  JWST is uncovering the properties of ever increasing numbers of galaxies at
z>6, during the epoch of reionization. Connecting these observed populations to
the process of reionization requires understanding how efficiently they produce
Lyman continuum (LyC) photons and what fraction (fesc) of these photons escape
into the intergalactic medium. By applying the Cox proportional hazards model,
a survival analysis technique, to the Low-redshift Lyman Continuum Survey
(LzLCS), we develop new, empirical, multivariate predictions for fesc. The
models developed from the LzLCS reproduce the observed fesc for z~3 samples,
which suggests that LyC emitters may share similar properties at low and high
redshift. Our best-performing models for the z~3 galaxies include information
about dust attenuation, ionization, and/or morphology. We then apply these
models to z$\gtrsim$6 galaxies. For large photometric samples, we find a median
predicted fesc=0.047-0.14. For smaller spectroscopic samples, which may include
stronger emission line galaxies, we find that $\geq$33% of the galaxies have
fesc >0.2, and we identify several candidate extreme leakers with fesc
$\geq$0.5. The current samples show no strong trend between predicted fesc and
UV magnitude, but limited spectroscopic information makes this result
uncertain. Multivariate predictions can give significantly different results
from single variable predictions, and the predicted fesc for high-redshift
galaxies can differ significantly depending on whether star formation rate
surface density or radius is used as a measure of galaxy morphology. We provide
all parameters necessary to predict fesc for additional samples of
high-redshift galaxies using these models.
