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Estimation of median survival and its 95% confidence interval depends on the choice of the survival function, standard error, and a method for constructing the confidence interval. This paper outlines several available possibilities in SAS® (version 9.4) PROC LIFETEST and compares them on theoretical grounds and using simulated data, with criteria: ability to estimate the 95% CI, coverage probability, interval width, and appropriateness for practical use. Data are generated with varying hazard patterns, N, % censoring, and censoring patterns (early, uniform, late, last visit). LIFETEST was run using the Kaplan-Meier and Nelson-Aalen estimators and the transformations available (linear, log, logit, complementary log-log, and arcsine square root). Using the Kaplan-Meier estimator with the logarithmic transformation as well as with the logit leads to a high frequency of LIFETEST not being able to estimate the 95% CI. The combination of Kaplan-Meier with the linear transformation is associated with poor coverage achieved. For small samples, late/last visit censoring has a negative effect on being able to estimate the 95% CI. Heavy early censoring can lead to low coverage of the 95% CI of median survival for sample sizes up to and including N  = 40. The two combinations that are optimal for being able to estimate the 95% CI and having adequate coverage are the Kaplan-Meier estimator with complementary log-log transformation, and the Nelson-Aalen estimator with linear transformation. The former fares best on the third criterion (smaller width) and is also the SAS® default and validates the choice of default.

The paper provides computations comparing the accuracy of the saddlepoint approximation approach and the normal approximation method in approximating the mid-p-value of Wilcoxon and log-rank tests for the left-truncated data using a truncated binomial design. The paper uses real data examples to apply the comparison, along with some simulated studies. Confidence intervals are provided by the inversion of the tests under consideration.