Lifetime Data Analysis

, Volume 11, Issue 1, pp 117–129 | Cite as

Pair Chart Test for an Early Survival Difference



The log-rank test is commonly used in comparing survival distributions between treatment and control groups in clinical trials. However, in many studies, the treatment is only effective at the early stage of the trial. Especially when the two survival curves cross, the log-rank test has a low statistical power to show the survival difference. We propose a test statistic for detecting such an early difference between the two treatment arms. The new test has an intuitive geometric interpretation based on a pair chart and is shown to have more power than the log-rank test when the treatment effect only appears in the early phase of the study. This advantage is evaluated for finite sample sizes in simulation studies. Finally, the proposed method is illustrated with a real data example of patients with gastric cancer.


early treatment effect log-rank test pair chart statistic survival comparison 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Agung, I. N., Sen, P. K. 1982“The generalized pair chart for right-censored observations”Calcutta Statistical Association Bulletin311325Google Scholar
  2. B. Efron, “The two-sample problem with censored data”, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability vol. 4 pp. 831–853, 1967.Google Scholar
  3. Fleming, T. R., Harrington, D. P., O’Sullivan, M. 1987“Supremum versions of the log-rank and generalized Wilcoxon statistics”Journal of the American Statistical Association82312320Google Scholar
  4. Fleming, T. R., Harrington, D. P. 1991Counting Processes and Survival AnalysisWileyNew YorkGoogle Scholar
  5. Gill, R. D. 1990Censoring and Stochastic Integrals, Mathematical Centre Tracts 124Mathematisch CentrumAmsterdamGoogle Scholar
  6. Harrington, D. P., Fleming, T. R. 1982“A class of rank test procedures for censored survival data”Biometrika69553566Google Scholar
  7. Kaplan, E. L., Meier, P. 1958“Non-parametric estimation from incomplete observations”Journal of the American Statistical Association53457481Google Scholar
  8. Moreau, T., O’Quigley, J., Mesbah, M. 1985“A global goodness-of-fit statistic for the proportional hazards model”Applied Statistics34212218Google Scholar
  9. Quade, D. 1973“The pair chart”Statistica Neerlandica272945Google Scholar
  10. Wu, L., Gilbert, P. 2002“Flexible weighted log-rank tests optimal for detecting early and/or late survival differences”Biometrics589971004Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Department of Biostatistics, M. D. Anderson Cancer CenterThe University of TexasUSA
  2. 2.Department of BiostatisticsUniversity of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations