Toward Robust and Transparent Estimation of the Effects of Time-dependent Interventions

Abstract

In real-world scenarios and within the causal inference framework, interventions may vary over time. The causal relationships between time-dependent interventions and outcomes are widely discussed across various fields such as medical science, health science, and social science. However, despite extensive research on this topic, there are still unresolved questions regarding improving estimation approaches for the causal effects of time-dependent interventions. Even in this era of big data, analyses of longitudinal studies frequently encounter limitations due to insufficient information when attempting to estimate these effects. Inspired by these challenges, we conduct three case studies on intervention evaluation and strive to obtain stable, efficient, robust, and transparent effect estimates. Below are summaries of each chapter, with their connections further discussed in the Introduction section.

Chapter 1. During the early phase of the COVID-19 pandemic, we curated an integrated dataset from Chile (March 3 through June 15, 2020) and applied an augmented synthetic control method to estimate the effect of localized lockdowns under interference, disentangling their direct and indirect causal effects on SARS-CoV-2 transmission. Our results show that the effects of localized lockdowns are strongly modulated by their duration and the lockdown statuses of neighboring geographic areas. While extending localized lockdowns can slow the pandemic’s progression, our analysis suggests that such intervention alone is insufficient to curb contagion, especially when neighboring areas not under lockdown contribute to transmission. These empirical insights also shed light on the varied effectiveness of localized lockdowns across different geographic areas.

Chapter 2. To adjust time-varying covariates in a transparent way for estimating treatment effects, we provide a longitudinal stable balancing weighting (LSBW) approach, building from the work in Resa Juárez (2017). This approach regularizes weights by minimizing their variation while ensuring covariate balance to acquire consistency and asymptotically normal estimators. This novel procedure gains efficiency by prioritizing balancing the functional forms of time-varying covariates that influence the outcome. Through the dual form of the optimization problem, the weights converge to the true inverse propensities and guarantee robustness to the misspecification of those functional forms. In a practical application, we use LSBW in a longitudinal observational study investigating the impact of attending private voucher school versus public school on students’ language and math scores in university admission tests in Chile. Our results show that entering a private voucher school has a significant positive effect on students’ academic outcomes and uncover that switching school types midway through the educational journey has a detrimental and accumulative impact on students’ performance.

Chapter 3. To improve the estimation of the effects of static time-varying treatment regimes by selecting from candidate weighted estimators, we present a unifying framework from the standpoint of covariate balance for the g-computation formula, inverse probability weighting (IPW), augmented IPW, some of their variants, and LSBW from Chapter 2. We show the interconnections and distinctions among these methods by homologating them as weighting approaches. Each weighted estimator exhibits distinct performance under condition violations, resulting in varying mean error losses and asymptotic behaviors. To evaluate weighted estimators, we propose a diagnostic procedure based on covariate imbalance and weights distribution. In a case study, we analyze the effects of drug use on psychopathic traits among justice-involved male adolescents and find the average effects are neither additive nor monotonic. The findings indicate that among all the possible exposure pathways, the drug relapse pattern, on average, leads to the most adverse outcome for the male adolescents in the study.