  Gamma-ray bursts (GRBs), which have been observed up to redshifts z approx
9.5 can be good probes of the early universe and have the potential of testing
cosmological models. The analysis by Dainotti of GRB Swift afterglow
lightcurves with known redshifts and definite X-ray plateau shows an
anti-correlation between the rest frame time when the plateau ends (the plateau
end time) and the calculated luminosity at that time (or approximately an
anti-correlation between plateau duration and luminosity). We present here an
update of this correlation with a larger data sample of 101 GRBs with good
lightcurves. Since some of this correlation could result from the redshift
dependences of these intrinsic parameters, namely their cosmological evolution
we use the Efron-Petrosian method to reveal the intrinsic nature of this
correlation. We find that a substantial part of the correlation is intrinsic
and describe how we recover it and how this can be used to constrain physical
models of the plateau emission, whose origin is still unknown. The present
result could help clarifing the debated issue about the nature of the plateau
emission.
