Presented By: Department of Statistics Dissertation Defenses
Robust Methods for Causal Inference and Policy Learning with Applications to Mobile Health
Easton Huch
This dissertation comprises three essays that develop robust methods for causal effect estimation and policy learning, especially in the context of micro-randomized trials (MRTs)—a longitudinal experimental design used in mobile health (mHealth).
The first essay develops methods for integrating data across multiple MRTs for the purpose of causal effect estimation. Compared to a single-study analysis, the methods produce increased statistical efficiency by borrowing information across related studies. Methodologically, we relate the studies by assuming that certain conditional causal effects are equal across studies; then we estimate these effects and appropriately average them to target prespecified marginal estimands.
Whereas the first essay develops methods for integrating data across MRTs that have already been implemented, the second essay introduces the robust mixed-effects (RoME) algorithm for optimizing treatment policies during an MRT. RoME is a contextual bandit algorithm that makes use of mixed-effects modeling, network cohesion penalties, doubly robust estimators, and double/debiased machine learning (DML) to address the specific challenges of mHealth: treatment effect heterogeneity, cluster structure, nonstationarity, and nonlinear relationships. We establish a high-probability regret bound that depends solely on the dimension of the differential-reward model, enabling strong regret bounds even when the baseline reward is highly complex.
The third essay steps back from the MRT setting and develops Bayesian Randomization Inference (BRI): a general framework for Bayesian estimation of treatment effects based principally on the physical act of randomization. BRI involves fixing the observed potential outcomes, positing a probabilistic model for the causal effects, and forming a likelihood based on the randomization distribution of a statistic. In many cases, BRI does not require specification of marginal outcome distributions, resulting in weaker assumptions compared to Bayesian superpopulation-based methods. We prove several theoretical properties for BRI, including a Bernstein–von Mises theorem and large-sample properties of posterior expectations.
The first essay develops methods for integrating data across multiple MRTs for the purpose of causal effect estimation. Compared to a single-study analysis, the methods produce increased statistical efficiency by borrowing information across related studies. Methodologically, we relate the studies by assuming that certain conditional causal effects are equal across studies; then we estimate these effects and appropriately average them to target prespecified marginal estimands.
Whereas the first essay develops methods for integrating data across MRTs that have already been implemented, the second essay introduces the robust mixed-effects (RoME) algorithm for optimizing treatment policies during an MRT. RoME is a contextual bandit algorithm that makes use of mixed-effects modeling, network cohesion penalties, doubly robust estimators, and double/debiased machine learning (DML) to address the specific challenges of mHealth: treatment effect heterogeneity, cluster structure, nonstationarity, and nonlinear relationships. We establish a high-probability regret bound that depends solely on the dimension of the differential-reward model, enabling strong regret bounds even when the baseline reward is highly complex.
The third essay steps back from the MRT setting and develops Bayesian Randomization Inference (BRI): a general framework for Bayesian estimation of treatment effects based principally on the physical act of randomization. BRI involves fixing the observed potential outcomes, positing a probabilistic model for the causal effects, and forming a likelihood based on the randomization distribution of a statistic. In many cases, BRI does not require specification of marginal outcome distributions, resulting in weaker assumptions compared to Bayesian superpopulation-based methods. We prove several theoretical properties for BRI, including a Bernstein–von Mises theorem and large-sample properties of posterior expectations.
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