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Abstract:
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In longitudinal studies, marginal structural models (MSM) are widely used to estimate the effect of time-dependent treatments in the presence of time-dependent confounders. Under a sequential ignorability assumption, MSM yield unbiased treatment effect estimates by weighing each observation by the inverse of the probability of the observed treatment given the history of observed covariates. However, these probabilities are typically estimated by fitting a model and the resulting weights can fail to adjust for observed covariates due to model misspecification. Also, these weights tend to yield very unstable estimates if the predicted probabilities are close to zero. To address these problems, instead of modeling the probabilities of treatment, we take a design-based approach and directly find the weights of minimum variance that adjust for the covariates across all possible treatment histories. For this, we analyze the role of weighting in longitudinal studies of treatment effects and pose a convex optimization problem that we can solve efficiently. In a simulation study we show that this approach outperforms standard methods, providing less biased and more precise effect estimates.
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