Paired t-test of Age vs % change in DNA methylation data yields ridiculously high p-values (indicating this is an inappropriate way of measurement).

Clearly, a solution to this problem is to create an age-dummy (i.e. age = 1 if age > 40, and age = 0 if age < 40) and perform a standard OLS-regression (linear regression). However, it seems as if our data does not fit a linear model. Is there any statistical method (preferable paired t-test) whereby I can test the impact of age on % change in DNA methylation levels, without creating a dummy variable or performing a linear regression?

If important in any respect, the programming is made in "R".

Reply much appreciated.

Best