Confidence Bands for Survival Functions with Censored Data: A Comparative Study

Consider the problem of obtaining simultaneous confidence bands for the survival function S(x) when the data are arbitrarily right censored. 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). It is compared with the censored versions of the Kolmogorov band and the Rényi 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. The bands are illustrated by applying them to data from a mechanical-switch life test.