Statistical Methods for Assessing Time-varying Causal Effects: Novel Estimands and Inference

Abstract

The rapid advancements in wearable technologies and smartphone-based mobile health (mHealth) interventions have revolutionized the field of personalized interventions across various domains of health sciences. An innovative experimental design called the micro-randomized trial (MRT) has emerged to evaluate the effectiveness of mHealth intervention components. In MRTs, individuals are randomized hundreds or thousands of times, to receive treatment interventions. This paradigm shift in trial design has led to the development of a novel class of causal estimands called “causal excursion effects”, which provide insights into intervention effectiveness and its temporal dynamics, as well as the moderation effects of various factors. To analyze these causal excursion effects, semiparametric inference methods, such as the weighted, centered least squares (WCLS) criterion, are employed.

This dissertation advanced the statistical analysis tools for assessing intervention effects in the context of time-varying treatments and repeated outcomes. The primary objective is to extend and improve the WCLS criterion, resulting in more relevant, valid, and precise estimations for complex scenarios.

In Chapter II, we present a set of novel estimands for causal excursion effects in the context of binary outcomes, complemented by identification results based on a cluster-based conceptualization of potential outcomes. The motivation for this chapter stems from the recognition that existing definitions and methods in causal analysis assume between-subject independence and non-interference, which may not hold in interventional mHealth studies involving clusters of subjects. To address these limitations, we propose an inferential method that effectively handles within-cluster interference, accounts for the cluster-level treatment heterogeneity, allows treatment probabilities to depend on joint cluster-level history, and ensures consistent point estimation and uncertainty quantification.

In Chapter III, we introduce a method for improving the precision of causal excursion effect estimation by incorporating auxiliary variables, which extends the covariate adjustment approach beyond single-time-point treatment to a sequence of time-varying treatments. We introduce a general method called “A2-WCLS” that incorporates auxiliary variable adjustment into the WCLS framework. Under mild conditions, this method yields a consistent and asymptotically more efficient estimate of the moderated causal excursion effect compared to existing inferential methods.

In Chapter IV, we take a meta-learner perspective and propose two inferential procedures that enhance the efficiency and robustness of the causal excursion effect estimator. Current data analysis methods for estimating causal excursion effects require pre-specified features of the observed high-dimensional history to construct a working model of an important nuisance parameter, which is a non-trivial task. To overcome this challenge, we integrate the Debiased/Double Machine Learning (DML) framework into the inferential process, enabling the analyst to effectively handle high-dimensional history information while remaining agnostic about the choice of supervised learning algorithms used for estimating nuisance parameters. In this chapter, we establish the asymptotic properties of the proposed estimators and demonstrate their relative efficiency gains over the existing approach through extensive simulation experiments.