Enriching Society by Using Innovative Statistics to Address Non-adherence in Clinical Trials

Randomized controlled trials (RCTs) aim to estimate the effect of an intervention. When individuals adhere to their assigned intervention, the effects of randomization approximate the effects of the intervention. In the presence of noncompliance, assignment to the intervention may not approximate well the receipt of the intervention. Noncompliance is even more significant in pragmatic RCTs, where researchers do not control the administration of the intervention. Many methods have been developed to address noncompliance at the analysis stage of RCTs. Limited experimental designs have been developed to address noncompliance while the RCT is ongoing. Adaptive designs define possible study modifications at the design stage of a RCT. We propose an adaptive design to address noncompliance with multi-component intervention. We frame the design within the counterfactuals causal inference framework and describe both the design and analysis procedures for this design. Using simulations, we show that the proposed adaptive RCT results in a statistically valid procedure with shorter interval estimates, compared to trials that do not adjust for noncompliance. 

The difference-in-differences method estimates causal effects under unmeasured confounding, relying on the parallel trends assumption. Ye et al. (2023) relaxed this by introducing the bracketed trends assumption, requiring two control groups with negatively correlated outcome trends relative to the treatment group. While this enables partial identification of the average treatment effect on the treated, uncertainty accumulates over time, making the bounds overly conservative. Identifying feasible control groups also remains a challenge.
We address these issues by proposing an alternative bracketed trends assumption, requiring negative correlation over a period rather than at each step. We explore its relationship with the original assumption and establish sufficient conditions for the assumption to hold under a multi-factor interactive fixed effects model. Factor loadings guide the selection of control units, and we provide an asymptotically valid statistical inference procedure. We validate our approach through simulations and apply it to estimate the effect of the Election Day Registration policy on U.S. voter turnout.
 

Three critical issues for causal inference that often occur in modern, complicated experiments are interference, treatment nonadherence, and missing outcomes. A great deal of research efforts has been dedicated to developing causal inferential methodologies that address these issues separately. However, methodologies that can address these issues simultaneously are lacking. We propose a Bayesian causal inference methodology to address this gap. Our methodology extends existing causal frameworks and methods, specifically, two-staged randomized experiments and the principal stratification framework. In contrast to existing methods that invoke strong structural assumptions to identify principal causal effects, our Bayesian approach uses flexible distributional models that can accommodate the complexities of interference and missing outcomes, and that ensure that principal causal effects are weakly identifiable. We illustrate our methodology via simulation studies and a re-analysis of real-life data from an evaluation of India's National Health Insurance Program. Our methodology enables us to identify new active causal effects that were not identified in past analyses. Ultimately, our simulation studies and case study demonstrate how our methodology can yield more informative analyses in modern experiments with interference, treatment nonadherence, missing outcomes, and complicated outcome generation mechanisms. 

Within the principal stratification framework in causal inference, the majority of the literature has focused on binary compliance with an intervention and modelling means. Yet in some research areas, compliance is partial, and research questions - and hence analyses - are concerned with causal effects on (possibly high) quantiles rather than on shifts in average outcomes. Modelling partial compliance is challenging because it can suffer from lack of identifiability. We develop an approach to estimate quantile causal effects within a principal stratification framework, where principal strata are defined by the bivariate vector of (partial) compliance to the two levels of a binary intervention. We propose a conditional copula approach to impute the missing potential compliance and estimate the principal quantile treatment effect surface at high quantiles, allowing the copula association parameter to vary with the covariates. A bootstrap procedure is used to estimate the parameter to account for inflation due to imputation of missing compliance. Moreover, we describe precise assumptions on which the proposed approach is based, and investigate the finite sample behaviour of our method by a simulation study. The proposed approach is used to study the 90th principal quantile treatment effect of executive stay-at-home orders on mitigating the risk of COVID-19 transmission in the United States.