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Simultaneous Inferences on the Contrast of Two Hazard Functions with Censored Observations
Author(s) -
Gilbert Peter B.,
Wei L. J.,
Kosorok Michael R.,
Clemens John D.
Publication year - 2002
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.0006-341x.2002.00773.x
Subject(s) - contrast (vision) , hazard , confidence interval , statistics , nonparametric statistics , hazard ratio , econometrics , proportional hazards model , survival analysis , mathematics , interval (graph theory) , function (biology) , computer science , artificial intelligence , chemistry , organic chemistry , combinatorics , evolutionary biology , biology
Summary. 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.