  Factorial survival designs with right-censored observations are commonly
inferred by Cox regression and explained by means of hazard ratios. However, in
case of non-proportional hazards, their interpretation can become cumbersome;
especially for clinicians. We therefore offer an alternative: median survival
times are used to estimate treatment and interaction effects and null
hypotheses are formulated in contrasts of their population versions.
Permutation-based tests and confidence regions are proposed and shown to be
asymptotically valid. Their type-1 error control and power behavior are
investigated in extensive simulations, showing the new methods' wide
applicability. The latter is complemented by an illustrative data analysis.
