# How EGDS (endurance genetic distance score) is calculated?

Can anybody please make me understand how EGDS5 has been calculated to 40.8 in this paper at page#31?

The formula has been described in this paper but when i tried the same, I am not getting the same results.

According to paper describing the formula:

$EGDS = 100 - \frac {100\cdot d} { n \cdot w }$

where

$n =$ number of studied polymorphisms

$w =$ score given to worst genotype

$d =$ euclidean distance calculated as follows

$d = \sqrt{ \sum_{i = 1}^{n} (2 - x_i)^2}$

$x_i =$ genotype score of corresponding polymorphism

$2 =$ optimal genotype score

here is what I tried. Given below is the genotype score of 5 genes:

$x = (1,1,1,1,0)$

$d = \sqrt { (2-1)^2 + (2-1)^2 + (2-1)^2 + (2-1)^2 + (2-0)^2 }$

$= \sqrt { 1 + 1 + 1 + 1 + 4}$

$= \sqrt 8 \approx 2.82$

Now, $EGDS5 = 100 - \frac{ 100 }{ 5 \cdot 4 } \cdot 2.82$

$= 100 - 5 \cdot 2.82$

$= 85.9$

which is not equal to 40.8.

In my opinion, there must be something wrong with the formula given in the paper. The rationale behind the conversion of $d$ into the range 0-100 is stated in the papera as follows:

An EGDS9 of 100 represents an “optimal” endurance genetic profile, that is, all GS’s are 2. In contrast, an EGDS9 of 0 represents the “worst” possible profile for endurance genetic profile, that is, all GS’s are 0.

So what they are basically saying is that they want

$d_{max} = \sqrt{\sum_{i=1}^n(2-0)^2} = \sqrt{4n} = 2\sqrt{n} \Longrightarrow EDGS_n \stackrel{!}{=} 0$

$d_{min} = \sqrt{\sum_{i=1}^n(2-2)^2} = \sqrt{0} = 0 \Longrightarrow EGDS_n \stackrel{!}{=} 100$

So let's just define EGSD as the percentage of reaching the minimum possible distance:

$EGDS_n =100 \cdot \frac{2\sqrt{n} - d}{2\sqrt{n}} = 100 \cdot \left(1 -\frac d {2\sqrt{n}} \right) = 100 - \frac {100\cdot d}{2\sqrt{n}}$

Which gives us a formula very similar to the given. (Actually their formula is just missing the squre root in the denominator).

Let's apply this formula now to the case of the other paperb in discussion:

$EGDS_5 =100 \cdot \frac{2\sqrt{5} - \sqrt{8}}{2\sqrt{5}} \approx 36.754$

Not quite 40.8, but closer. Now, what if we assume the people in the other paper used this formula but made a mistake when calculating d, getting $d = \sqrt{7}$?

$EGDS_5 =100 \cdot \frac{2\sqrt{5} - \sqrt{7}}{2\sqrt{5}} \approx 40.839$

Interestingly, the other score 33.8 comes from apparently calculating

$EGDS_4 =100 \cdot \frac{2\sqrt{4} - \sqrt{7}}{2\sqrt{4}} \approx 33.856$

In their table, there are actually five rows but the last row has no value in its column?

I would say these are just bad papers, IMHO.

References

a Meckel, Yoav, et al. "Practical uses of genetic profile assessment in athletic training–an illustrative case study." Acta Kinesiologiae Universitatis Tartuensis 20 (2014): 25-39. (http://ojs.utlib.ee/index.php/AKUT/article/view/11961)

b Ben-Zaken, Sigal, et al. "Genetic profiles and prediction of the success of young athletes’ transition from middle-to long-distance runs: an exploratory study." Pediatric exercise science 25.3 (2013): 435-447. (https://www.ncbi.nlm.nih.gov/pubmed/23877193)

• Thank you! I've been trying to make sense of this for over an hour. Now I have to spend an hour forgetting about it. Commented May 20, 2017 at 14:31