Two Simulation Methods for Constructing Confidence Bands Under the Additive Risk Model

Abstract

With right-censored failure time data, we propose procedures to construct simultaneous confidence bands for the survival curve of a given subject under the additive risk model. The distribution of the subject–specific cumulative hazard function can be approximated with a zero-mean Gaussian process, which can be generated through simulation methods. We propose two different simulation schemes to obtain the distribution of the supremum of the cumulative hazard process over the entire time range. The two simulation approaches are asymptotically equivalent, whereas the numerical forms are different. We construct two types of confidence bands, namely the equal precision band and the Hall–Wellner type band, through choosing suitable weight functions. Monte Carlo simulation studies show that both of the proposed confidence bands are appropriate for finite sample sizes. We illustrate the new proposal with a real example.

Key Words:

• Confidence band
• Estimating equation
• Failure time data
• Proportional hazards

Acknowledgments

We thank the editor and two referees for their critical reading of the manuscript and constructive comments, which led to great improvement of the earlier version. We also thank Dr. Karen Moller for providing the VIN III data set.