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Biometrika 1999 86(1):45-57; doi:10.1093/biomet/86.1.45
© 1999 by Biometrika Trust
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Monitoring a general class of two-sample survival statistics with applications

M GuA1, D FollmannA2,Z and NL GellerA2,ZZ

A1 Department of Statistics, The Chinese University of Hong Kong, New Territory, Hong Kong, PRC minggao@cuhk.edu.hk A2 Office of Biostatistics Research, National Heart Lung and Blood Institute, 2 Rockledge Center, Bethesda Maryland 20892-7938, USA Z follmann@helix.nih.gov ZZ ng@helix.nih.gov

This paper considers a general class of statistics for testing the equality of two survival distributions in clinical trials with sequential monitoring. The tests can be expressed as Lebesgue-Stieltjes integrals of a weight function with respect to the difference between two survival distributions. Prominent members of this class include the two-sample difference in Kaplan-Meier estimates, the test of medians (Brookmeyer & Crowley, 1982), a truncated version of Efron's (1967) test and the Pepe-Fleming statistic (Pepe & Fleming, 1989, 1991). Statistics in this class are shown to converge to a Gaussian process, indexed by information time, under both null and local alternatives even if different statistics are used at different information times. Properly standardised, statistics in a subclass converge to Gaussian processes with independent increments so that the usual group sequential techniques for monitoring a clinical trial can be applied. The design of a trial comparing two treatments with respect to mother-to-newborn transmission of HIV is used to illustrate practical aspects of monitoring.

Keywords:Clinical trial; Failure time data; Group sequential monitoring; Pepe-Fleming statistic.


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