Date of Award

2026-05-01

Degree Name

Master of Science

Department

Mathematical Sciences

Advisor(s)

Xiaogang Su

Abstract

This thesis develops and validates a diagnostic framework for assessing potential confounding in generalized linear models (GLMs) with collapsible link functions. Under collapsibility and effect homogeneity, the absence of confounding implies equality between marginal and covariate-adjusted treatment effects on the link scale, which motivates the change-in-estimate parameter δ = γ − γ(c) as the target of a formal hypothesis test. Two complementary inferential routes are developed: a nonparametric bootstrap and an independent estimating equation (IEE) procedure based on a stacked-data construction that yields a closed-form sandwich variance and is implementable in standard generalized estimating equation software. A backward elimination procedure embeds this test inside an iterative algorithm for identifying a parsimonious adjustment set, replacing the arbitrary thresholds of conventional change-in-estimate heuristics with formal statistical inference. Comprehensive simulation studies across continuous, binary (risk-difference and risk-ratio), and count outcomes confirm the validity of the asymptotic chi-squared approximation in moderate samples, document favorable empirical power, and establish that the IEE procedure offers better small-sample calibration and substantially greater computational efficiency than the bootstrap. An application to data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) examines the relationship between baseline amyloid positivity and short-term progression in mild cognitive impairment patients, considering both 12-month hippocampal atrophy and two-year clinical conversion to dementia as outcomes. The dominant confounder identified by the diagnostic differs systematically between the two outcomes - baseline hippocampal volume for the structural endpoint, baseline cognitive function (MMSE) for the clinical endpoint - demonstrating that confounding structure is outcome-specific in this clinical domain and that no single standard adjustment set is optimal across the range of outcomes studied in early Alzheimer's disease research.

Language

en

Provenance

Received from ProQuest

File Size

115 p.

File Format

application/pdf

Rights Holder

Samuel Dela Gadah

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