Likelihood Ratio-Based Confidence Bands for Survival Functions

Abstract

Thomas and Grunkemeier introduced a nonparametric likelihood ratio approach to confidence interval estimation of survival probabilities based on right-censored data. We construct simultaneous confidence bands using this approach. The boundaries of the bands are contained within [0, 1]. A procedure essentially equivalent to a bias correction is developed. The resulting increase in coverage accuracy is illustrated by an example and a simulation study. We look at various versions of log-likelihood ratio-based confidence bands and compare them to the Hall-Wellner band and Nair's equal precision band. We also construct likelihood ratio-based bands for cumulative hazard functions.

Key Words:

• Bias correction
• Cumulative hazard rate
• Kaplan-Meier estimator
• Likelihood ratio statistic