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Adjusted Kaplan–Meier estimator and log‐rank test with inverse probability of treatment weighting for survival data
Author(s) -
Xie Jun,
Liu Chaofeng
Publication year - 2005
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.2174
Subject(s) - statistics , kaplan–meier estimator , mathematics , inverse probability , estimator , inverse probability weighting , survival analysis , survival function , log rank test , weighting , proportional hazards model , confounding , censoring (clinical trials) , econometrics , medicine , bayesian probability , posterior probability , radiology
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. Copyright © 2005 John Wiley & Sons, Ltd.