P-Trend, what does it mean and how being calculated?

Hello all :)

I need your help...

I am trying to make analysis based on a similar paper, and I can't understand the statistical method to be used.

Let's say I have a continuous variable Y and a continuous variable X, which is divided into 3 groups based on the tertiles of X: T1, T2, T3.

I am interested in something called P-Trend. According to the example I have (will give you a link in a second), I am suppose to take each group, i.e. each tertile, to calculate it's median, and to set the median as the representative value of X. Then, I am supposed to model Y vs. X with a linear regression. The P-Value will be the P-Trend.

My questions to you are:

1. Did I understand correctly according to the following link ?
2. Does it makes sense ? Why not modeling Y vs X directly ??

Thank you in advance !

The paper is here:


I refer to the Statistical analysis section in page 1467, row number 12 from beginning of this section.

Thanks again for any input !