to be large enough to fully explain the lack of difference in delta 25(OH)D levels for individuals with dark and fair skin.

A widely cited dermatology researcher, Antony Young, published an invited commentary on this study in the same journal issue (Young, 2010). The commentary points out some weaknesses in the study, but is generally favorable. The weaknesses include the use of small sub-samples.

References

Bogh, M.K.B., Schmedes, A.V., Philipsen, P.A., Thieden, E., & Wulf, H.C. (2010). Vitamin D production after UVB exposure depends on baseline vitamin D and total cholesterol but not on skin pigmentation. Journal of Investigative Dermatology, 130(2), 546–553.

Young, A.R. (2010). Some light on the photobiology of vitamin D. Journal of Investigative Dermatology, 130(2), 346–348.