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 (f _esc) 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 f _esc. The models developed from the LzLCS reproduce the observed f _esc 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 ≳ 6 galaxies. For large photometric samples, we find a median predicted f _esc = 0.047–0.14. For smaller spectroscopic samples, which may include stronger emission-line galaxies, we find that ≥33% of the galaxies have f _esc > 0.2, and we identify several candidate extreme leakers with f _esc ≥ 0.5. The current samples show no strong trend between predicted f _esc 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 f _esc 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 f _esc for additional samples of high-redshift galaxies using these models. ^* Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs GO-15626, GO-13744, GO-14635, GO-15341, and GO-15639.