arXiv subjects
Publications and source records attributed to Haben Michael.
Meta-analyses are often based on too few studies to justify the asymptotic methods underlying the statistical procedures applied to them. We consider higher-order asymptotics as a remedy. We derive the Bartlett correction for the idealized Gaussian case, correcting the formula currently appearing in the literature.
Robins 1997 introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. In his work, identification of MSM parameters is established under a sequential randomization assumption (SRA), which rules out unmeasured confounding of treatment assignment over time. We consider sufficient conditions for identification of the parameters of a subclass, Marginal Structural Mean Models (MSMMs), when sequential randomization fails to hold due to unmeasured confounding, using instead a time-varying instrumental variable. Our identification conditions require that no unobserved confounder predicts compliance type for the time-varying treatment. We describe a simple weighted estimator and examine its finite-sample properties in a simulation study. We apply the proposed estimator to examine the effect of delivery hospital on neonatal survival probability.
Robins (1998) introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding. He established identification of MSM parameters under a sequential randomization assumption (SRA), which essentially rules out unmeasured confounding of treatment assignment over time. In this technical report, we consider sufficient conditions for identification of MSM parameters with the aid of a time-varying instrumental variable, when sequential randomization fails to hold due to unmeasured confounding. Our identification conditions essentially require that no unobserved confounder predicts compliance type for the time-varying treatment, the longitudinal generalization of the identifying condition of Wang and Tchetgen Tchetgen (2018). Under this assumption, We derive a large class of semiparametric estimators that extends standard inverse-probability weighting (IPW), the most popular approach for estimating MSMs under SRA, by incorporating the time-varying IV through a modified set of weights. The set of influence functions for MSM parameters is derived under a semiparametric model with sole restriction on observed data distribution given by the MSM, and is shown to provide a rich class of multiply robust estimators, including a local semiparametric efficient estimator.