Repeated confidence intervals for the median survival time

SUMMARY We describe methods for the construction of a confidence interval for median survival time based on right-censored data. These methods are extended to the construction of repeated confidence intervals for the median, based on accumulating data; here, the overall probability that all intervals contain the true median is guaranteed at a fixed level. The use of repeated confidence intervals for median survival time in post- marketing surveillance is discussed. A confidence interval for median survival time provides a useful summary of the survival experience of a group of patients. If confidence intervals are calculated repeatedly, as data accumulates, the probability that at least one interval fails to contain the median may be much higher than the error rate for a single interval, and if these confidence intervals are used in a decision making process the probability of an incorrect decision increases accordingly. Jennison & Turnbull (1984) have proposed methods for calculating repeated confidence intervals appropriate to such situations. Similar ideas have also been discussed by Lai (1984). In ? 2 we propose a new form of single-sample nonparametric confidence interval; this interval has asymptotically correct coverage probability and Monte Carlo simulations suggest it is superior to its competitors for small sample sizes. Repeated confidence intervals for the median are presented in ? 3 and their stnall sample size performance is assessed by Monte Carlo simulation; an example of their use is given in ? 4. All the methods considered can easily be modified to give confidence intervals for other quantiles or for the survival probability at a fixed time.