GWU STAT Student Seminar

Speaker 1: Wu Xue, GWU

Title: Bayesian Sensitivity Analysis for Missing Data Using the E-value

Abstract: Sensitivity Analysis is a framework to assess how conclusions drawn from missing outcome data may be vulnerable to departures from untestable underlying assumptions. We extend the E-value, a popular metric for quantifying robustness of causal conclusions, to the setting of missing outcomes. With motivating examples from partially-observed Facebook conversion events, we present methodology for conducting Sensitivity Analysis at scale with three contributions. First, we develop a method for the Bayesian estimation of sensitivity parameters leveraging noisy benchmarks (e.g., aggregated reports for protecting unit-level privacy); both empirically derived subjective and objective priors are explored. Second, utilizing the Bayesian estimation of the sensitivity parameters we propose a mechanism for posterior inference of the E-value via simulation. Finally, closed form distributions of the E-value are constructed to make direct inference possible when posterior simulation is infeasible due to computational constraints. We demonstrate gains in performance over asymptotic inference of the E-value using data-based simulations, supplemented by a case-study of Facebook conversion events.

Speaker 2: Yang Liu, GWU

Title: Statistical Issues of Unobserved Covariates in Covariate-Adaptive Randomized Trials

Abstract: Balancing important baseline covariates is often critical to ensure the comparability of the treatment groups in clinical trials and other comparative studies. Covariate-adaptive randomization procedures are commonly used to balance observed covariates in practice, but their properties with respect to the unobserved covariates have often been questioned in the literature. Since the trial may always involve certain unobserved important factors, e.g., the gene profiles, privacy issues, etc., the properties of covariate-adaptive randomization with respect to the unobserved covariates are important to ensure the comparability of the treatment groups as well as the validity of the statistical inference.  In this talk, we discuss the balance properties of the covariate-adaptive randomization procedures with respect to the unobserved covariates as well as the subsequent statistical inference following these procedures. In particular, we derive their theoretical properties and demonstrate their benefits for balancing the unobserved covariates. We further study the statistical inference following these procedures. We show that the balance itself is not enough to guarantee the validity of the statistical inference. Moreover, we demonstrate the relationships between the balance with respect to unobserved covariates and the reduced type I error of hypothesis tests when the effects of interests can be correctly estimated. We propose a residual-based adjusted test to restore the conservativeness due to the balance with respect to the unobserved covariates.  Numerical studies are presented to evaluate our theoretical results.