Symmetric tests and confidence intervals for survival probabilities and quantiles of censored survival data

We describe existing tests and introduce two new tests concerning the value of a survival function. These tests may be used to construct a confidence interval for the survival probability at a given time or for a quantile of the survival distribution. Simulation studies show that error rates can differ substantially from their nominal values, particularly at survival probabilities close to zero or one. We recommend our new constrained bootstrap test for its good overall performance.