## Monday, October 26, 2015

### 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 trigs. = 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).

Anyway, an online calculator that implements both equations (Friedewald and Iranian) is linked here; it was the top Google hit on a search for “Iranian equation LDL” at the time of this post’s writing.

As you will see if you try it, the online calculator linked above is useful in showing the difference in calculated LDL cholesterol, using both equations, when fasting triglycerides are very low (e.g., below 50).

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.