Highly Robust Semiparametric Method and Its Applications in Biomedical Studies

Abstract

Causal inference has garnered renewed attention as the result of increased demand in comparative observational studies, and clinical trials utilizing real-world data, which are playing an increasingly more important role in biomedical investigations, economics and other fields. However, a significant methodological barrier is that existing approaches rely on uncheckable model assumptions. Thus, robust modeling is a critical component in valid analysis, which examines alternative models under much fewer assumptions. The more robust a model with respect to its assumptions, the more reliable inference results we have. The doubly robust estimator (DRE) is a significant development in causal inference. However, in practice, many outcome measures are functionals of multiple distributions that can only be estimated using U-statistics, and the existing DREs do not apply.

This dissertation focuses on three closely related topics in robust causal inference. The first proposes and studies a broad class of semiparametric U-statistic DREs (DRUEs), which construct the U-statistic using semiparametric specifications for both the propensity score and outcome models. As a result, the proposed DRE has a much wider application scope and is more resilient than current DREs. We investigate the asymptotic properties of the proposed estimators in detail and conduct comprehensive simulation studies to evaluate their finite sample behavior and compare them to the corresponding parametric U-statistics and naïve estimators, which demonstrate considerable advantages of the proposed method. The approach is then applied to real data obtained from the AIDS Clinical Trials Group.

The second part extends the DRUE approach to multiple endpoints and applies it to the analysis of the Knee Osteoarthritis clinical trial.

In the third part, we propose a semiparametric DRE for causal comparisons of multiple (>2) groups, derive its asymptotic properties and demonstrate its superiority through simulations. The approach is then applied to the study of the National Epidemiology Follow-up Study's multi-group smoking-intensity data.