title: Simultaneous inferences on the contrast of two hazard functions with censored observations.
abstract: In survival analysis, often times the pattern of instantaneous risk over time is more interesting than that of the cumulative risk. For this case, a nonparametric hazard function estimate is more appropriate for summarizing the risk experience of a group of patients than the corresponding Kaplan-Meier estimate. In comparing a new treatment with a standard therapy, it is important to know if the treatment loses it potency during the follow-up period, and if it does, one would like to know when it becomes ineffective. Unfortunately, with a plot of the differences of two Kaplan-Meier curves, it is rather difficult to capture such temporal trends. In this article, we propose simple procedures for constructing confidence bands for the contrast of two hazard functions with censored data. The simultaneous interval estimates are quite useful for identifying possible values of the contrast over time with a certain degree of confidence. The new proposals are illustrated with an example and a small simulation study.
authors.affiliation: Fred Hutchinson Cancer Research Center and Department of Biostatistics, University of Washington, Seattle, Washington 98109, USA. pgilbert@scharp.org
authors.forename: Peter B
authors.initials: PB
authors.lastname: Gilbert
authors.forename: L J
authors.initials: LJ
authors.lastname: Wei
authors.forename: Michael R
authors.initials: MR
authors.lastname: Kosorok
authors.forename: John D
authors.initials: JD
authors.lastname: Clemens
mesh_terms: D000328:Adult; D001459:Bangladesh; D001699:Biometry / Q000379:methods*; D002648:Child; D002771:Cholera / Q000517:prevention & control; D022121:Cholera Vaccines / Q000276:immunology; D003198:Computer Simulation; D016001:Confidence Intervals; D005260:Female; D006801:Humans; D016016:Proportional Hazards Models; D016019:Survival Analysis
chemical_list: D022121:Cholera Vaccines