Statistics and Its Interface

Volume 7 (2014)

Number 1

We dedicate this special issue to Dr. Gang Zheng, a great colleague and dear friend to many of us.

Estimation of the relative risk following group sequential procedure based upon the weighted log-rank statistic

Pages: 27 – 42



Grant Izmirlian (Biometry Research Group, Division of Cancer Prevention, National Cancer Institute, Bethesda, Maryland, U.S.A.)


This paper considers a group sequentially monitored trial on a survival endpoint, monitored using a weighted log-rank (WLR) statistic with bounded weight function. Results and discussion center on the theoretical and practical concerns encountered in this setting. We demonstrate the construction of Lan Demets boundaries and calculation of design adjusted p-values and confidence intervals. Central to this discussion is a bijection which exists between the weighted log-rank statistic and a weighted averaged logged relative risk which is shown to exist when there is no sign change in the weighting function. We also show under parametric assumptions that the bijection can be estimated at each interim analysis. The results are benchmarked in a simulation study and a section is devoted to the decisions made in applying the methods to monitoring in the the National Lung Screening Trial (NLST).


weighted log-rank statistic, group sequential, interim analysis, estimation

2010 Mathematics Subject Classification

Primary 62L12. Secondary 62N02.

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