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Multiply Robust Estimation: The Development and Evaluation of a Novel Method for Causal Analysis


Correct model specification for confounding control is likely the most common assumption made in causal inference. Yet the validity of this assumption cannot be verified using data or statistical tests. Typically, investigators collect as much data on confounders as possible and then consider multiple models singly. This is a tedious process, thus making multiply robust estimation, an extension of doubly robust estimation, particularly appealing as it affords investigators with more than two chances to specify a correct model within a union model, obviating multiple results presentation. This dissertation introduces a multiply robust approach that combines three or more estimators in one union model, yielding unbiased effect estimates provided at least one of the estimators is correctly specified, no new bias is introduced, and there is no uncontrolled confounding. This dissertation focuses on the development and evaluation of multiply robust estimation in single and multilevel models and in the presence of effect modification and interaction. Monte Carlo simulations are used to assess performance and present a proof of concept, and illustrative examples based on global health data will be used to demonstrate applications of the MR estimation method. A framework for doubly and multiply robust estimators is also presented using directed acyclic graphs to show how multiple adjustment schemes can be combined to yield a consistent effect estimate. Interpretation of doubly robust and multiply robust estimates is also discussed, and it is proposed that a partial-marginal and partial-conditional framework for interpretation is necessary. Results showed that effect estimates for the exposure(s) of interest obtained using MR estimation had higher chances of being valid, or robust to misspecification, whenever at least one of the underlying estimators was not misspecified. This approach allows investigators who disagree about appropriate covariate adjustment schemes to merge their views and obtain a single set of results without forcing them to agree on one model. Although the assumption of correct model specification cannot be verified, multiply robust estimation nevertheless pools opportunities by specifying more than two estimators in one union model in an attempt to hedge a bet on consistently getting a valid effect estimate.

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