Estimation Methods with Recurrent Causal Events

Abstract

This dissertation presents a comprehensive exploration on causal effects of treatment strategies on recurrent events within complex longitudinal settings. Utilizing a series of advanced statistical methodologies, this work focuses on addressing challenges in causal inference when faced with the complexities related to various treatment strategies, recurrent outcomes and time-varying covariates that are confounded or censored.

The first chapter lays the groundwork by introducing two real-life datasets that provide a practical context for investigating recurrent causal events. In this chapter, we establish the foundation of essential concepts and terminologies. An overview of conventional causal estimands and various estimation methods in non-recurrent event settings is described, providing the necessary tools and knowledge base for effective causal analysis in more intricate longitudinal studies with recurrent event outcomes discussed in subsequent chapters.

Chapter two extends the traditional time-fixed measure of marginal odds ratios (MORs) to a more complex, causal longitudinal setting. The novel Aggregated Marginal Odds Ratio (AMOR) is introduced to manage scenarios where treatment varies in time and outcome also recurs. Through Monte Carlo simulations, we demonstrate that AMOR can be estimated with low bias and stable variance, when employing appropriate stabilized weight models, for both absorbing and non-absorbing treatment settings. With the 1997 National Longitudinal Study of Youth dataset, we investigate the causal effect of youth smoking on their recurrent enrollment and dropout from school, with the proposed AMOR estimator.

In the third chapter, the focus shifts to the causal effect of static treatment on recurrent event outcomes with time-varying covariates. We derive the identifying assumptions and employ a variety of estimators for the average causal effect estimation, addressing the issues of time-varying confounding and censoring. We conduct simulations to verify the robustness of these methods against potential model misspecifications. Among the proposed estimators, we conclude that the targeted maximum likelihood (TML) estimator is the appropriate one for complex longitudinal settings. Therefore, we implement targeted maximum likelihood estimation to the Systolic Blood Pressure Intervention Trial (SPRINT) dataset. Adopting an intention-to-treat analysis, we estimate the average causal effect of intensive versus standard blood pressure lowering therapy on acute kidney injury recurrences for participants surviving the first four years of SPRINT.

Chapter four further investigates the average causal effect of time-varying treatments on the recurrence outcome of interest with censoring. Building on the methodologies in Chapter \ref{ch:tmle1_tf}, this chapter explores the singly and doubly robust estimators, especially the TML estimator, in the time-varying treatment context. Then simulation studies are conducted to support the theoretical derivations and validate the robustness of the estimators. The application of the proposed methods on the SPRINT yields some insightful findings. By incorporating participants' medication adherence levels over time as part of the treatment, we are able to investigate various adherence-related questions, and shifting from intention-to-treat to per-protocol analysis for causal effects estimation comparing the intensive versus standard blood pressure therapies.

The dissertation concludes with a summary of the main findings and a discussion of significant and promising areas for future research in Chapter five. The studies conducted demonstrate the potential of advanced causal inference methods in handling the complexities of longitudinal data in medical and social research, offering valuable insights into how treatment strategies affect the recurrent causal outcomes over time. This work not only contributes to the theoretical advancements in statistical methodologies but also provides practical implications for the analysis of clinical trials and observational studies involving recurrent events.