Generalized Log-Rank Tests for Interval-Censored Failure Time Data

Abstract

Several non-parametric test procedures have been proposed for incomplete survival data: interval-censored failure time data. However, most of them have unknown asymptotic properties with heuristically derived and/or complicated variance estimation. This article presents a class of generalized log-rank tests for this type of survival data and establishes their asymptotics. The methods are evaluated using simulation studies and illustrated by a set of real data from a cancer study. Copyright 2005 Board of the Foundation of the Scandinavian Journal of Statistics..

Addressing post-transplant summer water stress in Pinus pinea and Quercus ilex seedlings

“…The generalized log-rank test results confirmed a statistically significant difference between treatments, which was more significant in stone pine (p<0.001, for both tests) than in holm oak (p<0.01 for the test of Zhao & Sun (2004), and p<0.01 for the test of Sun et al (2005)). Results show that mulching was not a significant predictor of survival once irrigation was applied.…”

“…In a first step, we estimated and represented the survival distribution of stone pine and holm oak seedlings in each treatment using a nonparametric maximum likelihood estimator (NPMLE), which is computed through the algorithm developed by Wellner & Zhan (1997). In a second step, we used two generalized log-rank tests developed for interval-censored failure time data to test the hypothesis of whether there was a significant treatment effect or not (Zhao & Sun 2004, Sun et al 2005. These two firsts steps of the survival analysis were implemented in SAS using the macros developed by So & Johnston (2010).…”

Nonparametric tests for left-truncated and interval-censored data

“…There exists a lot literature on interval-censored data associated with the extension of the Wilcoxon and log-rank tests, see for example, Fay, [14,15] Sun, [16] Fay and Shih, [17] Fang et al, [18] Zhao and Sun, [19] Sun et al [20] Other authors such as Fang et al [18] extended Pepe and Fleming's [9] test to continuous interval-censored data and derive the asymptotic distributions of the generalized test statistics, Petroni and Wolfe [21] considered a similar test where the survival times can only take on a finite number of values. Furthermore, Lim and Sun [22] proposed several nonparametric tests which are sensitive to nonproportional/nonmonotone alternatives.…”

Analysis of progression‐free survival in oncology trials: some common statistical issues

“…give a generalized formulation of the log rank test applicable to interval-censored data that provides a score statistic to test equality of survival [25]. While there is no means given for estimating an overall treatment effect such as the hazard ratio, at least a p-value can be obtained to assess the strength of evidence against the null.…”