Lifetime Data Analysis

, Volume 24, Issue 3, pp 509–531 | Cite as

Two-sample tests for survival data from observational studies

  • Chenxi Li


When observational data are used to compare treatment-specific survivals, regular two-sample tests, such as the log-rank test, need to be adjusted for the imbalance between treatments with respect to baseline covariate distributions. Besides, the standard assumption that survival time and censoring time are conditionally independent given the treatment, required for the regular two-sample tests, may not be realistic in observational studies. Moreover, treatment-specific hazards are often non-proportional, resulting in small power for the log-rank test. In this paper, we propose a set of adjusted weighted log-rank tests and their supremum versions by inverse probability of treatment and censoring weighting to compare treatment-specific survivals based on data from observational studies. These tests are proven to be asymptotically correct. Simulation studies show that with realistic sample sizes and censoring rates, the proposed tests have the desired Type I error probabilities and are more powerful than the adjusted log-rank test when the treatment-specific hazards differ in non-proportional ways. A real data example illustrates the practical utility of the new methods.


Inverse probability of treatment weighting Inverse probability of censoring weighting Weighted log-rank tests Renyi-type tests 



This work was partially supported by National Institute of Dental and Craniofacial Research Grant 1R03DE023889. The kidney transplant data used here have been supplied by the Minneapolis Medical Research Foundation (MMRF) as the contractor for the Scientific Registry of Transplant Recipients (SRTR). The interpretation and reporting of these data are the responsibility of the author and in no way should be seen as an official policy of or interpretation by the SRTR or the U.S. Government.


  1. Fleming TR, Harrington DP (1981) A class of hypothesis tests for one and two sample censored survival data. Commun Stat Theory Methods 10(8):763–794MathSciNetCrossRefzbMATHGoogle Scholar
  2. Fleming TR, Harrington DP (1991) Counting processes and survival analysis. Wiley, New YorkzbMATHGoogle Scholar
  3. Gill R (1980) Censoring and stochastic integrals. Mathematical Centre Tracts, Mathematisch Centrum.
  4. Prentice RL (1978) Linear rank tests with right censored data. Biometrika 65(1):167–179. doi: 10.1093/biomet/65.1.167,,
  5. Schaubel DE, Wei G (2011) Double inverse-weighted estimation of cumulative treatment effects under nonproportional hazards and dependent censoring. Biometrics 67(1):29–38. doi: 10.1111/j.1541-0420.2010.01449.x MathSciNetCrossRefzbMATHGoogle Scholar
  6. Tsiatis A (2006) Semiparametric theory and missing data. Springer, BerlinzbMATHGoogle Scholar
  7. van der Vaart AW, Wellner JA (1996) Weak convergence and empirical processes. Springer, BerlinCrossRefzbMATHGoogle Scholar
  8. Xie J, Liu C (2005) Adjusted Kaplan–Meier estimator and log-rank test with inverse probability of treatment weighting for survival data. Stat Med 24(20):3089–3110. doi: 10.1002/sim.2174 MathSciNetCrossRefGoogle Scholar
  9. Zhang M, Schaubel DE (2012) Double-robust semiparametric estimator for differences in restricted mean lifetimes in observational studies. Biometrics 68(4):999–1009. doi: 10.1111/j.1541-0420.2012.01759.x MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Epidemiology and BiostatisticsMichigan State UniversityEast LansingUSA

Personalised recommendations