  Current estimates of the normalized accretion rates of quasars (L/L_Edd),
rely on measuring the velocity widths of broad optical-UV emission lines (e.g.,
H$\beta$ and Mg II $\lambda2800$). However, such lines tend to be weak or
inaccessible in the most distant quasars, leading to increasing uncertainty in
L/L_Edd estimates at $z > 6$. Utilizing a carefully selected sample of 53
radio-quiet quasars that have H$\beta$ and C IV $\lambda1549$ spectroscopy as
well as {\sl Chandra} coverage, we searched for a robust accretion-rate
indicator for quasars, particularly at the highest-accessible redshifts ($z
\sim 6-7$). Our analysis explored relationships between the H$\beta$-based
L/L_Edd, the equivalent width (EW) of C IV, and the optical-to-X-ray spectral
slope (a_ox). Our results show that EW(C IV) is the strongest indicator of the
H$\beta$-based L/L_Edd parameter, consistent with previous studies, although
significant scatter persists particularly for sources with weak C IV lines. We
do not find evidence for the a_ox parameter improving this relation, and we do
not find a significant correlation between a_ox and H$\beta$-based L/L_Edd.
This absence of an improved relationship may reveal a limitation in our sample.
X-ray observations of additional luminous sources, found at $z \gtrsim 1$, may
allow us to mitigate the biases inherent in our archival sample and test
whether X-ray data could improve L/L_Edd estimates. Furthermore, deeper X-ray
observations of our sources may provide accurate measurements of the hard-X-ray
power-law photon index ($\Gamma$), which is considered an unbiased L/L_Edd
indicator. Correlations between EW(C IV) and a_ox with $\Gamma$-based L/L_Edd
may yield a more robust prediction of a quasar normalized accretion rate.
