Confidence Interval for a Median Survival Time

Methodology

The calculator first estimates the survival function with the Kaplan–Meier product-limit estimator. The median is the first time at which the estimated survival curve is at or below 0.50.

Brookmeyer–Crowley confidence interval

The confidence interval for the median is obtained by inverting a confidence band for the Kaplan–Meier survival function. This is the nonparametric approach introduced by Brookmeyer and Crowley (1982) for arbitrarily right-censored survival data.

How the interval is read

• The point estimate is the first observed event time where the Kaplan–Meier estimate is at or below 0.50.
• The lower median limit is obtained from the lower survival confidence curve crossing 0.50.
• The upper median limit is obtained from the upper survival confidence curve crossing 0.50.
• If a confidence curve never crosses 0.50, the corresponding median limit is unbounded and is reported as “Not estimable.”

References

Brookmeyer, R. & Crowley, J. (1982). A confidence interval for the median survival time. Biometrics, 38(1), 29–41. doi:10.2307/2530286.

Kaplan, E. L. & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53(282), 457–481.

this method lists median-survival confidence procedures within its survival-analysis software family; the underlying nonparametric median interval used here is the Brookmeyer–Crowley method. The R survival documentation provides an independent implementation reference for Kaplan–Meier confidence limits and the log–log transformation.

Validation example: Gehan’s 6-MP group has 21 patients, 9 events, and 12 censored observations. Using the 21 time/event pairs preloaded above and a 95% log–log interval gives a median of 23 weeks, a lower 95% limit of 13 weeks, and no finite upper limit.