title: Adjusted Kaplan-Meier estimator and log-rank test with inverse probability of treatment weighting for survival data.
abstract: 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.
authors.affiliation: Department of Statistics, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067, USA. junxie@stat.purdue.edu
authors.forename: Jun
authors.initials: J
authors.lastname: Xie
authors.forename: Chaofeng
authors.initials: C
authors.lastname: Liu
mesh_terms: D000328:Adult; D000368:Aged; D044383:Black People; D002690:Chlamydia Infections / Q000453:epidemiology; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D005260:Female; D006069:Gonorrhea / Q000453:epidemiology; D006801:Humans; D016013:Likelihood Functions; D008105:Liver Cirrhosis, Biliary / Q000188:drug therapy; D008297:Male; D008875:Middle Aged; D009010:Monte Carlo Method; D010396:Penicillamine / Q000627:therapeutic use; D016032:Randomized Controlled Trials as Topic; D012737:Sex Factors; D016019:Survival Analysis; D044465:White People
chemical_list: D010396:Penicillamine