Estimation of median survival time and its 95% confidence interval using SAS PROC LIFETEST

ABSTRACT

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.

KEYWORDS:

• Survival analysis
• confidence interval
• median
• PROC LIFETEST

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