Statistics student Zi Wang defense titled " Mediation Analysis of Semi-Competing Risks Data and Interim Analysis of SMART Survival Data". This dissertation comprises two distinct projects related to treatment effects evaluation for time-to-event data. The first project focuses on causal mediation analysis. A treatment may have an effect on a nonterminal event (e.g., disease progression), which in turn may influence a terminal event (e.g., death), or treatment may affect the terminal event directly. We are thus interested in evaluating the mediational effect of the treatment through the nonterminal event and the direct treatment effect on the terminal event. However, the conventional definitions of natural direct effect and natural indirect effect are not appropriate here because of the semi-competing risks data structure, where time to a non-terminal event may be censored by a terminal event, but not vice versa. A principal stratification approach is adopted to define the natural direct and indirect effects in the “always diseased” stratum. We propose nonparametric estimators of the direct and indirect effects under suitable assumptions. The theoretical properties of the proposed estimators are established, and their good finite sample performance is illustrated through numerical studies. This work provides a flexible approach to estimating natural causal mediation effects and offers valuable insights into mediation mechanisms in semi-competing risks settings.

Sequential multiple assignment randomized trials mimic the actual treatment processes experienced by physicians and patients in clinical settings and inform the comparative effectiveness of dynamic treatment regimes. In such trials, patients go through multiple stages of treatment, and the treatment assignment is adapted over time based on individual patient characteristics such as disease status and treatment history. In the second project, we develop and evaluate statistically valid interim monitoring approaches to allow for early termination of sequential multiple assignment randomized trials for efficacy targeting survival outcomes. A weighted log-rank Chi-square statistic is proposed to account for overlapping treatment paths and quantify how the log-rank statistics at two different analysis points are correlated. Efficacy boundaries at multiple interim analyses can then be established using the Pocock, O'Brien Fleming, and Lan-Demets boundaries. We run extensive simulations to evaluate the operating characteristics (type I error and power) of our interim monitoring procedure based on the proposed statistic and another existing statistic. The methods are demonstrated via an analysis of a neuroblastoma dataset.

Committee Chair and Advisor: Dr. Yu Cheng