Abstract:

Marginal structural models (MSMs) are a very useful tool to estimate the effect of timedependent treatments in longitudinal studies in the presence of confounders that are also affected by previous treatments. These models appropriately adjust for these covariates 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 and also yield very unstable estimates if the predicted probabilities of treatment are very close to zero, which is often the case in practice. To address these problems, instead of modeling the probabilities of treatment, we take a designbased approach and solve a convex optimization problem to directly find the weights of minimum variance that adjust for the covariates across all possible treatment histories. We conduct a simulation study to show the performance of this approach, and find that the proposed weights provide less biased and more precise estimates than other standard methods.
