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Biometrics. 2011 Mar;67(1):29-38. doi: 10.1111/j.1541-0420.2010.01449.x.

Double inverse-weighted estimation of cumulative treatment effects under nonproportional hazards and dependent censoring.

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Department of Biostatistics, University of Michigan, Ann Arbor, Michigan 48109-2029, U.S.A. Amgen Inc., South San Francisco, California 94080, USA.


In medical studies of time-to-event data, nonproportional hazards and dependent censoring are very common issues when estimating the treatment effect. A traditional method for dealing with time-dependent treatment effects is to model the time-dependence parametrically. Limitations of this approach include the difficulty to verify the correctness of the specified functional form and the fact that, in the presence of a treatment effect that varies over time, investigators are usually interested in the cumulative as opposed to instantaneous treatment effect. In many applications, censoring time is not independent of event time. Therefore, we propose methods for estimating the cumulative treatment effect in the presence of nonproportional hazards and dependent censoring. Three measures are proposed, including the ratio of cumulative hazards, relative risk, and difference in restricted mean lifetime. For each measure, we propose a double inverse-weighted estimator, constructed by first using inverse probability of treatment weighting (IPTW) to balance the treatment-specific covariate distributions, then using inverse probability of censoring weighting (IPCW) to overcome the dependent censoring. The proposed estimators are shown to be consistent and asymptotically normal. We study their finite-sample properties through simulation. The proposed methods are used to compare kidney wait-list mortality by race.

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