Robust sensitivity analysis for quantiles of hidden biases and treatment effects in matched observational studies

This thesis comprises two papers discussing robust sensitivity analysis for quantiles of hidden biases and treatment effects in matched observational studies. Chapter1: Causal conclusions from observational studies may be sensitive to unmeasured confounding. In such cases, a sensitivity analysis is often conducted, which tries to infer the minimum amount of hidden biases or the minimum strength of unmeasured confounding needed in order to explain away the observed association between treatment and outcome. If the needed bias is large, then the treatment is likely to have significant effects. The Rosenbaum sensitivity analysis is a modern approach for conducting sensitivity analysis in matched observational studies. It investigates what magnitude the maximum of hidden biases from all matched sets needs to be in order to explain away the observed association. However, such a sensitivity analysis can be overly conservative and pessimistic, especially when investigators suspect that some matched sets may have exceptionally large hidden biases. In this paper, we generalize Rosenbaum's framework to conduct sensitivity analysis on quantiles of hidden biases from all matched sets, which are more robust than the maximum. Moreover, the proposed sensitivity analysis is simultaneously valid across all quantiles of hidden biases and is thus a free lunch added to the conventional sensitivity analysis. The proposed approach works for general outcomes, general matched studies and general test statistics. In addition, we demonstrate that the proposed sensitivity analysis also works for bounded null hypotheses when the test statistic satisfies certain properties. An R package implementing the proposed approach is available online. Chapter 2: Robust sensitivity analyses are becoming increasingly important in observational studies, especially in studies where researchers suspect extreme hidden biases exist during matching process, and wish to take heterogeneity of individual effects into consideration. This paper addresses these concerns by developing a robust sensitivity analysis framework for quantiles of individual treatment effects and focusing on generalized null hypotheses that bound quantiles of individual treatment effects in matched pair studies. The existing inference either assumes constant treatment effects, or focuses on average treatment effects that can be sensitive to extreme individual effects. This paper focuses on quantiles of individual treatment effects, which can be more robust in the presence of extreme individual effects, and the corresponding sensitivity analysis based on quantiles of hidden biases provides robust inference for observational studies. These offer more robust tools for dealing with heterogeneity in hidden biases and treatment effects. These methods and the corresponding R packages provide researchers with valuable resources for improving the reliability of their findings in matched observational studies.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2024

Author dc:creator

• Wu, Dongxiao

Contributors dc:contributor

• Li, Xinran
• Yu, Ruoqi
• Shao, Xiaofeng
• Zhu, Ruoqing

• Causal Inference
• Sensitivity Analysis, Observational Studies
• Randomization Test
• Unmeasured Confounding

Statement dc:rights

• Copyright 2024 Dongxiao Wu

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/127346

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F127346