UBC Theses and Dissertations
Regularized relative risk regression : a non-GLM approach with emphasis on large p, small N simulations You, Xinyuan (Chloe)
In clinical research, the determination of the association's strength between two events is paramount. This may involve probing the relationship between a risk factor and a health outcome, or evaluating the link between a treatment and its efficacy. The Odds Ratios (OR) and Relative Risks (RR) stand out as the predominant measures for such evaluations. While logistic regression is commonly employed for OR modeling, and Poisson regression for RR, each has its set of limitations in practical applications. In light of these limitations, Richardson et al. (2017) introduced a novel non-GLM binary regression approach for direct RR estimation using a log odds-product nuisance model. This technique elegantly sidesteps the intertwined dependence of RR on baseline risk. However, this method encountered challenges in high-dimensional and sparse model estimation (p > N). To address these issues, this study introduces a novel estimator founded on the binary regression model, which is further refined with an algorithm using Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) to solve the optimization problem. This algorithm encourages sparsity in the solution and enables variable selection, thereby improving the utility for high-dimensional and sparse models. This thesis examines the properties of the estimator through simulation studies and discusses the potential for future enhancements and applications. The presented work represents a step forward in creating alternative methodologies for estimating relative risks in diverse data landscapes.
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