Uniqueness of permuted treatment estimator distributions in the proportional hazards model

We discuss findings regarding the permutation distributions of treatment effect estimators in the proportional hazards model. For fixed sample size n, we will prove that all uncensored and untied event times yield the same permutation distribution of treatment effect estimators in the proportional hazards model. In other words this distribution is irrelevant with respect to the actual event times. We will show several uniqueness properties under different conditions. These properties are useful for small sample permutation tests and also helpful to large sample cases.