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Multiply robust estimators for causal effects of grace period treatment initiation strategies
Estimating the effect of treatment strategies from longitudinal observational data often requires g-methods, such as inverse probability weighting (IPW) or the iterative conditional expectation (ICE) g-formula. These estimators are singly robust in the sense that there is only one opportunity to get valid estimates. Multiply robust estimators that combine IPW and ICE offer more than one opportunity for valid estimation. This is important because some degree of model misspecification is almost always expected in practice. Though several multiply robust estimators exist, they have never been applied to grace period initiation strategies that are better aligned with real world decision making, and it is unclear whether the increased complexity of these methods is worthwhile. Via simulation studies we show that multiply robust estimators confer more protection against model misspecification than singly robust estimators, and that certain multiply robust estimators offer more protection than others. We also compare these methods in an analysis of a large epidemiological study and provide guidelines for practitioners interested in implementing these methods in estimating the effect of grace period treatment initiation strategies on survival outcomes.