Width-scaled confidence bands for survival functions

Abstract

A popular simultaneous confidence band for survival functions is the equal precision band of Nair [1984. Confidence bands for survival functions with censored data: a comparative study. Technometrics 26, 265–275] This band is found by adjusting the level of Wald-type pointwise confidence intervals centered on the Kaplan–Meier estimator. The present paper develops a complementary method of adjusting pointwise confidence intervals to produce a simultaneous band. Our approach is to scale the width, rather than the level, of the pointwise confidence intervals. The resulting adjustment of the pointwise band, called a width-scaled band, provides an attractive alternative to the equal precision band. Empirical likelihood-based width-scaled bands are studied in the one- and two-sample censored data settings. An example with real data is included.