Oh, and as for the model used, Cox multifactorial analysis is fine, except they forgot to add an unknown member to the parameter set. Without it, this cannot measure unknown unknowns and you cannot say if the analysis makes sense. If unknown covariate has higher hazard ratio than known covariate, something is off. Another way to validate is to calculate goodness of fit for each covariate.

The strong assumption in Cox model is that hazards are independent constant multiplicative which might not be true at all. (Such as limited detoxication capacities or hazards varying over time, or hazard clusters, or synergy between hazards. These are all examples of nonlinearities.)

In case anyone wants a primer: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2394368/

FAMD and MFA would show whether the simple nonparametric linear constant hazard model holds between paired variables.