How EGDS (endurance genetic distance score) is calculated?

Question

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.

Answer 1

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 paper^a 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 paper^b 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)