Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weighting for survival data

Stat Med. 2005 Oct 30;24(20):3089-110. doi: 10.1002/sim.2174.


Estimation and group comparison of survival curves are two very common issues in survival analysis. In practice, the Kaplan-Meier estimates of survival functions may be biased due to unbalanced distribution of confounders. Here we develop an adjusted Kaplan-Meier estimator (AKME) to reduce confounding effects using inverse probability of treatment weighting (IPTW). Each observation is weighted by its inverse probability of being in a certain group. The AKME is shown to be a consistent estimate of the survival function, and the variance of the AKME is derived. A weighted log-rank test is proposed for comparing group differences of survival functions. Simulation studies are used to illustrate the performance of AKME and the weighted log-rank test. The method proposed here outperforms the Kaplan-Meier estimate, and it does better than or as well as other estimators based on stratification. The AKME and the weighted log-rank test are applied to two real examples: one is the study of times to reinfection of sexually transmitted diseases, and the other is the primary biliary cirrhosis (PBC) study.

Publication types

  • Comparative Study

MeSH terms

  • Adult
  • Aged
  • Black People
  • Chlamydia Infections / epidemiology
  • Computer Simulation
  • Data Interpretation, Statistical*
  • Female
  • Gonorrhea / epidemiology
  • Humans
  • Likelihood Functions
  • Liver Cirrhosis, Biliary / drug therapy
  • Male
  • Middle Aged
  • Monte Carlo Method
  • Penicillamine / therapeutic use
  • Randomized Controlled Trials as Topic
  • Sex Factors
  • Survival Analysis*
  • White People


  • Penicillamine