  Gamma Ray Bursts (GRBs) visible up to very high redshift have become
attractive targets as potential new distance indicators. It is still not clear
whether the relations proposed so far originate from an unknown GRB physics or
result from selection effects. We investigate this issue in the case of the
$L_X-T^*_a$ correlation (hereafter LT) between the X-ray luminosity $L_X (T_a)$
at the end of the plateau phase, $T_a$, and the rest frame time $T^{*}_a$. We
devise a general method to build mock data sets starting from a GRB world model
and taking into account selection effects on both time and luminosity. This
method shows how not knowing the efficiency function could influence the
evaluation of the intrinsic slope of any correlation and the GRB density rate.
We investigate biases (small offsets in slope or normalization) that would
occur in the LT relation as a result of truncations, possibly present in the
intrinsic distributions of $L_X$ and $T^*_a$. We compare these results with the
ones in Dainotti et al. (2013) showing that in both cases the intrinsic slope
of the LT correlation is $\approx -1.0$. This method is general, therefore
relevant to investigate if any other GRB correlation is generated by the biases
themselves. Moreover, because the farthest GRBs and star-forming galaxies probe
the reionization epoch, we evaluate the redshift-dependent ratio
$\Psi(z)=(1+z)^{\alpha}$ of the GRB rate to star formation rate (SFR). We found
a modest evolution $-0.2\leq \alpha \leq 0.5$ consistent with Swift GRB
afterglow plateau in the redshift range $0.99<z<9.4$.
