  To understand how galaxies reionized the universe, we must determine how the
escape fraction of Lyman Continuum (LyC) photons (fesc) depends on galaxy
properties. Using the z~0.3 Low-redshift Lyman Continuum Survey (LzLCS), we
develop and analyze new multivariate predictors of fesc. These predictions use
the Cox proportional hazards model, a survival analysis technique that
incorporates both detections and upper limits. Our best model predicts the
LzLCS fesc detections with a root-mean-square (RMS) scatter of 0.31 dex, better
than single-variable correlations. According to ranking techniques, the most
important predictors of fesc are the equivalent width (EW) of Lyman-series
absorption lines and the UV dust attenuation, which track line-of-sight
absorption due to HI and dust. The HI absorption EW is uniquely crucial for
predicting fesc for the strongest LyC emitters, which show properties similar
to weaker LyC emitters and whose high fesc may therefore result from favorable
orientation. In the absence of HI information, star formation rate surface
density ($\Sigma_{\rm SFR}$) and [O III]/[O II] ratio are the most predictive
variables and highlight the connection between feedback and fesc. We generate a
model suitable for z>6, which uses only the UV slope, $\Sigma_{\rm SFR}$, and
[O III]/[O II]. We find that $\Sigma_{\rm SFR}$ is more important in predicting
fesc at higher stellar masses, whereas [O III]/[O II] plays a greater role at
lower masses. We also analyze predictions for other parameters, such as the
ionizing-to-non ionizing flux ratio and Ly=alpha escape fraction. These
multivariate models represent a promising tool for predicting fesc at high
redshift.
