Advisor(s)

Hemant Tiwari

Committee Member(s)

InmacUlada Aban
Megan McCabe
Satwik Acharyya
Tony Merriman

Document Type

Dissertation

Date of Award

6-18-2026

Degree Name

Doctor of Philosophy (PhD)

School

School of Public Health

Department

Biostatistics

Abstract

Instrumental variable (IV) methods are widely used for estimating causal effects in observational studies where unmeasured confounding may bias traditional regression estimates. The core idea is to use a variable referred to as an instrument that is associated with the exposure of interest, independent of unmeasured confounders, and influences the outcome only through the exposure. While originally developed in econometrics, IV methods have been increasingly adopted in epidemiology and genetic research under the framework of Mendelian Randomization (MR), where genetic variants, most commonly single nucleotide polymorphisms (SNPs), serve as instruments. MR provides a powerful tool for investigating causal relationships between modifiable risk factors and health outcomes. However, most existing MR methods, including the Wald estimator, two-stage least squares (TSLS), and limited information maximum likelihood (LIML), rely on strong assumptions such as linearity and normally distributed continuous variables. These assumptions often don’t hold in practice, particularly when the exposure or outcome is binary, count-based, or otherwise non-normal. In addition, weak instruments, where the SNP association with the exposure is weak or violations of IV assumptions can lead to biased estimates. Although more flexible MR methods have been developed to address some of these limitations, most are designed for use with summary-level data rather than individual-level data. This dissertation develops and evaluates statistical methods for Mendelian Randomization that relax assumptions of linearity and normality and remain robust in the presence of weak instruments, with an emphasis on individual-level data. The first aim of this dissertation is to compare the performance of two-stage predictor substitution (TSPS) and two-stage residual inclusion (TSRI) for MR analyses involving count exposures and outcomes. The second aim proposes a copula-based regression framework for MR that accommodates non-normal and mixed outcome types by separating marginal distributions from the dependence structure between the exposure and outcome. The third aim addresses nonlinear exposure–outcome relationships by proposing a polynomial MR framework focusing on quadratic terms that extends two-stage and copula-based MR methods through the inclusion of a squared exposure term. This dissertation culminates in three papers that expand MR methodology for realistic epidemiologic settings and provide flexible tools for causal inference using genetic instruments.

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