Confidence bands for survival functions with censored data: A comparative study.

Consider the problem of obtaining simultaneous confidence bands for the survival functions when the data are arbitrarily right censored. We show that the usual pointwise confidence intervals based on Greenwood's variance formula can be adapted to yield a large-sample confidence band. This band has, in a certain sense, equal precision at each point of S(x). We compare it was the censored versions of the Kolmogorov band and the Renyi band. The comparisons are made in terms of the widths and the adequacy of large-sample approximations, and are carried out under various censoring models and degrees of censoring.